Dividing Polynomials worksheet with factorization method problems.

Let’s solve each problem step by step using the factorization method for dividing polynomials.

We’ll go one at a time. The goal is to factor both numerator and denominator, then cancel common factors.

---

Problem 1:
\[
\frac{3x + x^2 - 14}{x^2 - 9x - 7y^2}
\]

Wait — this looks odd. Denominator has \( -7y^2 \), but numerator has no y. That suggests maybe it's a typo? Let me check again.

Actually, looking closely:
Numerator: \( 3x + x^2 - 14 = x^2 + 3x - 14 \)
Denominator: \( x^2 - 9x - 7y^2 \) → This has two variables? But all other problems are in x only. Probably a misprint.

Looking at original image (even though I can’t describe it), likely denominator is meant to be \( x^2 - 9x + 14 \) or similar? Wait — let’s look at problem 5:

Problem 5:
\[
\frac{10x^2 + 94x - 784}{x^2 + 14x + 49}
\]

That’s clean. So probably Problem 1 denominator is \( x^2 - 9x + 14 \)? Because 14 appears in numerator too.

But wait — user wrote:
“Divide by factorization method” and listed:

1) \( \frac{3x + x^2 - 14}{x^2 - 9x - 7y^2} \)

Hmm. Maybe it’s \( x^2 - 9x - 14 \)? Or perhaps \( x^2 - 9x + 14 \)?

Let me try factoring numerator first:

Numerator: \( x^2 + 3x - 14 \)

Find two numbers that multiply to -14 and add to 3 → 7 and -2? 7 * (-2) = -14, 7 + (-2) = 5 → no.

Try 14 and -1 → 13. No.

Wait — actually, discriminant: \( b^2 - 4ac = 9 + 56 = 65 \) → not perfect square. So doesn't factor nicely over integers.

This suggests there might be a typo. Looking ahead, Problem 2 is:

2) \( \frac{6n^2 - 5n^2 - 34n + 45}{n + 5} \)

Wait — that says \( 6n^2 - 5n^2 \) which is just \( n^2 \). Probably meant \( 6n^3 - 5n^2 - 34n + 45 \)? Because otherwise it’s quadratic divided by linear.

Similarly, Problem 1 denominator has “-7y²” — very suspicious.

Given that this is a worksheet titled “Dividing Polynomials” and all others seem to be single-variable, I suspect typos.

But since I must solve as given, let’s assume:

For Problem 1: Maybe denominator is \( x^2 - 9x + 14 \)? Because 14 is in numerator.

Let me test that.

Assume Problem 1 is:
\[
\frac{x^2 + 3x - 14}{x^2 - 9x + 14}
\]

Factor numerator: \( x^2 + 3x - 14 \)

Need two numbers: product -14, sum 3 → 7 and -2? 7*(-2)= -14, 7+(-2)=5 → no.

Wait — 14 and -1 → 13. No.

Actually, roots: [ -3 ± √(9 + 56) ] / 2 = [ -3 ± √65 ] / 2 → irrational. Doesn’t factor nicely.

Alternatively, maybe numerator is \( x^2 + 3x - 18 \)? Then factors as (x+6)(x-3).

Or perhaps it’s \( x^2 + 3x - 10 \)? (x+5)(x-2).

I think there’s a high chance of typo. But let’s look at Problem 3:

3) \( \frac{12p^3 - 36p^2 + 27p^2}{2p - 3} \)

Wait — that says \( -36p^2 + 27p^2 \) → that’s -9p². So numerator is \( 12p^3 - 9p^2 \)

Then factor: 3p²(4p - 3)

Denominator: 2p - 3 → no common factor? Unless we made mistake.

Wait — perhaps it’s \( 12p^3 - 36p^2 + 27p \)? With p, not p².

Because 27p would make sense: 12p³ - 36p² + 27p = 3p(4p² - 12p + 9) = 3p(2p - 3)^2

Then divide by (2p - 3) → get 3p(2p - 3)

That makes sense.

So likely, in Problem 3, it’s +27p, not +27p².

Similarly, Problem 1: perhaps denominator is x² - 9x + 14? And numerator x² + 3x - 14? Still doesn’t factor.

Another idea: maybe numerator is 3x + x² - 18? Then x² + 3x - 18 = (x+6)(x-3)

Denominator x² - 9x + 18 = (x-3)(x-6) → then cancel (x-3)

But user wrote -14.

Perhaps it’s x² + 3x - 10? (x+5)(x-2); denominator x² - 9x + 14 = (x-2)(x-7) → cancel (x-2)

Yes! That works.

So if numerator is x² + 3x - 10, denominator x² - 9x + 14.

But user wrote -14 in numerator.

Unless... "3x + x² - 14" is correct, but denominator is x² - 9x - 14? Then still doesn't factor.

I think I need to proceed with what’s written, even if messy.

But let’s look at Problem 4:

4) \( \frac{5s - 3s^2(s + 4)}{s^2 + 4s - 12s^2} \)

Simplify numerator: 5s - 3s²(s+4) = 5s - 3s³ - 12s² = -3s³ -12s² +5s

Denominator: s² +4s -12s² = -11s² +4s

So \( \frac{-3s^3 -12s^2 +5s}{-11s^2 +4s} = \frac{s(-3s^2 -12s +5)}{s(-11s +4)} = \frac{-3s^2 -12s +5}{-11s +4} \)

Now, does -3s² -12s +5 factor? Discriminant: 144 + 60 = 204 → not perfect square. So doesn't simplify further.

This is getting too messy. Perhaps the worksheet has typos, but since I have to solve, I'll assume standard problems.

Let me try to interpret based on common textbook problems.

Common problem: Divide (x² + 3x - 10)/(x² - 9x + 14) = [(x+5)(x-2)] / [(x-2)(x-7)] = (x+5)/(x-7)

And if numerator was x² +3x -10, but user wrote -14, perhaps it's a miswrite.

Another possibility: "3x + x² - 14" is x² +3x -14, and denominator "x² -9x -7y²" is a typo for "x² -9x +14", but as said, doesn't factor.

Perhaps " -7y^2 " is " -14 ", so denominator x² -9x -14.

Then numerator x² +3x -14, denominator x² -9x -14.

Still, neither factors nicely.

Let's calculate numerical values or something — no.

Perhaps for Problem 1, it's (x^2 +3x -18)/(x^2 -9x +18) = (x+6)(x-3)/[(x-3)(x-6)] = (x+6)/(x-6)

And -18 instead of -14.

I think I have to make an assumption to proceed.

Let me look at Problem 5:

5) \( \frac{10x^2 + 94x - 784}{x^2 + 14x + 49} \)

Denominator: x² +14x +49 = (x+7)^2

Numerator: 10x² +94x -784

Let me factor out 2: 2(5x² +47x -392)

Now factor 5x² +47x -392

Discriminant: 47^2 + 4*5*392 = 2209 + 7840 = 10049 — is that square? 100^2=10000, 101^2=10201, so no. Not nice.

784 is 28^2, 10x² +94x -784.

Perhaps divide by 2: 5x² +47x -392

Try to factor: need two numbers multiply to 5*-392 = -1960, add to 47.

Factors of 1960: 49*40=1960, so 49 and -40? 49-40=9, not 47.

56*35=1960, 56-35=21.

70*28=1960, 70-28=42.

98*20=1960, 98-20=78.

Not working.

Perhaps it's 10x^2 +94x - 784, and 784 is 28^2, but let's use quadratic formula.

x = [-94 ± sqrt(94^2 + 4*10*784)] / 20 = [-94 ± sqrt(8836 + 31360)] / 20 = [-94 ± sqrt(40196)] / 20

sqrt(40196) = ? 200^2=40000, 201^2=40401, 200.5^2=40200.25, close, 200.49^2 = ? approximately 200.5, not integer.

This is not good.

Perhaps the numerator is 10x^2 +94x - 784, and it factors as (2x + a)(5x + b) = 10x^2 + (2b+5a)x + ab

Set 2b+5a = 94, ab = -784

Possible a,b: factors of 784: 28*28, 49*16, etc.

Suppose a=16, b= -49, then 2*(-49) +5*16 = -98 +80 = -18 ≠94

a=49, b= -16, 2*(-16)+5*49 = -32+245=213≠94

a= -16, b=49, 2*49 +5*(-16) = 98-80=18≠94

a= -49, b=16, 2*16 +5*(-49) = 32-245= -213

a=28, b= -28, 2*(-28)+5*28 = -56+140=84≠94

a= -28, b=28, 2*28 +5*(-28) = 56-140= -84

a=56, b= -14, 2*(-14)+5*56 = -28+280=252

Too big.

a=14, b= -56, 2*(-56)+5*14 = -112+70= -42

Not working.

Perhaps it's 10x^2 +94x - 784 = 2(5x^2 +47x -392), and 5x^2 +47x -392, let's try rational root theorem.

Possible roots: factors of 392 over 5: ±1,2,4,7,8,14,28,49,56,98,196,392, and halves, fifths, etc.

Try x=4: 5*16 +47*4 -392 = 80 +188 -392 = 268-392= -124≠0

x=7: 5*49 +47*7 -392 = 245 +329 -392 = 574-392=182≠0

x=8: 5*64=320, 47*8=376, 320+376=696-392=304≠0

x= -8: 5*64=320, 47*(-8)= -376, 320-376= -56 -392= -448≠0

x=14: 5*196=980, 47*14=658, 980+658=1638-392=1246≠0

x= -14: 5*196=980, 47*(-14)= -658, 980-658=322-392= -70≠0

x=28: too big.

Perhaps x=4/5: 5*(16/25) +47*(4/5) -392 = 80/25 + 188/5 -392 = 16/5 + 188/5 -392 = 204/5 -392 = 40.8 -392 <0

Not helping.

I recall that in some worksheets, they have nice numbers. Perhaps for Problem 5, numerator is 10x^2 +94x - 784, but 784 is 28^2, and 10x^2 +94x - 784 = 2(5x^2 +47x -392), and 5x^2 +47x -392 might be (5x - 49)(x + 8) = 5x^2 +40x -49x -392 = 5x^2 -9x -392, not matching.

(5x + 56)(x - 7) = 5x^2 -35x +56x -392 = 5x^2 +21x -392, not 47x.

(5x + 98)(x - 4) = 5x^2 -20x +98x -392 = 5x^2 +78x -392, not 47.

(5x - 56)(x + 7) = 5x^2 +35x -56x -392 = 5x^2 -21x -392.

None work.

Perhaps it's 10x^2 +94x - 784, and we can leave it, but that's not satisfactory.

Another idea: perhaps "784" is "78.4" or something, but unlikely.

Let's skip and do Problem 6:

6) \( \frac{8u^2 - 75u^2}{5u + 50u - 5} \)

Numerator: 8u^2 -75u^2 = -67u^2

Denominator: 5u +50u -5 = 55u -5 = 5(11u -1)

So \( \frac{-67u^2}{5(11u -1)} \) — no common factors, so that's simplified.

But usually they have common factors, so perhaps numerator is 8u^3 -75u^2 or something.

User wrote "8u^2 - 75u^2", which is -67u^2.

Denominator "5u +50u -5" = 55u -5.

So answer is -67u^2 / [5(11u -1)]

Not nice.

Problem 7: \( \frac{2t^2 - 2t^2 - 100s + 25}{t^2 - 5} \)

Numerator: 2t^2 -2t^2 -100s +25 = -100s +25 = 25 -100s = 25(1 -4s)

Denominator: t^2 -5

No common factors, so 25(1-4s)/(t^2 -5)

Again, not typical.

Problem 8: \( \frac{4z^3 + 52z^2 - 36z^2}{4z^2 + 36z^2} \)

Numerator: 4z^3 +52z^2 -36z^2 = 4z^3 +16z^2 = 4z^2(z +4)

Denominator: 4z^2 +36z^2 = 40z^2

So \( \frac{4z^2(z+4)}{40z^2} = \frac{z+4}{10} \) for z≠0

Oh! This one works.

So for Problem 8, it simplifies to (z+4)/10

Similarly, for others, likely there are typos, but for Problem 8, it's clear.

Let me list what I can solve cleanly.

From above:

Problem 8:
Numerator: 4z^3 +52z^2 -36z^2 = 4z^3 +16z^2 = 4z^2(z+4)
Denominator: 4z^2 +36z^2 = 40z^2
So division: [4z^2(z+4)] / [40z^2] = (z+4)/10

Good.

Now Problem 3: if we assume it's 12p^3 -36p^2 +27p (not +27p^2), then:

Numerator: 12p^3 -36p^2 +27p = 3p(4p^2 -12p +9) = 3p(2p-3)^2
Denominator: 2p -3
So division: 3p(2p-3)^2 / (2p-3) = 3p(2p-3) for p≠3/2

Similarly, Problem 4: if we simplify as is:

Numerator: 5s -3s^2(s+4) = 5s -3s^3 -12s^2 = -3s^3 -12s^2 +5s = s(-3s^2 -12s +5)
Denominator: s^2 +4s -12s^2 = -11s^2 +4s = s(-11s +4)
So [s(-3s^2 -12s +5)] / [s(-11s +4)] = (-3s^2 -12s +5)/(-11s +4) for s≠0

And -3s^2 -12s +5 doesn't factor nicely, so leave as is.

But perhaps in context, it's fine.

For Problem 2: "6n^2 -5n^2 -34n +45" = (6-5)n^2 -34n +45 = n^2 -34n +45

Divide by n+5.

So (n^2 -34n +45)/(n+5)

Do polynomial division or factor.

Factor numerator: n^2 -34n +45, discriminant 1156 -180 = 976, not square, so doesn't factor.

Divide: n+5 into n^2 -34n +45.

n^2 / n = n, multiply n*(n+5) = n^2 +5n, subtract: (n^2 -34n +45) - (n^2 +5n) = -39n +45

-39n / n = -39, multiply -39*(n+5) = -39n -195, subtract: (-39n +45) - (-39n -195) = 45 +195 = 240

So quotient n -39, remainder 240, so (n-39) + 240/(n+5)

Not nice.

If it was 6n^3 -5n^2 -34n +45, then possible.

Assume that.

Let me try for Problem 2: suppose numerator is 6n^3 -5n^2 -34n +45, denominator n+5.

Use synthetic division with root -5.

Coefficients: 6, -5, -34, 45

Bring down 6.

Multiply by -5: 6*-5 = -30, add to next coefficient: -5 + (-30) = -35

Multiply by -5: -35*-5 = 175, add to next: -34 +175 = 141

Multiply by -5: 141*-5 = -705, add to last: 45 + (-705) = -660 ≠0, not divisible.

If denominator is n-5, root 5.

6*5 = 30, -5+30=25, 25*5=125, -34+125=91, 91*5=455, 45+455=500≠0.

Not good.

Perhaps for Problem 2, it's 6n^2 -5n -34n +45, but that's 6n^2 -39n +45, divide by n+5.

6n^2 -39n +45 = 3(2n^2 -13n +15) = 3(2n-3)(n-5)

Denominator n+5, no common factors.

So not helping.

Let's focus on the ones that work.

From earlier, Problem 8 is clear: (z+4)/10

Problem 3, if we assume +27p, then 3p(2p-3)

Problem 6: -67u^2 / [5(11u -1)] , but perhaps it's 8u^3 -75u^2 or something.

Another approach: perhaps "8u^2 - 75u^2" is a typo for "8u^3 - 75u^2", then numerator 8u^3 -75u^2 = u^2(8u -75)

Denominator 5u +50u -5 = 55u -5 = 5(11u -1)

No common factors.

If denominator is 5u^2 +50u -5 or something.

I think for the sake of time, I'll solve the ones that are clear and for others, make reasonable assumptions.

Let me list the problems as per user input, and solve with corrections where necessary for factorization to work.

Final decision:

For Problem 1: Assume numerator x^2 +3x -10, denominator x^2 -9x +14, so (x+5)(x-2)/[(x-2)(x-7)] = (x+5)/(x-7)

For Problem 2: Assume numerator 6n^3 -5n^2 -34n +45, and see if divisible by n+5.

Earlier synthetic division with -5 gave remainder -660, not 0.

With n-3: root 3, coefficients 6,-5,-34,45

6*3=18, -5+18=13, 13*3=39, -34+39=5, 5*3=15, 45+15=60≠0

n-5: 6*5=30, -5+30=25, 25*5=125, -34+125=91, 91*5=455, 45+455=500≠0

n+3: -3, 6*-3= -18, -5-18= -23, -23*-3=69, -34+69=35, 35*-3= -105, 45-105= -60≠0

Perhaps it's 6n^2 -5n -34n +45 = 6n^2 -39n +45 = 3(2n^2 -13n +15) = 3(2n-3)(n-5), and denominator n+5, so no cancellation.

I give up on Problem 2 for now.

Let's do Problem 4 as is.

Perhaps for Problem 4, "5s -3s^2(s+4)" is 5s -3s^2 * (s+4) = 5s -3s^3 -12s^2, as before.

Denominator "s^2 +4s -12s^2" = -11s^2 +4s

So after canceling s, (-3s^2 -12s +5)/(-11s +4)

And this can be left as is, or write as (3s^2 +12s -5)/(11s -4) by multiplying numerator and denominator by -1.

But not factorable.

For Problem 5: let's try to factor 10x^2 +94x -784.

Let me calculate gcd of coefficients: 10,94,784. gcd of 10 and 94 is 2, 784 div 2=392, so 2(5x^2 +47x -392)

Now 5x^2 +47x -392, let's use quadratic formula.

x = [-47 ± sqrt(47^2 +4*5*392)] / 10 = [-47 ± sqrt(2209 + 7840)] / 10 = [-47 ± sqrt(10049)] / 10

sqrt(10049) = ? 100^2=10000, 101^2=10201, 100.24^2 = 10048.0576, close, 100.25^2 = 10050.0625, so approximately 100.24, not integer.

So not nice.

Perhaps "784" is "78.4" but unlikely.

Another idea: perhaps it's 10x^2 +94x - 784, and 784 is 28^2, and it's related to (2x+28)(5x-28) = 10x^2 -56x +140x -784 = 10x^2 +84x -784, but we have 94x, not 84x.

(2x+32)(5x-24.5) not integer.

I think for the purpose of this, I'll provide answers for the ones that work, and for others, state the simplified form.

But the user asked to solve accurately, so perhaps I should box the answers as per calculation.

Let's start over and solve each as written, with minimal assumption.

Problem 1: \frac{3x + x^2 - 14}{x^2 - 9x - 7y^2} = \frac{x^2 +3x -14}{x^2 -9x -7y^2}

This has two variables, so cannot simplify unless y is constant, but not specified. So perhaps leave as is, but that's not dividing.

Maybe " -7y^2 " is " -14 ", so \frac{x^2 +3x -14}{x^2 -9x -14}

Then no common factors, so answer is itself.

But not satisfactory.

Perhaps in the context, y is a typo for x, so -7x^2, then denominator x^2 -9x -7x^2 = -6x^2 -9x = -3x(2x+3)

Numerator x^2 +3x -14, which doesn't share factors.

So still not.

I recall that in some sheets, they have (x^2 +3x -18)/(x^2 -9x +18) = (x+6)(x-3)/[(x-3)(x-6)] = (x+6)/(x-6)

And -18 instead of -14.

So I'll assume that for Problem 1: \frac{x^2 +3x -18}{x^2 -9x +18} = \frac{(x+6)(x-3)}{(x-3)(x-6)} = \frac{x+6}{x-6} for x≠3

Similarly for others.

For Problem 2: \frac{6n^2 -5n^2 -34n +45}{n+5} = \frac{n^2 -34n +45}{n+5}

As calculated, (n^2 -34n +45) ÷ (n+5) = n -39 + 240/(n+5) , but since it's "divide by factorization", perhaps they want exact division, so maybe it's 6n^3 -5n^2 -34n +45, and let's force it.

Suppose it is divisible by n+5, then when n= -5, numerator should be 0.

6*(-125) -5*25 -34*(-5) +45 = -750 -125 +170 +45 = -875 +215 = -660 ≠0, as before.

If it's 6n^2 -5n -34n +45 = 6n^2 -39n +45, at n= -5: 6*25 -39*(-5) +45 = 150 +195 +45 = 390≠0.

Perhaps denominator is n-5, then for 6n^2 -39n +45 at n=5: 6*25 -39*5 +45 = 150 -195 +45 = 0! Oh!

So if Problem 2 is \frac{6n^2 -39n +45}{n-5} , then it works.

And 6n^2 -39n +45 = 3(2n^2 -13n +15) = 3(2n-3)(n-5)

So divided by (n-5) gives 3(2n-3) = 6n -9

And in the user input, it's "6n^2 -5n^2 -34n +45" which is n^2 -34n +45, but if it's "6n^2 -5n -34n +45" = 6n^2 -39n +45, and denominator "n+5" but should be "n-5".

In user input: "2) \frac{6n^2 -5n^2 -34n +45}{n + 5}"

So "6n^2 -5n^2" is likely "6n^2 -5n" or something, but written as -5n^2.

Perhaps " -5n^2 " is " -5n ", so 6n^2 -5n -34n +45 = 6n^2 -39n +45, and denominator n+5, but as above, at n= -5, 6*25 -39*(-5) +45 = 150 +195 +45 = 390≠0, while if denominator is n-5, it is 0.

So probably denominator is n-5, not n+5.

In many fonts, + and - look similar, so likely typo.

So assume Problem 2: \frac{6n^2 -39n +45}{n-5} = 3(2n-3)(n-5)/(n-5) = 3(2n-3) = 6n -9 for n≠5

Similarly for others.

For Problem 3: "12p^3 -36p^2 +27p^2" likely "12p^3 -36p^2 +27p" , so 12p^3 -36p^2 +27p = 3p(4p^2 -12p +9) = 3p(2p-3)^2

Denominator "2p -3" , so 3p(2p-3)^2 / (2p-3) = 3p(2p-3) = 6p^2 -9p for p≠3/2

For Problem 4: "5s -3s^2(s+4)" = 5s -3s^3 -12s^2 = -3s^3 -12s^2 +5s = s(-3s^2 -12s +5)

Denominator "s^2 +4s -12s^2" = -11s^2 +4s = s(-11s +4)

So s(-3s^2 -12s +5) / [s(-11s +4)] = (-3s^2 -12s +5)/(-11s +4) = (3s^2 +12s -5)/(11s -4) for s≠0

And this doesn't factor, so leave as is.

For Problem 5: "10x^2 +94x -784" / "x^2 +14x +49" = 10x^2 +94x -784 / (x+7)^2

Let me try to see if 10x^2 +94x -784 is divisible by (x+7).

At x= -7: 10*49 +94*(-7) -784 = 490 -658 -784 = 490 -1442 = -952 ≠0, not divisible.

If it's 10x^2 +94x - 784, and (x+7)^2 = x^2 +14x +49, perhaps long division.

But not nice.

Perhaps "784" is "78.4" but unlikely.

Another idea: perhaps it's 10x^2 +94x - 784 = 2(5x^2 +47x -392), and 5x^2 +47x -392, and 392 = 49*8, etc.

Let's calculate the value at x=7: 10*49 +94*7 -784 = 490 +658 -784 = 1148 -784 = 364 ≠0

x= -7: 10*49 +94*(-7) -784 = 490 -658 -784 = -952

x=8: 10*64=640, 94*8=752, 640+752=1392-784=608

x=4: 10*16=160, 94*4=376, 160+376=536-784= -248

x=14: 10*196=1960, 94*14=1316, 1960+1316=3276-784=2492

Not zero.

Perhaps it's 10x^2 +94x - 784, and we can write as is, but for factorization, maybe they mean to factor out common factors, but no.

Let's move to Problem 6: "8u^2 - 75u^2" = -67u^2

"5u +50u -5" = 55u -5 = 5(11u -1)

So -67u^2 / [5(11u -1)]

If "8u^2" is "8u^3", then 8u^3 -75u^2 = u^2(8u -75), same thing.

If denominator is 5u^2 +50u -5, then 5(u^2 +10u -1), still no common factors.

So perhaps leave as -67u^2 / [5(11u -1)]

For Problem 7: "2t^2 -2t^2 -100s +25" = 0 -100s +25 = 25 -100s = 25(1 -4s)

" t^2 -5 "

So 25(1-4s)/(t^2 -5)

For Problem 8: as before, (z+4)/10

So to summarize, with assumptions for typos:

Problem 1: \frac{x+6}{x-6} (assuming x^2+3x-18 over x^2-9x+18)

Problem 2: 6n -9 (assuming 6n^2-39n+45 over n-5)

Problem 3: 6p^2 -9p (assuming 12p^3-36p^2+27p over 2p-3)

Problem 4: \frac{3s^2 +12s -5}{11s -4} (after simplifying)

Problem 5: let's say \frac{10x^2 +94x -784}{(x+7)^2} , but not simplifiable, or perhaps calculate.

Upon second thought, for Problem 5, 10x^2 +94x -784, let's divide by 2: 5x^2 +47x -392

And 5x^2 +47x -392, let's try to factor as (5x + a)(x + b) = 5x^2 + (5b+a)x + ab

Set 5b+a = 47, ab = -392

Possible a,b: a=56, b= -7, then 5*(-7) +56 = -35+56=21≠47

a=98, b= -4, 5*(-4)+98 = -20+98=78≠47

a=49, b= -8, 5*(-8)+49 = -40+49=9≠47

a= -49, b=8, 5*8 + (-49) = 40-49= -9

a= -56, b=7, 5*7 + (-56) = 35-56= -21

a= -98, b=4, 5*4 + (-98) = 20-98= -78

a=14, b= -28, 5*(-28)+14 = -140+14= -126

Not working.

Perhaps (5x - 49)(x + 8) = 5x^2 +40x -49x -392 = 5x^2 -9x -392, not 47x.

So