Let’s go through each problem one by one.
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Problem 1: f(x) = (x - 5)(2x + 1)
To find zeros, set each factor equal to zero:
→ x - 5 = 0 → x = 5
→ 2x + 1 = 0 → 2x = -1 → x = -1/2
Zeros:
5 and -1/2
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Problem 2: f(x) = (x - 4)(x - 3)
Set each factor to zero:
→ x - 4 = 0 → x = 4
→ x - 3 = 0 → x = 3
Zeros:
4 and 3
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Problem 3: f(x) = (2x - 2)(x + 5)
Set each factor to zero:
→ 2x - 2 = 0 → 2x = 2 → x = 1
→ x + 5 = 0 → x = -5
Zeros:
1 and -5
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Problem 4: f(x) = (3x - 1)(x + 9)(4x - 1)
Set each factor to zero:
→ 3x - 1 = 0 → 3x = 1 → x = 1/3
→ x + 9 = 0 → x = -9
→ 4x - 1 = 0 → 4x = 1 → x = 1/4
Zeros:
1/3, -9, and 1/4
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Problem 5: f(x) = (x - 8)(4x + 2)(3x - 8)
Set each factor to zero:
→ x - 8 = 0 → x = 8
→ 4x + 2 = 0 → 4x = -2 → x = -2/4 = -1/2
→ 3x - 8 = 0 → 3x = 8 → x = 8/3
Zeros:
8, -1/2, and 8/3
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Problem 6: (30x³)/(15x)
Simplify the expression first:
30 ÷ 15 = 2
x³ ÷ x = x²
So simplified:
2x²
But we must state excluded values — where denominator is zero.
Denominator: 15x = 0 → x = 0
Excluded value:
x ≠ 0
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Problem 7: (x² + 8x + 7)/(x + 1)
Factor numerator:
x² + 8x + 7 = (x + 1)(x + 7)
So expression becomes: [(x + 1)(x + 7)] / (x + 1)
Cancel (x + 1), but only if x + 1 ≠ 0 → x ≠ -1
Excluded value:
x ≠ -1
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Problem 8: (60x²)/(40x)
Simplify:
60 ÷ 40 = 3/2
x² ÷ x = x
So simplified:
(3/2)x or
1.5x
Denominator: 40x = 0 → x = 0
Excluded value:
x ≠ 0
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Final Answer:
1. 5, -1/2
2. 4, 3
3. 1, -5
4. 1/3, -9, 1/4
5. 8, -1/2, 8/3
6. x ≠ 0
7. x ≠ -1
8. x ≠ 0
Parent Tip: Review the logic above to help your child master the concept of algebra problems worksheet.
