FREE Solving Quadratic Equations By Factoring Worksheets [PDFs] - Free Printable

Here are the step-by-step solutions for each quadratic equation using factoring.

1) $v^2 + 5v + 6 = 0$
* Find two numbers that multiply to 6 and add to 5. Those numbers are 2 and 3.
* Factor: $(v + 2)(v + 3) = 0$
* Set each part to zero: $v + 2 = 0$ or $v + 3 = 0$
* Answer: $v = -2, v = -3$

2) $g^2 - 3g = 4$
* First, move the 4 to the left side to set the equation to zero: $g^2 - 3g - 4 = 0$
* Find two numbers that multiply to -4 and add to -3. Those numbers are -4 and 1.
* Factor: $(g - 4)(g + 1) = 0$
* Set each part to zero: $g - 4 = 0$ or $g + 1 = 0$
* Answer: $g = 4, g = -1$

3) $w^2 + 4w = 0$
* Factor out the common variable $w$: $w(w + 4) = 0$
* Set each part to zero: $w = 0$ or $w + 4 = 0$
* Answer: $w = 0, w = -4$

4) $s^2 - 8s + 12 = 0$
* Find two numbers that multiply to 12 and add to -8. Those numbers are -6 and -2.
* Factor: $(s - 6)(s - 2) = 0$
* Set each part to zero: $s - 6 = 0$ or $s - 2 = 0$
* Answer: $s = 6, s = 2$

5) $x^2 + 2x - 35 = 0$
* Find two numbers that multiply to -35 and add to 2. Those numbers are 7 and -5.
* Factor: $(x + 7)(x - 5) = 0$
* Set each part to zero: $x + 7 = 0$ or $x - 5 = 0$
* Answer: $x = -7, x = 5$

6) $r(r + 2) = 99$
* Distribute the $r$: $r^2 + 2r = 99$
* Move 99 to the left side: $r^2 + 2r - 99 = 0$
* Find two numbers that multiply to -99 and add to 2. Those numbers are 11 and -9.
* Factor: $(r + 11)(r - 9) = 0$
* Set each part to zero: $r + 11 = 0$ or $r - 9 = 0$
* Answer: $r = -11, r = 9$

7) $k(k - 4) = -3$
* Distribute the $k$: $k^2 - 4k = -3$
* Move -3 to the left side (it becomes +3): $k^2 - 4k + 3 = 0$
* Find two numbers that multiply to 3 and add to -4. Those numbers are -3 and -1.
* Factor: $(k - 3)(k - 1) = 0$
* Set each part to zero: $k - 3 = 0$ or $k - 1 = 0$
* Answer: $k = 3, k = 1$

8) $t^2 + 3t + 2 = 0$
* Find two numbers that multiply to 2 and add to 3. Those numbers are 2 and 1.
* Factor: $(t + 2)(t + 1) = 0$
* Set each part to zero: $t + 2 = 0$ or $t + 1 = 0$
* Answer: $t = -2, t = -1$

9) $m^2 - 81 = 0$
* This is a difference of squares ($9 \times 9 = 81$).
* Factor: $(m - 9)(m + 9) = 0$
* Set each part to zero: $m - 9 = 0$ or $m + 9 = 0$
* Answer: $m = 9, m = -9$

10) $h^2 - 17h + 70 = 0$
* Find two numbers that multiply to 70 and add to -17. Those numbers are -10 and -7.
* Factor: $(h - 10)(h - 7) = 0$
* Set each part to zero: $h - 10 = 0$ or $h - 7 = 0$
* Answer: $h = 10, h = 7$

Final Answer:
1) v = -2, -3
2) g = 4, -1
3) w = 0, -4
4) s = 6, 2
5) x = -7, 5
6) r = -11, 9
7) k = 3, 1
8) t = -2, -1
9) m = 9, -9
10) h = 10, 7