Question

name__________
equations by factoring
date________ period__
y factoring

1. $(a + 1)(a + 2) = 0$
2. $(2m + 3)(4m + 3) = 0$
3. $n^2 + 7n + 15 = 5$
4. $n^2 + 3n - 12 = 6$
5. $7r^2 - 14r = -7$

Explanation:

Problem 2:

Step1: Apply Zero Product Property

Set each factor equal to 0:
$a+1=0$ and $a+2=0$

Step2: Solve for $a$

$a=-1$ and $a=-2$

Problem 4:

Step1: Apply Zero Product Property

Set each factor equal to 0:
$2m+3=0$ and $4m+3=0$

Step2: Solve for $m$

$m=-\frac{3}{2}$ and $m=-\frac{3}{4}$

Problem 6:

Step1: Rewrite to standard form

Subtract 5 from both sides:
$n^2+7n+10=0$

Step2: Factor the quadratic

Find two factors of 10 that add to 7:
$(n+2)(n+5)=0$

Step3: Apply Zero Product Property

Set each factor equal to 0:
$n+2=0$ and $n+5=0$

Step4: Solve for $n$

$n=-2$ and $n=-5$

Problem 8:

Step1: Rewrite to standard form

Subtract 6 from both sides:
$n^2+3n-18=0$

Step2: Factor the quadratic

Find two factors of -18 that add to 3:
$(n+6)(n-3)=0$

Step3: Apply Zero Product Property

Set each factor equal to 0:
$n+6=0$ and $n-3=0$

Step4: Solve for $n$

$n=-6$ and $n=3$

Problem 10:

Step1: Rewrite to standard form

Add 7 to both sides:
$7r^2-14r+7=0$

Step2: Simplify the equation

Divide all terms by 7:
$r^2-2r+1=0$

Step3: Factor the quadratic

Factor the perfect square trinomial:
$(r-1)^2=0$

Step4: Solve for $r$

$r-1=0$ so $r=1$ (repeated root)

Answer:

1. $a=-1$ or $a=-2$
2. $m=-\frac{3}{2}$ or $m=-\frac{3}{4}$
3. $n=-2$ or $n=-5$
4. $n=-6$ or $n=3$
5. $r=1$ (double root)