Question

write three equations in factored form that are equivalent to $y = 2x^2 + 14x + 12$.
$y =$
$y =$
$y =$

Explanation:

Step1: Factor out the GCF

$y=2(x^2 + 7x + 6)$

Step2: Factor the quadratic trinomial

$y=2(x+1)(x+6)$

Step3: Rearrange factors (commutative)

$y=2(x+6)(x+1)$

Step4: Distribute 2 to first binomial

$y=(2x+2)(x+6)$

Step5: Distribute 2 to second binomial

$y=(x+1)(2x+12)$

Answer:

$y=2(x+1)(x+6)$
$y=2(x+6)(x+1)$
$y=(2x+2)(x+6)$
(Alternative valid third equation: $y=(x+1)(2x+12)$)