Question

Issac factored 8x2−20x−12 to (8x+4)(x−3) and claims his answer is correct because his factored solution simplifies back to the original quadratic expression. Is Issac correct? Why or why not?

Answer 1

Given the equation :

$8x^2-20x-12$

The factor of the equation will be as following:

$\begin{gathered} 8x^2=8x\cdot x\text{ or 4x }\cdot\text{ 2x} \\ 12=6\cdot2=4\cdot3 \end{gathered}$

So, we will choose the numbers whose sum of multiplication = 20

So, the factor will be :

$\begin{gathered} 8x^2-20x-12=(8x+4)(x-3) \\ or \\ 8x^2-20x-12=(4x+2)(2x-6) \end{gathered}$

the factor of the equation should be as following :

$8x^2-20x-12=4(2x+1)(x-3)$

So, the answer of the student is not correct because he did not make 4 as a common