Question

Isaac factored 8x^2-20x-12 to (8 x+4)(x-3) and claims this is the correct answer because his factored solution simplifies back to the original quadratic expression. is Issac's statement correct? please explain.

Answer 1

If we multiply the second expression by using the distributive property and it matches the first expression, then Isaac is correct.

The distributive property is:

`(a+b)(c+d)=ac+ad+bc+bd`

Let's use this property to multiply out the 2nd expression:

`\begin{gathered} (8x+4)(x-3) \\ =\mleft(8x\mright)\mleft(x\mright)-\mleft(8x\mright)\mleft(3\mright)+\mleft(4\mright)\mleft(x\mright)-\mleft(4\mright)\mleft(3\mright) \\ =8x^2-24x+4x-12 \\ =8x^2-20x-12 \end{gathered}`

This expression is exactly the same as the original expression. Thus, Isaac is correct.

Answer:

Isaac's statement is correct