Isaac was asked to factor the following expression completely:
8x^2-20x-12
Isaac got (8x+4)(x−3) as their answer and claims it is correct because when multiplying the factors it simplifies to the original polynomial expression.
Is Isaac correct? Why or why not?
wrong
better would be
4(2x+1)(x-3)
To assess whether Isaac's factorization is correct or not, we can verify it by expanding the factors.
Let's start by multiplying the factors: (8x+4)(x-3).
Using the distributive property, we multiply each term in the first factor by each term in the second factor:
= 8x * x + 8x * (-3) + 4 * x + 4 * (-3)
= 8x^2 - 24x + 4x - 12
Now, combining like terms, we have:
= 8x^2 - 20x - 12
As we can see, the expanded expression matches the original polynomial expression, which means Isaac's factorization is indeed correct.
Therefore, Isaac's claim that the factorization (8x+4)(x-3) is correct because it simplifies to the original polynomial expression is valid.
Isaac's answer is correct.
To check, we can use the FOIL method to multiply the factors:
(8x+4)(x-3) = 8x(x) + 8x(-3) + 4(x) + 4(-3)
= 8x^2 - 24x + 4x - 12
= 8x^2 - 20x - 12
Therefore, the factors (8x+4)(x-3) do simplify to the original polynomial expression 8x^2-20x-12.