when asked to factor the trinomial $8x^2 - 8x - 16$, a student gives the answer $(x - 2)(x + 1)$. what is…

when asked to factor the trinomial $8x^2 - 8x - 16$, a student gives the answer $(x - 2)(x + 1)$. what is one thing wrong with this answer?\n\na. the minus sign should be a plus sign\nb. 8 is also a factor of this trinomial\nc. there is nothing wrong with the answer\nd. the factors are not simplified

when asked to factor the trinomial $8x^2 - 8x - 16$, a student gives the answer $(x - 2)(x + 1)$. what is one thing wrong with this answer?\n\na. the minus sign should be a plus sign\nb. 8 is also a factor of this trinomial\nc. there is nothing wrong with the answer\nd. the factors are not simplified

Answer

Explanation:

Step1: Identify the greatest common factor

The coefficients of the trinomial $8x^2 - 8x - 16$ are $8$, $-8$, and $-16$, which all share a common factor of $8$. $$8(x^2 - x - 2)$$

Step2: Factor the remaining quadratic expression

Find two numbers that multiply to $-2$ and add to $-1$. These numbers are $-2$ and $1$. $$8(x - 2)(x + 1)$$

Step3: Compare with the student's answer

The student's answer is $(x - 2)(x + 1)$. Comparing this to the correct factorization $8(x - 2)(x + 1)$, the constant factor $8$ is missing. $$(x - 2)(x + 1) \neq 8x^2 - 8x - 16$$

Answer:

B. 8 is also a factor of this trinomial