Question
Factor the following polynomial completely, or state that the polynomial is prime. \( -2 x^{2}+32 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( -2 x^{2}+32=\square \) B. The polynomial is prime.
Ask by Bowman Ford. in the United States
Nov 05,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
A. \( -2x^{2}+32=2(4-x)(4+x) \)
Solution
Factor the expression \( -2x^2+32 \).
Factor the expression by following steps:
- step0: Factor:
\(-2x^{2}+32\)
- step1: Factor the expression:
\(2\left(-x^{2}+16\right)\)
- step2: Factor the expression:
\(2\left(4-x\right)\left(4+x\right)\)
The polynomial \( -2x^{2}+32 \) can be factored completely as \( 2(4-x)(4+x) \).
Therefore, the correct choice is:
A. \( -2x^{2}+32=2(4-x)(4+x) \)
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Simplify this solution Mind Expander
To factor the polynomial \(-2x^2 + 32\), we can start by factoring out the common factor of \(-2\): \(-2(x^2 - 16)\) Now, we notice that \(x^2 - 16\) is a difference of squares, which can be factored further: \(-2(x - 4)(x + 4)\) So the complete factorization is: \(-2(x - 4)(x + 4)\) This means the correct answer is: A. \(-2 x^{2}+32 = -2(x - 4)(x + 4)\)
