Factor the trinomial, or state that the trinomial is prime.

Select the correct choice below and fill in any answer boxes within
A.
B. The polynomial is prime.

Ask by Ruiz Alexander. in the United States

Mar 12,2025

Question

Factor the trinomial, or state that the trinomial is prime.

Select the correct choice below and fill in any answer boxes within
A.
B. The polynomial is prime.

Ask by Ruiz Alexander. in the United States

Mar 12,2025

UpStudy AI · Accepted Answer

We need to factor the trinomial
$$
x^{2}-14x-32.
$$
To do this, we look for two numbers whose product is $$-32$$ (the constant term) and whose sum is $$-14$$ (the coefficient of $$ x $$).

Let these two numbers be $$ a $$ and $$ b $$ so that:
$$
a \times b = -32 \quad \text{and} \quad a + b = -14.
$$

We try $$ a = -16 $$ and $$ b = 2 $$:
$$
-16 \times 2 = -32 \quad \text{and} \quad -16 + 2 = -14.
$$
Since both conditions are satisfied, we can write the factorization as:
$$
x^2 - 14x - 32 = (x - 16)(x + 2).
$$

Thus, the correct answer is:

A. $$ x^{2}-14x-32=(x-16)(x+2) $$
$$ x^{2}-14x-32=(x-16)(x+2) $$

Factor the trinomial, or state that the trinomial is prime.

Select the correct choice below and fill in any answer boxes within
A.
B. The polynomial is prime.

Upstudy AI Solution

Answer

Solution

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Factor the trinomial, or state that the trinomial is prime. Select the correct choice below and fill in any answer boxes within A. B. The polynomial is prime.

Upstudy AI Solution

Answer

Solution

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Factor the trinomial, or state that the trinomial is prime.

Select the correct choice below and fill in any answer boxes within
A.
B. The polynomial is prime.