Question

factor the trinomial completely.

\\-16x + 63 + x^2\\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. \\(-16x + 63 + x^2 = \\) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Rearrange the terms

Write the trinomial in standard form \(ax^2 + bx + c\):

$$ x^2 - 16x + 63 $$

Step 2: Find two numbers

Find two integers that multiply to \(63\) and add up to \(-16\):

$$ \text{Factors of } 63: -7 \text{ and } -9 $$

$$ (-7) \cdot (-9) = 63 $$

$$ (-7) + (-9) = -16 $$

Step 3: Write the factored form

Use these factors to write the binomial product:

$$ (x - 7)(x - 9) $$

Answer:

$$ -16x + 63 + x^2 = (x - 7)(x - 9) $$