Question

factor the perfect square trinomial.

\\36x^2 - 84x + 49\\

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

a. \\(36x^2 - 84x + 49 = \\) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Identify the terms

Identify the first and last terms as perfect squares:

$$ 36x^2 = (6x)^2 $$

$$ 49 = 7^2 $$

Step 2: Verify the middle term

Check if the middle term matches the pattern \( -2ab \):

$$ -2(6x)(7) = -84x $$

Since it matches, use the perfect square trinomial formula \( a^2 - 2ab + b^2 = (a - b)^2 \):

$$ (6x - 7)^2 $$

Answer:

A. \( 36x^2 - 84x + 49 = (6x - 7)^2 \)