Question

factor the trinomial completely.

(5x^2 - 9x - 2)

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

a. (5x^2 - 9x - 2 = ) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify coefficients

For the trinomial \(5x^2 - 9x - 2\):

$$ a = 5, \quad b = -9, \quad c = -2 $$

Step 2: Find factors

Find two numbers that multiply to \(a \cdot c = 5 \cdot (-2) = -10\) and add to \(b = -9\):

$$ -10 \text{ and } 1 $$

Step 3: Rewrite and factor by grouping

Rewrite the middle term using these factors:

$$ 5x^2 - 10x + x - 2 $$

Group the terms:

$$ (5x^2 - 10x) + (x - 2) $$

Factor out the greatest common factor from each group:

$$ 5x(x - 2) + 1(x - 2) $$

Factor out the common binomial \((x - 2)\):

$$ (5x + 1)(x - 2) $$

Answer:

A. \(5x^2 - 9x - 2 = (5x + 1)(x - 2)\)