3x^2-2x-5

Subject is factoring quadratic trinomials when a doesn't = 1

(3x-5) (x+1)

Step-by-step explanation:

For a general polynomial ax^2+bx+c, we need to find two numbers that multiply to ac and add up to b.

In this case, we need to find two numbers that multiply to 3 * (-5) = - 15 and add up to - 2. These are 3,-5. Rewrite the polynomial as:

3x^2+3x-5x-5

And then factor each pair:

3x (x+1) - 5 (x+1) = (3x-5) (x+1)

(x + 1) (3x - 5)

Step-by-step explanation:

Given

3x² - 2x - 5

To factor the quadratic

Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x - term

product = 3 * - 5 = - 15 and sum = - 2

The required factors are - 5 and + 3

Use these factors to split the x - term

3x² + 3x - 5x - 5 (factor the first/second and third/fourth terms)

= 3x (x + 1) - 5 (x + 1) ← factor out (x + 1) from each term

= (x + 1) (3x - 5) ← in factored form