Question

3x^2-2x-5
Subject is factoring quadratic trinomials when a doesn’t =1

Answer 1

(x + 1)(3x - 5)

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

Answer 2

(3x-5)(x+1)

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)