Factoring Quadratic trinomials: 4x^2 - 13x + 3

A.) (4x + 1) (x + 3)

B.) (4x - 1) (x + 3)

C.) (4x + 1) (x - 3)

D.) (4x - 1) (x - 3)

D

Step-by-step explanation:

Given

4x² - 13x + 3

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

product = 4 * 3 = 12 and sum = - 13

The factors are - 12 and - 1

Use these factors to split the x - term

4x² - 12x - x + 3 (factor the first/second and third/fourth terms)

= 4x (x - 3) - 1 (x - 3) ← factor out (x - 3) from each term

= (x - 3) (4x - 1)

Thus

4x² - 13x + 3 = (4x - 1) (x - 3) → D