Which of the following is a linear factor of 2x2 - x-6?

A. 2x-3

B. x+2

C. 2x+3

D. 2x-3

E. X-3

C

Step-by-step explanation:

Given

2x² - x - 6

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

product = 2 * - 6 = - 12 and sum = - 1

The factors are - 4 and + 3

Use these factors to split the x - term

2x² - 4x + 3x - 6 (factor the first/second and third/fourth terms)

= 2x (x - 2) + 3 (x - 2) ← factor out (x - 2) from each term

= (x - 2) (2x + 3) ← in factored form

Thus 2x + 3 is a factor → C