Question

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

Answer 1

Answer:

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