Which of the binomials below is a factor of this trinomial?x2 - 14x + 24A.x2 + 6B.x - 12C.x + 6D.x + 4SUBMITarrow_backPREVIOUS

To find out which binomial is a factor of the trinomial x² - 14x + 24, we need to factorize the trinomial.

The factors of a trinomial in the form of x² + bx + c are (x - p)(x - q), where p and q are the roots of the equation x² + bx + c = 0.

The roots of the equation can be found using the formula x = [-b ± sqrt(b² - 4ac)] / 2a.

In this case, a = 1, b = -14, and c = 24.

So, the roots are x = [14 ± sqrt((-14)² - 4124)] / 2*1 = [14 ± sqrt(196 - 96)] / 2 = [14 ± sqrt(100)] / 2 = [14 ± 10] / 2 = 12, 2

So, the factors of the trinomial are (x - 12) and (x - 2).

Therefore, the binomial x - 12 is a factor of the trinomial x² - 14x + 24. So, the correct answer is B. x - 12.