Question

question 4 of 10
which of the binomials below is a factor of this trinomial?
x² - 6x - 16
a. x + 4
b. x + 2
c. x - 4
d. x - 2

Explanation:

Step1: Factor the trinomial

To factor \(x^2 - 6x - 16\), we need two numbers that multiply to \(-16\) and add up to \(-6\). The numbers are \(-8\) and \(2\) because \(-8\times2=-16\) and \(-8 + 2=-6\).
So, \(x^2 - 6x - 16=(x - 8)(x + 2)\).

Step2: Identify the factor

From the factored form \((x - 8)(x + 2)\), we can see that \(x + 2\) is a factor. Looking at the options, option B is \(x + 2\).

Answer:

B. \(x + 2\)