Question

question 10 of 25
what value of ( b ) makes the trinomial below a perfect square?
( x^2 - bx + 16 )

a. 2

b. 4

c. 16

d. 8

Explanation:

Step1: Recall perfect square trinomial formula

A perfect square trinomial has the form \((x - a)^2 = x^2 - 2ax + a^2\). Comparing with \(x^2 - bx + 16\), we see that \(a^2 = 16\).

Step2: Solve for \(a\)

Taking the square root of both sides, \(a=\pm4\). But since the middle term is \(-bx\), we focus on the coefficient of \(x\). From the formula, the coefficient of \(x\) is \(-2a\), so \(-b=-2a\) or \(b = 2a\).

Step3: Find \(b\)

If \(a = 4\), then \(b=2\times4 = 8\). If \(a=- 4\), \(b = 2\times(-4)=-8\), but since we are looking at the options (positive values considered here as the options are positive), \(b = 8\).

Answer:

D. 8