Question

Find the value of k if x - 2 is a factor of $4x^3+3x^2-4x+k$

• A. -20
• B. 16
• C. -36
• D. 12

Answer 1

Answer:

C. -36

Factor Theorem:

Given polynomial p(x), if p(a)=0 for some number a, then (x - a) is a linear factor of p(x). Likewise if (x-a) is a linear factor of p(x) then p(a) = 0.

So here

$p(2)=0$

$p(2)=4x^3+3x^2-4x+k=0$

$4(2^3)+3(2^2)-4(2)+k=0$

$32+12-8+k=0$

$k= -36$