Question

Find the value of k if x - 1 is a factor of $4x^3+3x^2-4x+k$

• A. 2
• B. -3
• C. 0
• D. 1

Answer 1

Answer:

B. -3

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

$p(1) = 0$

$p(1) = 4(1^3)+3(1^2)-4(1)+k=0$

$\implies 4 + 3 -4 + k =0$

$3 + k =0$

$k = -3$