Question

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

• A. 5
• B. -11
• C. -5
• D. 11

Answer 1

Answer:

B. -11

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,

$p(1)=0$

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

$4+3+4+k=0$

$11+k=0$

$k=-11$