Question

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

• A. 1
• B. -1
• C. 2
• D. 0

Answer 1

Answer:

A. 1

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

$p(1)=0$

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

$2+1-4+k=0$

$-1+k=0$

$k=1$