Question

Find k such that f(x)=x^4+kx^3+2 has the factor x+1.

A) k = 0
B) k = 1
C) k = 2
D) k = 3

Answer 1

To find the value of k such that f(x) has the factor x+1, divide f(x) by x+1 and check if the remainder is zero. Option B

Step-by-step explanation:

To find the value of k such that f(x) has the factor x+1, we need to divide f(x) by x+1 and see if the remainder is equal to 0. If the remainder is 0, then x+1 is a factor of f(x). Let's perform the division:

We have f(x) = x^4 + kx^3 + 2

Dividing f(x) by x+1 will give us a quotient and a remainder. The remainder should be 0 for x+1 to be a factor.

Let's perform the division:

x+1 | x^4 + kx^3 + 2

After dividing, we get a remainder of k-1. For x+1 to be a factor, the remainder should be 0. Therefore, k-1 = 0, which implies k = 1.

So, the value of k such that f(x) has the factor x+1 is k = 1. Option b