Question

Find the value of c so that the polynomial p(x) s divisible by (x+2).
p(x)=4x^3+cx^2+x+2

Answer 1

To determine the value of c that allows the polynomial p(x) to be divisible by (x+2), you substitute -2 into p(x) and solve for c. The calculation leads to the conclusion that c must be 7.5.

Step-by-step explanation:

To find the value of c so that the polynomial p(x) is divisible by (x+2), we can use polynomial long division or synthetic division. However, since (x+2) is a factor of p(x), p(-2) must be equal to zero. Using the given polynomial p(x) = 4x^3 + cx^2 + x + 2, we substitute x with -2 and set the equation to zero:

p(-2) = 4(-2)^3 + c(-2)^2 - 2 + 2 = 0

Solving this equation will give us the value of c:

p(-2) = -32 + 4c + 2 = 0
Therefore, 4c = 30 and c = 30/4 = 7.5.

So, the value of c that makes p(x) divisible by (x+2) is 7.5.