Question

Let p(x) = x3 – 5x2 + cx + 4. For what value of c is (x - 2) a factor of p(x)?

Answer 1

Answer: 4

Explanation:

P(x)= x3-5x2+cx+4

X-2 is a factor of p(x)

Let p(x)= 0

X-2=0

X=2

Substitute for x=2 in p(x)

0=2^3-5(2)^2+2c+4

0=8-5(4)+2c+4

0=8-20+2c+4

Collect like terms

-8+20-4=2c

8=2c

C=8/2

C=4

The value of C is 4