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

Answer: 4

Step-by-step 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