Question

Find the value of c (x-2) is a factor of the polynomial p(x). P(x)=x^3-4x^2+3x+c

Answer 1

c = 2

Explanation:

P(x)=x^3-4x^2+3x+c

The polynomial has x - 2 as a factor

Rewriting the polynomial as:

• x^3-4x^2+3x+c =
• x^3 - 2x^2 - 2x^2 + 4x - x + c =
• x^2(x - 2) - 2x(x - 2) - (x - c)

As we see the first 2 terms have (x -2) as a factor, so the third term:

• (x - c) = (x - 2)
• c=2

Answer is c= 2