Question

Find the value of C so that (x-3) is a factor of the polynomial p(x)

Answer 1

c = 4

Explanation:

Given that (x - 3) is a factor of p(x) then x = 3 is a root and p(3) = 0

p(3) = - (3)³ + c(3)² - 4(3) + 3 = 0, hence

- 27 + 9c - 12 + 3 = 0

9c - 36 = 0 ( add 36 to both sides )

9c = 36 ( divide both sides by 9 )

c = 4

Answer 2

In general, you have that
`(x-x_0)` is a factor of a polynomial
`p(x)` if and only if
`p(x_0)=0`

So, we want
`p(3)=0`. We have

`p(3) = -3^3+ 9c -4\cdot 3 +3 = -27+9c-12+3 = 9c-36`

So, we have

`p(3) = 0 \iff 9c-36 = 0 \iff x = (36)/(9) = 4`