Question

Consider the polynomial functionP(x)=x³-8x²-29x+180.Verify that P(9) = 0. Since P(9) =0, what must one of the factors of P be?

Answer 1

One Factor: x-9

Explanation:

The polynomial function, P(x)=x³-8x²-29x+180

To verify: P(9)=0

Put x=9 into polynomial

`P(9)=9^3-8\cdot 9^2-29\cdot 9+180`

`P(9)=0`

At x=9, P(9)=0

Therefore, x-9 must be factor of P(x).

when divide x³-8x²-29x+180 by x-9 get remainder 0

`(x^3-8x^2-29x+180)/ (x-9)`

`\Rightarrow x^2+x-20`

Factor quadratic equation

`\Rightarrow (x+5)(x-4)`

Three factors are (x+5), (x-4) and (x-9)