Question

If (x-2) and (x+3) are factors of the polynomial f(x)=px³ + x² - 13x + pq ,find the value of P.​

Answer 1

Explanation:

If (x-2) and (x+3) are factors of the polynomial, f, then

`f(2) = 0`

and

`f( - 3) = 0`

Plug in 2 for x.

Plug in -3 for x and we will form of a system of equations

`8p - 22 + pq = 0`

Then for -3

`- 27p + 48 + pq = 0`

Subtract the two systems

`35p - 70 = 0`

`p = 2`

So P is 2

Extra:

Plug 2 in either the systems of equations

`16 - 22 + 2q = 0`

`2q = 6`

`q = 3`

`2 {x}^(3) + {x}^(2) - 13x + 6`