Question

F(x)= x3 + x2 + px+q

Answer 1

Answer:

p = - 22 and q = - 40

Step-by-step explanation:

Given that (x - 5) is a factor then x = 5 is a root and f(5) = 0, that is

f(5) = 5³ + 5² + 5p + q , so

125 + 25 + 5p + q = 0

150 + 5p + q = 0 ( subtract 150 from both sides )

5p + q = - 150 → (1)

Also

f(- 3) = (- 3)³ + (- 3)² - 3p + q, that is

- 27 + 9 - 3p + q = 8

- 18 - 3p + q = 8 ( add 18 to both sides )

- 3p + q = 26 → (2)

Subtract (2) from (1) term by term

8p = - 176 ( divide both sides by 8 )

p = - 22

Substitute p = - 22 into (1) and solve for q

(5 × - 22) + q = - 150

- 110 + q = - 150 ( add 110 to both sides )

q = - 40