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
