## f(x)= x3 + x2 + px+q where p and q are constants Given that (x – 5) is a factor and f(-3) = 8 (a) find the values of p and q.

Question

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## Answers ( )

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