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

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.

I’d appreciate any help!! ​

in progress 0
Alice 2 weeks 2021-11-25T09:42:32+00:00 1 Answer 0

Answers ( )

    0
    2021-11-25T09:44:16+00:00

    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

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )