6. Show that (x – 1) is a factor of 2x + (p+3)x3+px2 – (p + 5) x-p for all values of p. If (x + 2) is also a factor, find p. Find

Question

6.
Show that (x – 1) is a factor of 2x + (p+3)x3+px2 – (p + 5) x-p for all values of p. If (x + 2) is also
a factor, find p. Find all the factors for that value of p. Thus solve f(x) = 0.​

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Maria 1 month 2021-08-22T23:27:35+00:00 1 Answer 0 views 0

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    2021-08-22T23:28:51+00:00

    Given polynomial x

    3

    −px

    2

    +6x−p divided by x−p

    If divided by x−p then x−p=0 or x=p

    Replace x by p we get

    q(x)=x

    3

    −px

    2

    +6x−p

    q(p)=(p)

    3

    −p(p)

    2

    +6(p)−p

    ⇒q(p)=p

    3

    −p

    3

    +6p−p

    ⇒q(p)=5p

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