PreCalc

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When the polynomial p(x) is divided by (x–2), the remainder is 3 and when p(x) is divided by (x+1) the remainder is 9. Given that p(x) may be written in the form (x–2)(x+1)q(x) + Ax + B where q(x) is a polynomial and A and B are numbers, find the remainder when p(x) is divided by (x–2)(x+1).

  • PreCalc -

    Can someone please actually help?

  • PreCalc -

    impatient much? We don't all just sit by our computers all day waiting for postings. We also have lives.

    we are given
    p(2) = 3
    p(-1) = 9

    so, using those values (and recognizing that the (x–2)(x+1)q(x) part is zero),

    2A+B = 3
    -A+B = 9

    solve for A and B, and Ax+B is the remainder.

  • PreCalc -

    Steve,

    My apologies but the only reason I said that was because some random person kept spamming this question with random sayings and it kinda got annoying. I didn't mean to offend you in any way

  • PreCalc -

    yeah, that happens some here.

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