The polynomial f(x) leaves a remainder of – 3 and – 7 when divided by (3x – 1) and (x +1) respectively. Find the remainder when f(x) is

Question

The polynomial f(x) leaves a remainder of – 3 and – 7 when divided by (3x – 1) and (x +1) respectively.
Find the remainder when f(x) is divided by (3x^2 + 2x -1).

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Liliana 2 weeks 2021-09-28T04:22:58+00:00 1 Answer 0

Answers ( )

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    2021-09-28T04:24:40+00:00

    Step-by-step explanation:

    Here, f(x) is the given polynomial.

    By remainder Theorem,

    When divided by (3x-1),

    f(1/3) = -3……..(1)

    When divided by (x+1),

    f(-1) = -7………(2)

    Another polynomial is 3x²+2x1

    Solving,

    3x²+2x-1

    = 3x²+3x-x-1

    =3x(x+1)-(x+1)

    =(3x-1)(x+1)

    So

    f(x) = (3x-1)(x+1)Qx + (ax+b)

    For f(-1),

    -7 = -a+b

    b= a-7

    For f(1/3),

    -3 = a/3+b

    or, -3 = a/3+a-7

    or, 4×3 = 4a

    or a = 3

    Also, b = 3-7 =-4

    Hence, remainder is (3x-4)

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45:7+7-4:2-5:5*4+35:2 =? ( )