Divede (3 04 – 200² + x + x²-x-2) by x²+x+1) and check ​

Question

Divede (3 04 – 200² + x
+ x²-x-2) by
x²+x+1) and check

in progress 0
Allison 3 weeks 2021-09-09T13:25:34+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-09T13:26:54+00:00

    Answer:

    Quotient: 3x³-5x²+2x+4

    x²+x+1)3x⁵-2x⁴+0+x²+0-2(

    *********3x⁵+3x⁴+3x³

    __________________

    ***-5x⁴-3x³+x²

    *** -5x⁴-5x³-5x²

    __________________

    *** 2x³+6x²+0

    *** 2x³+2x²+2x

    __________________

    *** 4x²-2x-2

    *** 4x²+4x+4

    __________________

    Remainder (-6x-6)

    ___________________

    Dividend p(x) = 3x⁵-2x⁴+x²-2 ,

    Divisor g(x) = x² + x + 1,

    Quotient q(x) = 3x³ – 5x² + 2x + 4,

    Remainder r(x) = -6x – 6

    Verification:

    Dividend=Divisor×Quotient+Remainder

    g(x) × q(x ) + r(x)

    = (x² + x + 1)(3x³ – 5x² + 2x + 4)+(-6x – 6)

    = x²(3x³ – 5x² + 2x + 4)+x(3x³ – 5x² + 2x +4)+1(3x³- 5x² + 2x + 4)-6x – 6

    = 3x⁵-5x⁴+2x³+4x²+ 3x⁴-5x³+2x²+4x+ 3x³ – 5x² +2x + 4-6x -6

    = 3x⁵ +(-5+3)x⁴ + (2-5+3)x³+(4+2-5)x²+(4+2-6)x+4-6

    = 3x⁵-2x⁴+x²-2

    = Dividend

    •••♪

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