Question

Select the correct answer.Using long division, what is the quotient of this expression?x4 + 4x3 – 5x2 + x - 3/ x2 + x -3

Answer 1

we have that

(x^4 + 4x^3 – 5x^2 + x - 3)/ (x^2 + x -3)

x^2+3x-5

-x^4-x^3+3x^2

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3x^3-2x^2+x -3

-3x^3-3x^2+9x

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-5x^2+10x -3

5x^2+5x -15

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15x-18

therefore

(x^4 + 4x^3 – 5x^2 + x - 3)=(x^2 + x -3)(x^2+3x-5)+(15x-18)