Question

Consider the following division of polynomials. x^24+x^3+7x^2-6x+8 divide by x^2+2x+8 A) Use long division to determine the quotient of the polynomials. Show all of your work for full credit. B) Use mathematical methods to prove your answer. Show all of your work for full credit.

Answer 1

x² -x + 1 Quotient

Explanation:

Given in the question,

the numerator = x^4 + x³ + 7x² - 6x + 8

the denominator = x² + 2x + 8

Polynomial Long Division

Dividing :

x^4+x^3+7x^2-6x+8 ("Dividend")

By :

x2+2x+8 ("Divisor")

x² -x + 1 Quotient

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dividend x² + 2x + 8 | x^4 + x^3 + 7x² -6x + 8

divisor *x² x^4 + 2x^3 + 8x²

remainder -x³ - x² -6x + 8

divisor * -x1 -x³ -2x² . -8x

remainder x² +2x +8

divisor *1 x² +2x +8

remainder 0

B)

(x² -x + 1) (x² + 2x + 8)

= x^4 + x^3 + 7x² -6x + 8

hence proved