Question

June 17, 2021

# The quotient of (x5 – 3x3 – 3x2 – 10x + 15) and a polynomial is (x2 – 5). what is the polynomial?

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Answer

Thus p(x)= (x^5-3x^3-10x+15) *(x^2-5)

X^7- 5x^5-3x^5+15x^3-10x^3+50x+15x^2-75

The values of x with the same power are group together and added.

=x^7-8x^5-5x^3+15x^2+50x-75, thus this equation is the polynomial. The polynomial has the largest degree, with the remainder, having the smallest degree.

(x5- 3x3 – 3x2 -10x +15) ( x2 – 5)

x7- 5x5 – 3x5 + 15x3 – 3x4 + 15x2 - 10x3 + 50x +15x2 – 75

x7 – 8x5 – 3x4 +5x3 + 30x2 + 50x -75

The polynomial from the above quotients is x7 – 8x5 – 3x4 +5x3 + 30x2 + 50x -75

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