## Can x3 – 3x + 1 be the quotient on division of x5+ 2×3 + x – 1 by a polynomial in x of degree 3? Justify​

Question

Can x3 – 3x + 1 be the quotient on division of x5+ 2×3 + x – 1 by a polynomial in x of degree 3? Justify​

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2 months 2021-08-01T12:39:05+00:00 2 Answers 2 views 0

1. No, x

2

−1 cannot be the quotient on division of x

6

−2x

3

+x−1 by a

polynomial in degree 5 because the degree of the product of the

quotient and the divisor should be equal to the power of the dividend.

Here, the degree of the product of the quotient and the divisor is 7. But the degree of x

6

−2x

3

+x−1 is 6

No

Step-by-step explanation:

x⁵ + 2x³ + x – 1  -> degree of  the polynomial is 5

So, when x⁵ is divided by x³, the quotient should be x⁵⁻³ = x².

So, x³ – 3x + 1 cannot be a quotient