Can x3 – 3x + 1 be the quotient on division of x5+ 2×3 + x – 1 by a polynomial in x of degree 3? Justify August 1, 2021 by Delwyn Can x3 – 3x + 1 be the quotient on division of x5+ 2×3 + x – 1 by a polynomial in x of degree 3? Justify

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 Reply

Answer: 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 Reply

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

Answer: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