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

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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  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

    Reply
  2. 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

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