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Polynomials

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Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Solution

Here, the remainder is zero, hence x² + 3x + 1 is a factor of 3x⁴ + 5x³ – 1x² + 2x + 2.

Some More Questions From Polynomials Chapter

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x³ – 3x² + 5x – 3, g(x) = x²– 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
p(x) = x⁴ – 5x + 6, g(x) = 2 – x².

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
t² – 3, 2t⁴ + 3t³ – 2t²–9t – 12

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
x³ – 3x + 1, x⁵ –4x³ + x² + 3x + 1.

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