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Long Division Method to Divide Two Polynomials

Check whether...

Question

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

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Solution

=

Since the remainder is 0,

Hence, is a factor of .

Since the remainder is 0,

Hence, is a factor of .

Since the remainder ,

Hence, is not a factor of .

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Similar questions

Check whether the first polynomial is a factor of the second polynomial by dividing second polynomial by the first polynomial.
$x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

Q. Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm :

(i)

g (t) = t^{2} - 3, f (t) = 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12

g (x) = x^{3} - 3 x + 1, f (x) = x^{5} - 4 x^{3} + x^{2} + 3 x + 1

g (x) = 2 x^{2} - x + 3, f (x) = 6 x^{5} - x^{4} + 4 x^{3} - 5 x^{2} - x - 15

Q. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

t^{2} - 3, 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12

Question 2 (ii)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

$x^{2} + 3 x + 1, 3 x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 2$

Q. Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.

x^{3} - 3 x + 1, x^{5} - 4 x^{3} + x^{2} + 3 x + 1

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