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# Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

x^{2} – 4x + 3,x^{3} – x^{3} – 3x^{4} – x + 3

Answer :

Let us divide x^{3} – 3x^{2} – x + 3 by x^{2} – 4x + 3

The division process is

Here, the remainder is 0, therefore x^{2} – 4x + 3 is a factor of x^{3} – 3x^{2} – x + 3

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Divide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :

p(x) = x^{3} – 3x^{2} + 4x + 2 , g(x) = x – 1

Divide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :

p(x) = x^{3} – 3x^{2}– x + 3, g(x) = x^{2} – 4x + 3

When a polynomial p(x) is divided by (2x + 1), is it possible to have (x - 1) as a remainder? Justify your answer.

RS Aggarwal - MathematicsDivide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in each case :

p(x) = x^{4} + 2x^{3} – 3x^{2} + x – 1, g(x) = x – 2

Find all the zeroes of the polynomial given below having given numbers as its zeroes.

x^{4} – 6x^{3} – 26x^{2} + 138x – 35;2±√3