Given polynomial p(x) = $x^{5} - 3 x^{4} - 3 x^{3} + 9 x^{2} + 2 x - 6$ is completely divisble by $x^{4} - 3 x^{2} + 2$ the find quotient.

x + 3

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x – 3

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x + 2

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Solution

The correct option is B
x – 3

p(x) = $x^{5} - 3 x^{4} - 3 x^{3} + 9 x^{2} + 2 x - 6$

g(x) = $x^{4} - 3 x^{2} + 2$

$\begin{matrix} x - 3 x^{4} - 3 x^{2} + 2 x^{5} - 3 x^{4} - 3 x^{3} + 9 x^{2} + 2 x - 6 x^{5} - 3 x^{3} + 2 x - ------------- - - 3 x^{4} + 9 x^{2} - 6 - 3 x^{4} + 9 x^{2} - 6 - --------------- - 0 \end{matrix}$

Quotient = x – 3

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Similar questions

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

(i)

(ii)

(iii)

What is the coefficient of $x^{4}$ in the polynomial p(x)= $x^{7} + 3 x^{4} + 9 x^{2} + 1$ ?

Q. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder of the following.

p (x) = x^{4} - 3 x^{2} + 4 x + 5

g (x) = x^{2} + 1 - x

Divided the polynomial p (x) by the polynomial g (x) and find the quotient and remainder in each of the following

p (x) = x^{4} - 3 x^{3} + 4 x + 5 g (x) = x^{3} + 1 - x

Question 1 (ii)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: $p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x$

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Given polynomial p(x) = x5−3x4−3x3+9x2+2x−6 is completely divisble by x4−3x2+2 the find quotient.

The correct option is B x – 3 p(x) = x5−3x4−3x3+9x2+2x−6 g(x) = x4−3x2+2 x−3x4−3x2+2x5−3x4−3x3+9x2+2x−6x5−3x3+2x–––––––––––––––2−3x4+9x2−6−3x4+9x2−6–––––––––––––––––0 Quotient = x – 3

Given polynomial p(x) = $x^{5} - 3 x^{4} - 3 x^{3} + 9 x^{2} + 2 x - 6$ is completely divisble by $x^{4} - 3 x^{2} + 2$ the find quotient.