Question

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

Answer 1

Step-by-step explanation:

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Answer 2

Quotient = x - 3 and remainder = 7x - 9

Given :

Divide the polynomial p(x) by the polynomial g(x)

p(x) = x³ – 3 x² + 5x – 3 , g(x) = x² – 2

To find :

The quotient and remainder

Solution :

Step 1 of 2 :

Write down dividend and divisor

Dividend = p(x) = x³ – 3 x² + 5 x – 3

Divisor = g(x) = x² – 2

Step 2 of 2 :

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder

We divide the polynomial p(x) by the polynomial g(x) as below :

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:x - 3\:\:}}}\\ {\underline{\sf{ {x}^{2} - 2}}}& {\sf{ \: \: \: \: \: \: \: \: \: \: \: \: {x}^{3} - 3 {x}^{2} + 5x - 3}} \\{\sf{}}& \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ {x}^{3} \: \: \: \: \: \: \: \: \: \: \: \: - 2 x \: \: \: \: \: \: \: \: \: \: \: }} \\ {\underline{\sf{}}}&{\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -3 {x}^{2} + 7x - 3 }} \\{\sf{}}& \underline{\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -3 {x}^{2} \: \: \: \: \: \: \: \: \: \: + 6 }} \\ {\underline{\sf{}}}& {\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 7x - 9}} {\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

Quotient = x - 3 and remainder = 7x - 9

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