# Ex.2.3 Q4 Polynomials Solution - NCERT Maths Class 10

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## Question

On dividing $$x^{3} -3 x^{2}+x +2$$ by a polynomial $$g(x),$$ the quotient and remainder were $$x – 2$$ and $$–2x + 4,$$ respectively. Find $$g(x).$$

Video Solution
Polynomials
Ex 2.3 | Question 4

## Text Solution

What is unknown?

Divisor $$g(x)$$ of a polynomial $$p(x).$$

Reasoning:

This question is straight forward, you can solve it by using division algorithm

Dividend $$=$$ Divisor $$\times$$ Quotient $$+$$ Remainder

Put the given values in the above equation and simplify it, get the value of $$g(x).$$

Steps:

Dividend $$=$$ Divisor $$\times$$ Quotient $$+$$ Remainder

\begin{align}x^{3}-3 x^{2}+x+2&=g(x) \times x-2+(-2 x+4)\\\left(x^{3}-3 x^{2}+x+2\right)-(-2 x+4)&=g(x) \times x-2\\\left(x^{3}-3 x^{2}+x+2 x+2-4\right)&=g(x) \times x-2\\\left(x^{3}-3 x^{2}+3 x-2\right)&=g(x) \times x-2 \end{align}

Therefore, $$g\left( x \right) = {x^2} - x + 1$$

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