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

## 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 \(g(x).\)

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