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

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) To divide $p(x) = x^{3} - 3x^{2} + 5x - 3$ by $g(x) = x^{2} - 2$:
$1$. Divide the first term of the dividend $(x^{3})$ by the first term of the divisor $(x^{2})$ to get $x$. This is the first term of the quotient.
$2$. Multiply $x$ by $(x^{2} - 2)$ to get $x^{3} - 2x$. Subtract this from $p(x)$ to get $-3x^{2} + 7x - 3$.
$3$. Divide the first term of the new dividend $(-3x^{2})$ by the first term of the divisor $(x^{2})$ to get $-3$. This is the second term of the quotient.
$4$. Multiply $-3$ by $(x^{2} - 2)$ to get $-3x^{2} + 6$. Subtract this from the current remainder to get $7x - 9$.
Thus,the quotient is $x - 3$ and the remainder is $7x - 9$.

Explore More

Similar Questions

Verify that the numbers given alongside the cubic polynomials below are their zeroes. Also,verify the relationship between the zeroes and the coefficients in each case: $x^{3}-4x^{2}+5x-2; 2, 1, 1$.

Difficult
View Solution

Look at the graph given below. It is the graph of $y = p(x)$ where $p(x)$ is a polynomial. Find the number of zeroes of $p(x)$.

Find the zeroes of the quadratic polynomial $3x^{2}-x-4$ and verify the relationship between the zeroes and the coefficients.

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: $6x^{2}-3-7x$.

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: $4u^{2} + 8u$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo