Find the quotient and the remainder when $2x^{2}-7x-15$ is divided by $2x+1$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) To find the quotient and remainder,we perform polynomial long division:
$1$. Divide the first term of the dividend $(2x^2)$ by the first term of the divisor $(2x)$: $2x^2 / 2x = x$. This is the first term of the quotient.
$2$. Multiply the divisor $(2x+1)$ by $x$: $x(2x+1) = 2x^2 + x$.
$3$. Subtract this from the dividend: $(2x^2 - 7x - 15) - (2x^2 + x) = -8x - 15$.
$4$. Divide the first term of the new expression $(-8x)$ by the first term of the divisor $(2x)$: $-8x / 2x = -4$. This is the second term of the quotient.
$5$. Multiply the divisor $(2x+1)$ by $-4$: $-4(2x+1) = -8x - 4$.
$6$. Subtract this from the current expression: $(-8x - 15) - (-8x - 4) = -8x - 15 + 8x + 4 = -11$.
Therefore,the Quotient is $x-4$ and the Remainder is $-11$.

Explore More

Similar Questions

Which of the following expressions is a polynomial? State the reason. If an expression is a polynomial,state whether it is a polynomial in one variable or not: $3x^2 + 5x - 7 + \frac{8}{x}$

$4x^{2} - 20x + 25 = (\ldots \ldots \ldots)^{2}$

Factorise the following quadratic polynomial by splitting the middle term:
$6 x^{2}+7 x-20$

Classify the following as linear,quadratic,or cubic polynomial: $4y + 11$.

The degree of the zero polynomial is

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