When nbsp-a polynomial is divided by -x-2- the nbsp-quotient nbsp-and remainder are -2x-1- and 3 respectively- Find the polynomial- 2x-2-6x-11-5x-2-3x-8-6x-2-3x-9-2x-2-3x-1-

The correct option is D 2x^2+3x+1 We know that, by divison algorithm, nbsp; Dividend = Divisor x Quotient + Remainder. ∴ P(x) = (x+2) × nbsp;(2x 1) + 3 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Division Algorithm for a Polynomial

When nbsp;a...

Question

When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.

$2 x^{2} + 6 x + 11$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$5 x^{2} + 3 x + 8$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$6 x^{2} + 3 x + 9$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$2 x^{2} + 3 x + 1$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
$2 x^{2} + 3 x + 1$

We know that, by divison algorithm,
Dividend = Divisor x Quotient + Remainder.

$∴ P (x) = (x + 2) \times (2 x - 1) + 3 = x (2 x - 1) + 2 (2 x - 1) + 3 = 2 x^{2} - x + 4 x - 2 + 3 P (x) = 2 x^{2} + 3 x + 1$

$∴ The required polynomial is 2 x^{2} + 3 x + 1.$

Suggest Corrections

Similar questions

Quotient and remainder of a polynomial when divided by $x + 2$ are $2 x - 1$ and $3$ respectively. Find the polynomial.

Q. If polynomial

p (x)

is divided by

x^{2} + 3 x + 5

, the quotient polynomial and the remainder polynomials are

2 x^{2} + x + 1

and

x = 3

respectively. Find

P (x)

Q. A polynomial p(x) is divided by (2x - 1). The quotient and remainder obtained are

(7 x^{2} + x + 5)

and 4 respectively. Find p(x).
OR
Find the quotient and remainder using synthetic division.

(3 x^{3} - 2 x^{2} + 7 x - 5) \div (x + 3)

Q. On dividing

3 x^{3} + x^{2} + 2 x + 5

by a polynomial

g (x)

, the quotient and remainder are

(3 x - 5)

and

(9 x + 10)

respectively. Find

g (x)

Q. If a polynomial gives remainder

1

and

2

and same quotient on dividing by

x - 2

and

x - 1

respectively, then the remainder when that polynomial is divided by

x^{2} - 3 x + 2,

Join BYJU'S Learning Program

When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.

The correct option is D 2x2+3x+1 We know that, by divison algorithm, Dividend = Divisor x Quotient + Remainder. ∴P(x)=(x+2)×(2x−1)+3 =x(2x−1)+2(2x−1)+3 =2x2−x+4x−2+3P(x)=2x2+3x+1 ∴The required polynomial is 2x2+3x+1.