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

Long Division of Polynomials

When a polyno...

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

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

p (x)

x^{2} + 3 x + 5

2 x^{2} + x + 1

x = 3

P (x)

g (x)

p (x) = 4 x^{3} + 2 x^{2} - 10 x + 2

g (x)

(2 x^{2} + 4 x + 1)

5

p (x)

(2 x - 1)

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

4

p (x)

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

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

Join BYJU'S Learning Program