Find the remainder when $p (x) = - x + 3 x^{2} - 1$ is divided by $x + 1$ .

3

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

2

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

- 3

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

- 2

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

Open in App

Solution

The correct option is A $3$
Given that, the polynomial $p (x) = - x + 3 x^{2} - 1$ is divided by $(x + 1)$ .
To find out: The remainder.
According to the remainder theorem, the remainder of the division of a polynomial $f (x)$ by a linear polynomial $(x - a)$ is $f (a)$ .
Here $a = - 1$
$∴$ Remainder is $p (- 1)$
$\Rightarrow p (- 1) = - (- 1) + 3 (- 1)^{2} - 1 = 1 + 3 - 1 = 3$

Hence, the remainder when $p (x)$ is divided by $(x + 1)$ is $3$ .

Suggest Corrections

Similar questions

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$(p x) = 2 x^{3} + 3 x^{2} - 11 x - 3, g (x) = (x + \frac{1}{2})$ .

Q. Let p(x) be a polynomial of degree more than 2. When p(x) is divided by x-2, it leaves remainder 1 and when it is divided by x-3, it leaves remainder 3. Find the remainder, when p(x) is divided by (x-2)(x-3).

Q. Question 2
The polynomial

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

when divided by x + 1 leaves the remainder 19. Find the value of a. Also , find the remainder when p(x) is divided by x + 2.

Q. If

p (x) = 2 x^{3} - 3 x^{2} + 4 x - 5

. Find the remainder when

p (x)

is divided by ,

x + 3

Q. The polynomial

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

when divided by

x + 1

leaves the remainder

19

.
Find the value of

a

. Also find the remainder when

p (x)

is divided by

x + 2

Join BYJU'S Learning Program

Find the remainder when p(x)=−x+3x2−1 is divided by x+1.

Find the remainder when $p (x) = - x + 3 x^{2} - 1$ is divided by $x + 1$ .