If $p (x) = 2 x^{3} + 5 x^{2} - 3 x - 2$ is divided by $x - 1$ , then find the remainder.

Open in App

Solution

Given, polynomial, $p (x) = 2 x^{3} + 5 x^{2} - 3 x - 2$ divided by $(x - 1)$ .

The polynomial is divided by $(x - 1)$ .
Then put $(x - 1) = 0 ⟹$ $x = 1$
we get,
$p (1) =$ $2 (1)^{3} + 5 (1)^{2} - 3 (1) - 2$
$\Rightarrow p (1) = 2 + 5 - 3 - 2$
$\Rightarrow p (1) = 2 + 5 - 5$
$\Rightarrow p (1) = 2$ .

So, when $p (x) =$ $2 x^{3} + 5 x^{2} - 3 x - 2$ is divided by $x - 1$ , the remainder obtained is $2$ .

Suggest Corrections

Similar questions

Q. If

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

. Find the remainder when

p (x)

is divided by ,

x - 2

Q. When

q (x) = 2 x^{3} - 5 x^{2} + 3 x + 7

is divided by

x + 2

, then the remainder is

R_{1}

. The value of

R_{1}^{2}

Q. If p(x) = 2x³ + ax² + 3x − 5 and q(x) = 2x³ + ax² + 3x − 5 leave the same remainder when divided by (x − 2), show that

a = \frac{- 13}{3}

Q. If

p (x) = a x^{3} + 3 x - 13

and

q (x) = 2 x^{3} - 5 x + 1

are divided by

x + 2

remainder is same in each case. find the value of

a

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

Join BYJU'S Learning Program

If p(x)=2x3+5x2−3x−2 is divided by x−1, then find the remainder.

Given, polynomial, p(x)=2x3+5x2−3x−2 divided by (x−1).The polynomial is divided by (x−1) .Then put(x−1)=0⟹ x=1 we get,p(1)= 2(1)3+5(1)2−3(1)−2⇒p(1)=2+5−3−2⇒p(1)=2+5−5⇒p(1)=2.So, when p(x)= 2x3+5x2−3x−2 is divided by x−1, the remainder obtained is 2.

If $p (x) = 2 x^{3} + 5 x^{2} - 3 x - 2$ is divided by $x - 1$ , then find the remainder.