If a polynomial $2 x^{2} - 7 x - 1$ is divided by $(x + 3)$ , then the remainder is

Open in App

Solution

Find the remainder of the given polynomial
According to the Remainder theorem,
When a polynomial $f (x)$ is divided by a divisor $(x - a)$ , the remainder obtained is given by $f (a)$
Let us assume given polynomial to be $f (x) = 2 x^{2} - 7 x - 1$
Comparing $(x + 3)$ with $(x - a)$ , we get $a = - 3$
Applying Remainder theorem, we get
Remainder $= f (a) = f (- 3)$
$f (- 3) = 2 {(- 3)}^{2} - 7 (- 3) - 1$
$= 2 \times 9 + 21 - 1$
$f (- 3) = 38$
Hence, the remainder obtained on dividing $2 x^{2} - 7 x - 1$ by $x + 3$ is $38$

Suggest Corrections

Similar questions

When the polynomial $x^{3} + 2 x^{2} - 5 a x - 7$ is divided by $(x - 1)$ , the remainder is A and when the polynomial $x^{3} + a x^{2} - 12 x + 16$ is divided by $(x + 2)$ , the remainder is B. Find the value of 'a' if $2 A + B = 0$ .

Q. If the polynomial f(x) = 5x⁵ – 3x³ + 2x² – k gives remainder 1 when divided by x + 1, then k = __________.

Q. If a polynomial

f (x)

is divided by

x^{2} - 16

then remainder is

5 x + 3

, what will be the remainder when the same polynomial is divided by

(x + 4)

Q. If

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

is divided by a polynomial ______, then the quotient is

2 x^{2} + x + 3

and the remainder is 0.

Q. Find the remainder when

x^{3} + 2 x^{2} + 4 x + 3

is divided by the polynomial

x - 1

Join BYJU'S Learning Program

If a polynomial 2x2-7x-1 is divided by (x+3), then the remainder is

If a polynomial $2 x^{2} - 7 x - 1$ is divided by $(x + 3)$ , then the remainder is