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 $P (x)$ .

Open in App

Solution

We know that the division algorithm states that:
Dividend $=$ Divisor $\times$ Quotient $+$ Remainder

It is given that the divisor is $x^{2} + 3 x + 5$ , the quotient is $2 x^{2} + x + 2$ and the remainder is $3$ . And let the dividend be $p (x)$ . Therefore, using division algorithm we have:

$p (x) = [(x^{2} + 3 x + 5) (2 x^{2} + x + 1)] + 3 = [x^{2} (2 x^{2} + x + 1) + 3 x (2 x^{2} + x + 1) + 5 (2 x^{2} + x + 1)] + 3 = 2 x^{4} + x^{3} + x^{2} + 6 x^{3} + 3 x^{2} + 3 x + 10 x^{2} + 5 x + 5 + 3 = 2 x^{4} + 7 x^{3} + 14 x^{2} + 8 x + 8$

Hence, the dividend $p (x)$ is $2 x^{4} + 7 x^{3} + 14 x^{2} + 8 x + 8$ .

Suggest Corrections

Similar questions

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)

p (x)

g (x)

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

g (x) = x^{2} + 1 - x

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

g (x) = x^{2} + 1 - x

p (x)

(x - 1 - x^{2})

(x - 2)

3

p (x)

Join BYJU'S Learning Program