In the division algorithm of polynomials the divisor is $(x + 2)$ , quotient is $(x + 1)$ and the remainder is $4$ . Find the dividend?

Open in App

Solution

Given $: b = x + 2, q = x + 1, r = 4$
By Euclid's division lemma, $a = b q + r$
$\Rightarrow a = (x + 2) (x + 1) + 4$
$\Rightarrow a = x^{2} + (2 + 4) x + 2 \times 1 + 4$
$\Rightarrow a = x^{2} + 6 x + 6$
$∴$ Dividend $= x^{2} + 6 x + 6$

Suggest Corrections

Similar questions

2 x^{2} + 3 x + 1

(x - 2)

= 15

= 2 x + 7

Find dividend using the division formula.
Given: Quotient = 20, Divisor = 5 and Remainder = 4

(x^{3} + 2 x^{2} + x + 2) \div (x - 1)

=

\times

+

x^{3} - 64; x - 4

If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ and divisor = $(x - 1)$ , find the quotient, $q (x)$ and remainder $r (x)$ .

Join BYJU'S Learning Program