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Long Division Method to Divide Two Polynomials

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Question

Divide using the long division method and check the answer.
$x^{2} + 5 x + 10$ by $x + 3$

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Solution

We divide $x^{2} + 5 x + 10$ by $(x + 3)$ as shown in the above image:

From the division, we observe that the quotient is $x + 2$ and the remainder is $4$ .

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

We apply the division algorithm to check the answer as follows:

$D i v i d e n d = D i v i s o r \times Q u o t i e n t + R e m a i n d e r x^{2} + 5 x + 10 = [(x + 3) (x + 2)] + 4 x^{2} + 5 x + 10 = (x^{2} + 2 x + 3 x + 6) + 4 x^{2} + 5 x + 10 = x^{2} + 5 x + 6 + 4 x^{2} + 5 x + 10 = x^{2} + 5 x + 10 H e n c e v e r i f i e d .$

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