# Explain how you can check polynomial division.

Explain how you can check polynomial division.
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Isaac Molina
The result of polynomial division can be checked by finding the product of the quotient and divisor and then adding the remainder to the product. The division is correct if adding the remainder and product gives the dividend.
For example, to check the result of $\frac{{x}^{2}+3x+1}{x-2}=x+5+\frac{11}{x-2}$ multiplying the quotient of x+5 and divisior of x-2 gives:
$\left(x+5\right)\left(x-2\right)={x}^{2}-2x+5x-10$
$={x}^{2}+3x-10$
Adding the remainder of 11 to ${x}^{2}+3x-10$ then gives $\left({x}^{2}+3x-10\right)+11={x}^{2}+3x+1$ which is equal to the dividend.
Result:
Find the product of the quotient and divisor and then add the remainder to verify it equals the dividend.