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Algebra Examples Simplifying Polynomials

Divide

$x^{2} - 5 x + 6$ , $x + 6$

Step 1

Divide the first expression by the second expression.

$\frac{x^{2} - 5 x + 6}{x + 6}$

Step 2

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$x$

+

$6$

$x^{2}$

-

$5 x$

+

$6$

Step 3

Divide the highest order term in the dividend $x^{2}$ by the highest order term in divisor $x$ .

					$x$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$

Step 4

Multiply the new quotient term by the divisor.

					$x$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				+	$x^{2}$	+	$6 x$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $x^{2} + 6 x$

					$x$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				-	$x^{2}$	-	$6 x$

Step 6

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

					$x$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				-	$x^{2}$	-	$6 x$
						-	$11 x$

Step 7

Pull the next terms from the original dividend down into the current dividend.

					$x$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				-	$x^{2}$	-	$6 x$
						-	$11 x$	+	$6$

Step 8

Divide the highest order term in the dividend $- 11 x$ by the highest order term in divisor $x$ .

					$x$	-	$11$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				-	$x^{2}$	-	$6 x$
						-	$11 x$	+	$6$

Step 9

Multiply the new quotient term by the divisor.

					$x$	-	$11$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				-	$x^{2}$	-	$6 x$
						-	$11 x$	+	$6$
						-	$11 x$	-	$66$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 11 x - 66$

					$x$	-	$11$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				-	$x^{2}$	-	$6 x$
						-	$11 x$	+	$6$
						+	$11 x$	+	$66$

Step 11

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

					$x$	-	$11$
	$x$	+	$6$		$x^{2}$	-	$5 x$	+	$6$
				-	$x^{2}$	-	$6 x$
						-	$11 x$	+	$6$
						+	$11 x$	+	$66$
								+	$72$

Step 12

The final answer is the quotient plus the remainder over the divisor.

$x - 11 + \frac{72}{x + 6}$

Enter YOUR Problem

Simplifying Polynomials

More step-by-step Algebra examples from this chapter.

Simplifying Multiplication Polynomial Addition Polynomial Subtraction Polynomial Multiplication Evaluate the Expression Using the Given Values Determining if the Expression is a Polynomial Multiplying Polynomials Using FOIL Operations on Polynomials Simplifying Expressions Negative Exponents Rewriting Using Negative Exponents

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$