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Algebra Examples Simplifying Polynomials

Divide Using Long Polynomial Division

$(5 x^{2} + 36 x + 40) \div (x + 6)$

Step 1

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

$x$

+

$6$

$5 x^{2}$

+

$36 x$

+

$40$

Step 2

Divide the highest order term in the dividend $5 x^{2}$ by the highest order term in divisor $x$ .

					$5 x$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$

Step 3

Multiply the new quotient term by the divisor.

					$5 x$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				+	$5 x^{2}$	+	$30 x$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $5 x^{2} + 30 x$

					$5 x$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				-	$5 x^{2}$	-	$30 x$

Step 5

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

					$5 x$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				-	$5 x^{2}$	-	$30 x$
						+	$6 x$

Step 6

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

					$5 x$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				-	$5 x^{2}$	-	$30 x$
						+	$6 x$	+	$40$

Step 7

Divide the highest order term in the dividend $6 x$ by the highest order term in divisor $x$ .

					$5 x$	+	$6$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				-	$5 x^{2}$	-	$30 x$
						+	$6 x$	+	$40$

Step 8

Multiply the new quotient term by the divisor.

					$5 x$	+	$6$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				-	$5 x^{2}$	-	$30 x$
						+	$6 x$	+	$40$
						+	$6 x$	+	$36$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $6 x + 36$

					$5 x$	+	$6$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				-	$5 x^{2}$	-	$30 x$
						+	$6 x$	+	$40$
						-	$6 x$	-	$36$

Step 10

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

					$5 x$	+	$6$
	$x$	+	$6$		$5 x^{2}$	+	$36 x$	+	$40$
				-	$5 x^{2}$	-	$30 x$
						+	$6 x$	+	$40$
						-	$6 x$	-	$36$
								+	$4$

Step 11

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

$5 x + 6 + \frac{4}{x + 6}$

Enter YOUR Problem

Simplifying Polynomials

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

Simplifying Multiplication Polynomial Addition Polynomial Subtraction Polynomial Multiplication Polynomial Division 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

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