Pre-Algebra Examples

$(11 x^{2} - 82 x + 35) \div (x - 7)$

Step 1

Rewrite the division as a fraction.

$\frac{11 x^{2} - 82 x + 35}{x - 7}$

Step 2

Factor by grouping.

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Step 2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 11 \cdot 35 = 385$ and whose sum is $b = - 82$ .

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Step 2.1.1

Factor $- 82$ out of $- 82 x$ .

$\frac{11 x^{2} - 82 (x) + 35}{x - 7}$

Step 2.1.2

Rewrite $- 82$ as $- 5$ plus $- 77$

$\frac{11 x^{2} + (- 5 - 77) x + 35}{x - 7}$

Step 2.1.3

Apply the distributive property.

$\frac{11 x^{2} - 5 x - 77 x + 35}{x - 7}$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$\frac{(11 x^{2} - 5 x) - 77 x + 35}{x - 7}$

Step 2.2.2

Factor out the greatest common factor (GCF) from each group.

$\frac{x (11 x - 5) - 7 (11 x - 5)}{x - 7}$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $11 x - 5$ .

$\frac{(11 x - 5) (x - 7)}{x - 7}$

Step 3

Cancel the common factor of $x - 7$ .

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Step 3.1

Cancel the common factor.

$\frac{(11 x - 5) (x - 7)}{x - 7}$

Step 3.2

Divide $11 x - 5$ by $1$ .

$11 x - 5$