Precalculus Examples

$\frac{8 x^{2} - 28 x + 12}{- 2 x + 6}$

Step 1

Cancel the common factor of $8 x^{2} - 28 x + 12$ and $- 2 x + 6$ .

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Step 1.1

Factor $2$ out of $8 x^{2}$ .

$\frac{2 (4 x^{2}) - 28 x + 12}{- 2 x + 6}$

Step 1.2

Factor $2$ out of $- 28 x$ .

$\frac{2 (4 x^{2}) + 2 (- 14 x) + 12}{- 2 x + 6}$

Step 1.3

Factor $2$ out of $2 (4 x^{2}) + 2 (- 14 x)$ .

$\frac{2 (4 x^{2} - 14 x) + 12}{- 2 x + 6}$

Step 1.4

Factor $2$ out of $12$ .

$\frac{2 (4 x^{2} - 14 x) + 2 (6)}{- 2 x + 6}$

Step 1.5

Factor $2$ out of $2 (4 x^{2} - 14 x) + 2 (6)$ .

$\frac{2 (4 x^{2} - 14 x + 6)}{- 2 x + 6}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $2$ out of $- 2 x$ .

$\frac{2 (4 x^{2} - 14 x + 6)}{2 (- x) + 6}$

Step 1.6.2

Factor $2$ out of $6$ .

$\frac{2 (4 x^{2} - 14 x + 6)}{2 (- x) + 2 (3)}$

Step 1.6.3

Factor $2$ out of $2 (- x) + 2 (3)$ .

$\frac{2 (4 x^{2} - 14 x + 6)}{2 (- x + 3)}$

Step 1.6.4

Cancel the common factor.

$\frac{2 (4 x^{2} - 14 x + 6)}{2 (- x + 3)}$

Step 1.6.5

Rewrite the expression.

$\frac{4 x^{2} - 14 x + 6}{- x + 3}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $2$ out of $4 x^{2} - 14 x + 6$ .

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Step 2.1.1

Factor $2$ out of $4 x^{2}$ .

$\frac{2 (2 x^{2}) - 14 x + 6}{- x + 3}$

Step 2.1.2

Factor $2$ out of $- 14 x$ .

$\frac{2 (2 x^{2}) + 2 (- 7 x) + 6}{- x + 3}$

Step 2.1.3

Factor $2$ out of $6$ .

$\frac{2 (2 x^{2}) + 2 (- 7 x) + 2 (3)}{- x + 3}$

Step 2.1.4

Factor $2$ out of $2 (2 x^{2}) + 2 (- 7 x)$ .

$\frac{2 (2 x^{2} - 7 x) + 2 (3)}{- x + 3}$

Step 2.1.5

Factor $2$ out of $2 (2 x^{2} - 7 x) + 2 (3)$ .

$\frac{2 (2 x^{2} - 7 x + 3)}{- x + 3}$

Step 2.2

Factor by grouping.

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Step 2.2.1

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 $a \cdot c = 2 \cdot 3 = 6$ and whose sum is $b = - 7$ .

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Step 2.2.1.1

Factor $- 7$ out of $- 7 x$ .

$\frac{2 (2 x^{2} - 7 (x) + 3)}{- x + 3}$

Step 2.2.1.2

Rewrite $- 7$ as $- 1$ plus $- 6$

$\frac{2 (2 x^{2} + (- 1 - 6) x + 3)}{- x + 3}$

Step 2.2.1.3

Apply the distributive property.

$\frac{2 (2 x^{2} - 1 x - 6 x + 3)}{- x + 3}$

Step 2.2.2

Factor out the greatest common factor from each group.

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Step 2.2.2.1

Group the first two terms and the last two terms.

$\frac{2 ((2 x^{2} - 1 x) - 6 x + 3)}{- x + 3}$

Step 2.2.2.2

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

$\frac{2 (x (2 x - 1) - 3 (2 x - 1))}{- x + 3}$

Step 2.2.3

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$\frac{2 ((2 x - 1) (x - 3))}{- x + 3}$

$\frac{2 (2 x - 1) (x - 3)}{- x + 3}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x - 3$ and $- x + 3$ .

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Step 3.1.1

Factor $- 1$ out of $x$ .

$\frac{2 (2 x - 1) (- 1 (- x) - 3)}{- x + 3}$

Step 3.1.2

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{2 (2 x - 1) (- 1 (- x) - 1 (3))}{- x + 3}$

Step 3.1.3

Factor $- 1$ out of $- 1 (- x) - 1 (3)$ .

$\frac{2 (2 x - 1) (- 1 (- x + 3))}{- x + 3}$

Step 3.1.4

Cancel the common factor.

$\frac{2 (2 x - 1) (- 1 (- x + 3))}{- x + 3}$

Step 3.1.5

Divide $2 (2 x - 1) \cdot (- 1)$ by $1$ .

$2 (2 x - 1) \cdot (- 1)$

Step 3.2

Apply the distributive property.

$(2 (2 x) + 2 \cdot - 1) \cdot - 1$

Step 3.3

Multiply.

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Step 3.3.1

Multiply $2$ by $2$ .

$(4 x + 2 \cdot - 1) \cdot - 1$

Step 3.3.2

Multiply $2$ by $- 1$ .

$(4 x - 2) \cdot - 1$

Step 3.4

Apply the distributive property.

$4 x \cdot - 1 - 2 \cdot - 1$

Step 3.5

Multiply.

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Step 3.5.1

Multiply $- 1$ by $4$ .

$- 4 x - 2 \cdot - 1$

Step 3.5.2

Multiply $- 2$ by $- 1$ .

$- 4 x + 2$