Pre-Algebra Examples

$(2 x^{2} + 3 x - 2) \div (2 x + 4)$

Step 1

Rewrite the division as a fraction.

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

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 $a \cdot c = 2 \cdot - 2 = - 4$ and whose sum is $b = 3$ .

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Step 2.1.1

Factor $3$ out of $3 x$ .

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

Step 2.1.2

Rewrite $3$ as $- 1$ plus $4$

$\frac{2 x^{2} + (- 1 + 4) x - 2}{2 x + 4}$

Step 2.1.3

Apply the distributive property.

$\frac{2 x^{2} - 1 x + 4 x - 2}{2 x + 4}$

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.

$\frac{(2 x^{2} - 1 x) + 4 x - 2}{2 x + 4}$

Step 2.2.2

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

$\frac{x (2 x - 1) + 2 (2 x - 1)}{2 x + 4}$

Step 2.3

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

$\frac{(2 x - 1) (x + 2)}{2 x + 4}$

Step 3

Factor $2$ out of $2 x + 4$ .

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Step 3.1

Factor $2$ out of $2 x$ .

$\frac{(2 x - 1) (x + 2)}{2 (x) + 4}$

Step 3.2

Factor $2$ out of $4$ .

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

Step 3.3

Factor $2$ out of $2 x + 2 \cdot 2$ .

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

Step 4

Cancel the common factor of $x + 2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{2 x - 1}{2}$

Step 5

Split the fraction $\frac{2 x - 1}{2}$ into two fractions.

$\frac{2 x}{2} + \frac{- 1}{2}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

$\frac{2 x}{2} + \frac{- 1}{2}$

Step 6.2

Divide $x$ by $1$ .

$x + \frac{- 1}{2}$

Step 7

Move the negative in front of the fraction.

$x - \frac{1}{2}$