Basic Math Examples

$\frac{5 v^{2} + 17 v + 6}{25 v^{2 - 4}}$

Step 1

Move $v^{2 - 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{(5 v^{2} + 17 v + 6) v^{- (2 - 4)}}{25}$

Step 2

Simplify the numerator.

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Step 2.1

Factor by grouping.

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Step 2.1.1

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 $a \cdot c = 5 \cdot 6 = 30$ and whose sum is $b = 17$ .

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Step 2.1.1.1

Factor $17$ out of $17 v$ .

$\frac{(5 v^{2} + 17 (v) + 6) v^{- (2 - 4)}}{25}$

Step 2.1.1.2

Rewrite $17$ as $2$ plus $15$

$\frac{(5 v^{2} + (2 + 15) v + 6) v^{- (2 - 4)}}{25}$

Step 2.1.1.3

Apply the distributive property.

$\frac{(5 v^{2} + 2 v + 15 v + 6) v^{- (2 - 4)}}{25}$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$\frac{((5 v^{2} + 2 v) + 15 v + 6) v^{- (2 - 4)}}{25}$

Step 2.1.2.2

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

$\frac{(v (5 v + 2) + 3 (5 v + 2)) v^{- (2 - 4)}}{25}$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $5 v + 2$ .

$\frac{(5 v + 2) (v + 3) v^{- (2 - 4)}}{25}$

Step 2.2

Subtract $4$ from $2$ .

$\frac{(5 v + 2) (v + 3) v^{- - 2}}{25}$

Step 2.3

Multiply $- 1$ by $- 2$ .

$\frac{(5 v + 2) (v + 3) v^{2}}{25}$

Step 3

Reorder factors in $\frac{(5 v + 2) (v + 3) v^{2}}{25}$ .

$\frac{v^{2} (5 v + 2) (v + 3)}{25}$