Algebra Examples

$(3 v^{2} - 7 v - 10) {(v - 4)}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(3 v^{2} - 7 v - 10) \frac{1}{v - 4}$

Step 2

Multiply $3 v^{2} - 7 v - 10$ by $\frac{1}{v - 4}$ .

$\frac{3 v^{2} - 7 v - 10}{v - 4}$

Step 3

Factor by grouping.

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Step 3.1

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 $a \cdot c = 3 \cdot - 10 = - 30$ and whose sum is $b = - 7$ .

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Step 3.1.1

Factor $- 7$ out of $- 7 v$ .

$\frac{3 v^{2} - 7 (v) - 10}{v - 4}$

Step 3.1.2

Rewrite $- 7$ as $3$ plus $- 10$

$\frac{3 v^{2} + (3 - 10) v - 10}{v - 4}$

Step 3.1.3

Apply the distributive property.

$\frac{3 v^{2} + 3 v - 10 v - 10}{v - 4}$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$\frac{(3 v^{2} + 3 v) - 10 v - 10}{v - 4}$

Step 3.2.2

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

$\frac{3 v (v + 1) - 10 (v + 1)}{v - 4}$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $v + 1$ .

$\frac{(v + 1) (3 v - 10)}{v - 4}$