Calculus Examples

$\frac{5 x^{2} - 29 x - 6}{x^{2} + 19 x - 150}$

Step 1

Factor by grouping.

Tap for more steps...

Step 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 $b = - 29$ .

Tap for more steps...

Step 1.1.1

Factor $- 29$ out of $- 29 x$ .

$\frac{5 x^{2} - 29 (x) - 6}{x^{2} + 19 x - 150}$

Step 1.1.2

Rewrite $- 29$ as $1$ plus $- 30$

$\frac{5 x^{2} + (1 - 30) x - 6}{x^{2} + 19 x - 150}$

Step 1.1.3

Apply the distributive property.

$\frac{5 x^{2} + 1 x - 30 x - 6}{x^{2} + 19 x - 150}$

Step 1.1.4

Multiply $x$ by $1$ .

$\frac{5 x^{2} + x - 30 x - 6}{x^{2} + 19 x - 150}$

Step 1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.2.1

Group the first two terms and the last two terms.

$\frac{(5 x^{2} + x) - 30 x - 6}{x^{2} + 19 x - 150}$

Step 1.2.2

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

$\frac{x (5 x + 1) - 6 (5 x + 1)}{x^{2} + 19 x - 150}$

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $5 x + 1$ .

$\frac{(5 x + 1) (x - 6)}{x^{2} + 19 x - 150}$

Step 2

Factor $x^{2} + 19 x - 150$ using the AC method.

Tap for more steps...

Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 150$ and whose sum is $19$ .

$- 6, 25$

Step 2.2

Write the factored form using these integers.

$\frac{(5 x + 1) (x - 6)}{(x - 6) (x + 25)}$

Step 3

Cancel the common factor of $x - 6$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{(5 x + 1) (x - 6)}{(x - 6) (x + 25)}$

Step 3.2

Rewrite the expression.

$\frac{5 x + 1}{x + 25}$