Simplify (x^3+4x^2-x-4)/(x^2+3x-4)

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

Step 1

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Factor the polynomial by factoring out the greatest common factor, $x + 4$ .

$\frac{(x + 4) (x^{2} - 1)}{x^{2} + 3 x - 4}$

Rewrite $1$ as $1^{2}$ .

$\frac{(x + 4) (x^{2} - 1^{2})}{x^{2} + 3 x - 4}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{(x + 4) (x + 1) (x - 1)}{x^{2} + 3 x - 4}$

Step 2

Factor $x^{2} + 3 x - 4$ using the AC method.

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 $- 4$ and whose sum is $3$ .

$- 1, 4$

Write the factored form using these integers.

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Divide $x + 1$ by $1$ .

$x + 1$

Simplify (x^3+4x^2-x-4)/(x^2+3x-4)

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