Pre-Algebra Examples

$(x^{6} - 12 x^{3} + 35) \div (x^{3} - 7)$

Step 1

Rewrite the division as a fraction.

$\frac{x^{6} - 12 x^{3} + 35}{x^{3} - 7}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\frac{{(x^{3})}^{2} - 12 x^{3} + 35}{x^{3} - 7}$

Step 2.2

Let $u = x^{3}$ . Substitute $u$ for all occurrences of $x^{3}$ .

$\frac{u^{2} - 12 u + 35}{x^{3} - 7}$

Step 2.3

Factor $u^{2} - 12 u + 35$ using the AC method.

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Step 2.3.1

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 $35$ and whose sum is $- 12$ .

$- 7, - 5$

Step 2.3.2

Write the factored form using these integers.

$\frac{(u - 7) (u - 5)}{x^{3} - 7}$

Step 2.4

Replace all occurrences of $u$ with $x^{3}$ .

$\frac{(x^{3} - 7) (x^{3} - 5)}{x^{3} - 7}$

Step 3

Cancel the common factor of $x^{3} - 7$ .

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Step 3.1

Cancel the common factor.

$\frac{(x^{3} - 7) (x^{3} - 5)}{x^{3} - 7}$

Step 3.2

Divide $x^{3} - 5$ by $1$ .

$x^{3} - 5$