Calculus Examples

$x^{3} - 7 x^{2} - 49 x + 343$

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

$(x^{3} - 7 x^{2}) - 49 x + 343$

Step 1.2

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

$x^{2} (x - 7) - 49 (x - 7)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x - 7$ .

$(x - 7) (x^{2} - 49)$

Step 3

Rewrite $49$ as $7^{2}$ .

$(x - 7) (x^{2} - 7^{2})$

Step 4

Factor.

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Step 4.1

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 $b = 7$ .

$(x - 7) ((x + 7) (x - 7))$

Step 4.2

Remove unnecessary parentheses.

$(x - 7) (x + 7) (x - 7)$

Step 5

Combine exponents.

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Step 5.1

Raise $x - 7$ to the power of $1$ .

${(x - 7)}^{1} (x - 7) (x + 7)$

Step 5.2

Raise $x - 7$ to the power of $1$ .

${(x - 7)}^{1} {(x - 7)}^{1} (x + 7)$

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x - 7)}^{1 + 1} (x + 7)$

Step 5.4

Add $1$ and $1$ .

${(x - 7)}^{2} (x + 7)$