Algebra Examples

$x^{2} (x - 5) + 3 (x - 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 5 + 3 (x - 5)$

Step 1.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.2.1

Multiply $x^{2}$ by $x$ .

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Step 1.2.1.1

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

$x^{2} x^{1} + x^{2} \cdot - 5 + 3 (x - 5)$

Step 1.2.1.2

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

$x^{2 + 1} + x^{2} \cdot - 5 + 3 (x - 5)$

Step 1.2.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 5 + 3 (x - 5)$

Step 1.3

Move $- 5$ to the left of $x^{2}$ .

$x^{3} - 5 \cdot x^{2} + 3 (x - 5)$

Step 1.4

Apply the distributive property.

$x^{3} - 5 x^{2} + 3 x + 3 \cdot - 5$

Step 1.5

Multiply $3$ by $- 5$ .

$x^{3} - 5 x^{2} + 3 x - 15$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(x^{3} - 5 x^{2}) + 3 x - 15$

Step 2.2

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

$x^{2} (x - 5) + 3 (x - 5)$

Step 3

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

$(x - 5) (x^{2} + 3)$