Algebra Examples

$5 x^{2} + 50 x + 125$

Step 1

Factor $5$ out of $5 x^{2} + 50 x + 125$ .

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Step 1.1

Factor $5$ out of $5 x^{2}$ .

$5 (x^{2}) + 50 x + 125$

Step 1.2

Factor $5$ out of $50 x$ .

$5 (x^{2}) + 5 (10 x) + 125$

Step 1.3

Factor $5$ out of $125$ .

$5 x^{2} + 5 (10 x) + 5 \cdot 25$

Step 1.4

Factor $5$ out of $5 x^{2} + 5 (10 x)$ .

$5 (x^{2} + 10 x) + 5 \cdot 25$

Step 1.5

Factor $5$ out of $5 (x^{2} + 10 x) + 5 \cdot 25$ .

$5 (x^{2} + 10 x + 25)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$5 (x^{2} + 10 x + 5^{2})$

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 x = 2 \cdot x \cdot 5$

Step 2.3

Rewrite the polynomial.

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

Step 2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 5$ .

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