Finite Math Examples

$4 w^{2} - 40 w + 100$

Step 1

Factor out the GCF of $4$ from $4 w^{2} - 40 w + 100$ .

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Step 1.1

Factor out the GCF of $4$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $4$ from the expression $4 w^{2}$ .

$4 (w^{2}) - 40 w + 100$

Step 1.1.2

Factor out the GCF of $4$ from the expression $- 40 w$ .

$4 (w^{2}) + 4 (- 10 w) + 100$

Step 1.1.3

Factor out the GCF of $4$ from the expression $100$ .

$4 (w^{2}) + 4 (- 10 w) + 4 (25)$

Step 1.2

Since all the terms share a common factor of $4$ , it can be factored out of each term.

$4 (w^{2} - 10 w + 25)$

Step 2

Factor using the perfect square rule.

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Step 2.1

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

$4 (w^{2} - 10 w + 5^{2})$

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.

$10 w = 2 \cdot w \cdot 5$

Step 2.3

Rewrite the polynomial.

$4 (w^{2} - 2 \cdot w \cdot 5 + 5^{2})$

Step 2.4

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

$4 ({(w - 5)}^{2})$