Algebra Examples

$5 x^{2} + 27 x + 10$

Step 1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot 10 = 50$ and whose sum is $b = 27$ .

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Step 1.1

Factor $27$ out of $27 x$ .

$5 x^{2} + 27 (x) + 10$

Step 1.2

Rewrite $27$ as $2$ plus $25$

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

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.2

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

$x (5 x + 2) + 5 (5 x + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$(5 x + 2) (x + 5)$