Algebra Examples

$A (x) = 660 x^{2} + 524 x + 85$

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 $a \cdot c = 660 \cdot 85 = 56100$ and whose sum is $b = 524$ .

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Step 1.1

Factor $524$ out of $524 x$ .

$A (x) = 660 x^{2} + 524 (x) + 85$

Step 1.2

Rewrite $524$ as $150$ plus $374$

$A (x) = 660 x^{2} + (150 + 374) x + 85$

Step 1.3

Apply the distributive property.

$A (x) = 660 x^{2} + 150 x + 374 x + 85$

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.

$A (x) = (660 x^{2} + 150 x) + 374 x + 85$

Step 2.2

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

$A (x) = 30 x (22 x + 5) + 17 (22 x + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $22 x + 5$ .

$A (x) = (22 x + 5) (30 x + 17)$