Basic Math Examples

$20 y^{2} - 33 y + 10$

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 $a \cdot c = 20 \cdot 10 = 200$ and whose sum is $b = - 33$ .

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Step 1.1

Factor $- 33$ out of $- 33 y$ .

$20 y^{2} - 33 (y) + 10$

Step 1.2

Rewrite $- 33$ as $- 8$ plus $- 25$

$20 y^{2} + (- 8 - 25) y + 10$

Step 1.3

Apply the distributive property.

$20 y^{2} - 8 y - 25 y + 10$

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.

$(20 y^{2} - 8 y) - 25 y + 10$

Step 2.2

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

$4 y (5 y - 2) - 5 (5 y - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 y - 2$ .

$(5 y - 2) (4 y - 5)$