Algebra Examples

$- 3 + 2 y + 21 y^{2}$

Step 1

Reorder terms.

$21 y^{2} + 2 y - 3$

Step 2

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 $a \cdot c = 21 \cdot - 3 = - 63$ and whose sum is $b = 2$ .

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Step 2.1

Factor $2$ out of $2 y$ .

$21 y^{2} + 2 (y) - 3$

Step 2.2

Rewrite $2$ as $- 7$ plus $9$

$21 y^{2} + (- 7 + 9) y - 3$

Step 2.3

Apply the distributive property.

$21 y^{2} - 7 y + 9 y - 3$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

$(21 y^{2} - 7 y) + 9 y - 3$

Step 3.2

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

$7 y (3 y - 1) + 3 (3 y - 1)$

Step 4

Factor the polynomial by factoring out the greatest common factor, $3 y - 1$ .

$(3 y - 1) (7 y + 3)$