Finite Math Examples

$- 30 y + 62 y^{2} + 48 y^{3}$

Step 1

Factor $2 y$ out of $- 30 y + 62 y^{2} + 48 y^{3}$ .

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Step 1.1

Factor $2 y$ out of $- 30 y$ .

$2 y (- 15) + 62 y^{2} + 48 y^{3}$

Step 1.2

Factor $2 y$ out of $62 y^{2}$ .

$2 y (- 15) + 2 y (31 y) + 48 y^{3}$

Step 1.3

Factor $2 y$ out of $48 y^{3}$ .

$2 y (- 15) + 2 y (31 y) + 2 y (24 y^{2})$

Step 1.4

Factor $2 y$ out of $2 y (- 15) + 2 y (31 y)$ .

$2 y (- 15 + 31 y) + 2 y (24 y^{2})$

Step 1.5

Factor $2 y$ out of $2 y (- 15 + 31 y) + 2 y (24 y^{2})$ .

$2 y (- 15 + 31 y + 24 y^{2})$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

Reorder terms.

$2 y (24 y^{2} + 31 y - 15)$

Step 2.1.2

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 $a \cdot c = 24 \cdot - 15 = - 360$ and whose sum is $b = 31$ .

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Step 2.1.2.1

Factor $31$ out of $31 y$ .

$2 y (24 y^{2} + 31 (y) - 15)$

Step 2.1.2.2

Rewrite $31$ as $- 9$ plus $40$

$2 y (24 y^{2} + (- 9 + 40) y - 15)$

Step 2.1.2.3

Apply the distributive property.

$2 y (24 y^{2} - 9 y + 40 y - 15)$

Step 2.1.3

Factor out the greatest common factor from each group.

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Step 2.1.3.1

Group the first two terms and the last two terms.

$2 y ((24 y^{2} - 9 y) + 40 y - 15)$

Step 2.1.3.2

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

$2 y (3 y (8 y - 3) + 5 (8 y - 3))$

Step 2.1.4

Factor the polynomial by factoring out the greatest common factor, $8 y - 3$ .

$2 y ((8 y - 3) (3 y + 5))$

Step 2.2

Remove unnecessary parentheses.

$2 y (8 y - 3) (3 y + 5)$