Basic Math Examples

$16 t^{2} + 4 t - 72$

Step 1

Factor $4$ out of $16 t^{2} + 4 t - 72$ .

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Step 1.1

Factor $4$ out of $16 t^{2}$ .

$4 (4 t^{2}) + 4 t - 72$

Step 1.2

Factor $4$ out of $4 t$ .

$4 (4 t^{2}) + 4 (t) - 72$

Step 1.3

Factor $4$ out of $- 72$ .

$4 (4 t^{2}) + 4 t + 4 \cdot - 18$

Step 1.4

Factor $4$ out of $4 (4 t^{2}) + 4 t$ .

$4 (4 t^{2} + t) + 4 \cdot - 18$

Step 1.5

Factor $4$ out of $4 (4 t^{2} + t) + 4 \cdot - 18$ .

$4 (4 t^{2} + t - 18)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

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 $a \cdot c = 4 \cdot - 18 = - 72$ and whose sum is $b = 1$ .

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Step 2.1.1.1

Multiply by $1$ .

$4 (4 t^{2} + 1 t - 18)$

Step 2.1.1.2

Rewrite $1$ as $- 8$ plus $9$

$4 (4 t^{2} + (- 8 + 9) t - 18)$

Step 2.1.1.3

Apply the distributive property.

$4 (4 t^{2} - 8 t + 9 t - 18)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$4 ((4 t^{2} - 8 t) + 9 t - 18)$

Step 2.1.2.2

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

$4 (4 t (t - 2) + 9 (t - 2))$

Step 2.1.3

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

$4 ((t - 2) (4 t + 9))$

Step 2.2

Remove unnecessary parentheses.

$4 (t - 2) (4 t + 9)$