Basic Math Examples

$2 k^{2} - 9 k - 5$

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 $a \cdot c = 2 \cdot - 5 = - 10$ and whose sum is $b = - 9$ .

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Step 1.1

Factor $- 9$ out of $- 9 k$ .

$2 k^{2} - 9 (k) - 5$

Step 1.2

Rewrite $- 9$ as $1$ plus $- 10$

$2 k^{2} + (1 - 10) k - 5$

Step 1.3

Apply the distributive property.

$2 k^{2} + 1 k - 10 k - 5$

Step 1.4

Multiply $k$ by $1$ .

$2 k^{2} + k - 10 k - 5$

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.

$(2 k^{2} + k) - 10 k - 5$

Step 2.2

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

$k (2 k + 1) - 5 (2 k + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 k + 1$ .

$(2 k + 1) (k - 5)$