Algebra Examples

$10 x^{2} + x - 3$

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 $a \cdot c = 10 \cdot - 3 = - 30$ and whose sum is $b = 1$ .

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Step 1.1

Multiply by $1$ .

$10 x^{2} + 1 x - 3$

Step 1.2

Rewrite $1$ as $- 5$ plus $6$

$10 x^{2} + (- 5 + 6) x - 3$

Step 1.3

Apply the distributive property.

$10 x^{2} - 5 x + 6 x - 3$

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.

$(10 x^{2} - 5 x) + 6 x - 3$

Step 2.2

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

$5 x (2 x - 1) + 3 (2 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$(2 x - 1) (5 x + 3)$