Trigonometry Examples

$8 x^{2} - 10 x + 3$

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 $a \cdot c = 8 \cdot 3 = 24$ and whose sum is $b = - 10$ .

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Step 1.1

Factor $- 10$ out of $- 10 x$ .

$8 x^{2} - 10 (x) + 3$

Step 1.2

Rewrite $- 10$ as $- 4$ plus $- 6$

$8 x^{2} + (- 4 - 6) x + 3$

Step 1.3

Apply the distributive property.

$8 x^{2} - 4 x - 6 x + 3$

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.

$(8 x^{2} - 4 x) - 6 x + 3$

Step 2.2

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

$4 x (2 x - 1) - 3 (2 x - 1)$

Step 3

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

$(2 x - 1) (4 x - 3)$