Factor 10x^2-17x+3

$10 x^{2} - 17 x + 3$

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 $b = - 17$ .

Factor $- 17$ out of $- 17 x$ .

$10 x^{2} - 17 (x) + 3$

Rewrite $- 17$ as $- 2$ plus $- 15$

$10 x^{2} + (- 2 - 15) x + 3$

Apply the distributive property.

$10 x^{2} - 2 x - 15 x + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{2} - 2 x) - 15 x + 3$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 1$ .

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

Factor 10x^2-17x+3

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