Factor 10x^2-29x+10

$10 x^{2} - 29 x + 10$

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 $a \cdot c = 10 \cdot 10 = 100$ and whose sum is $b = - 29$ .

Factor $- 29$ out of $- 29 x$ .

$10 x^{2} - 29 (x) + 10$

Rewrite $- 29$ as $- 4$ plus $- 25$

$10 x^{2} + (- 4 - 25) x + 10$

Apply the distributive property.

$10 x^{2} - 4 x - 25 x + 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{2} - 4 x) - 25 x + 10$

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

$2 x (5 x - 2) - 5 (5 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 2$ .

$(5 x - 2) (2 x - 5)$

Factor 10x^2-29x+10

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