Factor 3x^2-10x+3

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

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 $a \cdot c = 3 \cdot 3 = 9$ and whose sum is $b = - 10$ .

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

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

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

$3 x^{2} + (- 1 - 9) x + 3$

Apply the distributive property.

$3 x^{2} - 1 x - 9 x + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 1 x) - 9 x + 3$

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

$x (3 x - 1) - 3 (3 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$(3 x - 1) (x - 3)$

Factor 3x^2-10x+3

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