Factor (2x^2-5x+3)(x-3)

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

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 $a \cdot c = 2 \cdot 3 = 6$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 x$ .

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

Rewrite $- 5$ as $- 2$ plus $- 3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Factor (2x^2-5x+3)(x-3)

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