Factor -3x+2x^2-5

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

Step 1

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$- 3 u + 2 u^{2} - 5$

Step 2

Factor by grouping.

Reorder terms.

$2 u^{2} - 3 u - 5$

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 $a \cdot c = 2 \cdot - 5 = - 10$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 u$ .

$2 u^{2} - 3 (u) - 5$

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

$2 u^{2} + (2 - 5) u - 5$

Apply the distributive property.

$2 u^{2} + 2 u - 5 u - 5$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 u^{2} + 2 u) - 5 u - 5$

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

$2 u (u + 1) - 5 (u + 1)$

Factor the polynomial by factoring out the greatest common factor, $u + 1$ .

$(u + 1) (2 u - 5)$

Step 3

Replace all occurrences of $u$ with $x$ .

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

Factor -3x+2x^2-5

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