Factor 3x^2y-8xy+5y

$3 x^{2} y - 8 x y + 5 y$

Step 1

Factor $y$ out of $3 x^{2} y - 8 x y + 5 y$ .

Factor $y$ out of $3 x^{2} y$ .

$y (3 x^{2}) - 8 x y + 5 y$

Factor $y$ out of $- 8 x y$ .

$y (3 x^{2}) + y (- 8 x) + 5 y$

Factor $y$ out of $5 y$ .

$y (3 x^{2}) + y (- 8 x) + y \cdot 5$

Factor $y$ out of $y (3 x^{2}) + y (- 8 x)$ .

$y (3 x^{2} - 8 x) + y \cdot 5$

Factor $y$ out of $y (3 x^{2} - 8 x) + y \cdot 5$ .

$y (3 x^{2} - 8 x + 5)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 3 \cdot 5 = 15$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 x$ .

$y (3 x^{2} - 8 (x) + 5)$

Rewrite $- 8$ as $- 3$ plus $- 5$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Remove unnecessary parentheses.

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

Factor 3x^2y-8xy+5y

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