Factor 8y^2-22y-21

$8 y^{2} - 22 y - 21$

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 $a \cdot c = 8 \cdot - 21 = - 168$ and whose sum is $b = - 22$ .

Factor $- 22$ out of $- 22 y$ .

$8 y^{2} - 22 (y) - 21$

Rewrite $- 22$ as $6$ plus $- 28$

$8 y^{2} + (6 - 28) y - 21$

Apply the distributive property.

$8 y^{2} + 6 y - 28 y - 21$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 y^{2} + 6 y) - 28 y - 21$

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

$2 y (4 y + 3) - 7 (4 y + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 y + 3$ .

$(4 y + 3) (2 y - 7)$

Factor 8y^2-22y-21

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