Factor 5z^2-17z+14

$5 z^{2} - 17 z + 14$

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 $a \cdot c = 5 \cdot 14 = 70$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 z$ .

$5 z^{2} - 17 (z) + 14$

Rewrite $- 17$ as $- 7$ plus $- 10$

$5 z^{2} + (- 7 - 10) z + 14$

Apply the distributive property.

$5 z^{2} - 7 z - 10 z + 14$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 z^{2} - 7 z) - 10 z + 14$

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

$z (5 z - 7) - 2 (5 z - 7)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 z - 7$ .

$(5 z - 7) (z - 2)$

Factor 5z^2-17z+14

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