Factor 4x^2-17x+18

$4 x^{2} - 17 x + 18$

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 $a \cdot c = 4 \cdot 18 = 72$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 x$ .

$4 x^{2} - 17 (x) + 18$

Rewrite $- 17$ as $- 8$ plus $- 9$

$4 x^{2} + (- 8 - 9) x + 18$

Apply the distributive property.

$4 x^{2} - 8 x - 9 x + 18$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 8 x) - 9 x + 18$

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

$4 x (x - 2) - 9 (x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 2$ .

$(x - 2) (4 x - 9)$

Factor 4x^2-17x+18

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