Algebra Examples

$4 x^{2} + 23 x - 6$

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 $a \cdot c = 4 \cdot - 6 = - 24$ and whose sum is $b = 23$ .

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Step 1.1

Factor $23$ out of $23 x$ .

$4 x^{2} + 23 (x) - 6$

Step 1.2

Rewrite $23$ as $- 1$ plus $24$

$4 x^{2} + (- 1 + 24) x - 6$

Step 1.3

Apply the distributive property.

$4 x^{2} - 1 x + 24 x - 6$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(4 x^{2} - 1 x) + 24 x - 6$

Step 2.2

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

$x (4 x - 1) + 6 (4 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 1$ .

$(4 x - 1) (x + 6)$