Algebra Examples

4 x^{2} - x - 3

$4 x^{2} - x - 3$

Step 1

For a polynomial of the form

a x^{2} + b x + c

$a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is

a \cdot c = 4 \cdot - 3 = - 12

$a \cdot c = 4 \cdot - 3 = - 12$ and whose sum is

b = - 1

$b = - 1$ .

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Step 1.1

Factor

- 1

$- 1$ out of

- x

$- x$ .

4 x^{2} - (x) - 3

$4 x^{2} - (x) - 3$

Step 1.2

Rewrite

- 1

$- 1$ as

3

$3$ plus

- 4

$- 4$

4 x^{2} + (3 - 4) x - 3

$4 x^{2} + (3 - 4) x - 3$

Step 1.3

Apply the distributive property.

4 x^{2} + 3 x - 4 x - 3

$4 x^{2} + 3 x - 4 x - 3$

4 x^{2} + 3 x - 4 x - 3

$4 x^{2} + 3 x - 4 x - 3$

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} + 3 x) - 4 x - 3

$(4 x^{2} + 3 x) - 4 x - 3$

Step 2.2

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

x (4 x + 3) - (4 x + 3)

$x (4 x + 3) - (4 x + 3)$

x (4 x + 3) - (4 x + 3)

$x (4 x + 3) - (4 x + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

4 x + 3

$4 x + 3$ .

(4 x + 3) (x - 1)

$(4 x + 3) (x - 1)$