Pre-Algebra Examples

$x - 4$ , $x^{2} - 8 x + 16$ , $x^{2} - 16$

Step 1

Subtract $8 x$ from $x$ .

$- 7 x - 4 + x^{2} + 16 + x^{2} - 16$

Step 2

Add $- 4$ and $16$ .

$- 7 x + x^{2} + 12 + x^{2} - 16$

Step 3

Add $x^{2}$ and $x^{2}$ .

$- 7 x + 2 x^{2} + 12 - 16$

Step 4

Subtract $16$ from $12$ .

$- 7 x + 2 x^{2} - 4$

Step 5

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$- 7 u + 2 u^{2} - 4$

Step 6

Factor by grouping.

Tap for more steps...

Step 6.1

Reorder terms.

$2 u^{2} - 7 u - 4$

Step 6.2

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 $a \cdot c = 2 \cdot - 4 = - 8$ and whose sum is $b = - 7$ .

Tap for more steps...

Step 6.2.1

Factor $- 7$ out of $- 7 u$ .

$2 u^{2} - 7 (u) - 4$

Step 6.2.2

Rewrite $- 7$ as $1$ plus $- 8$

$2 u^{2} + (1 - 8) u - 4$

Step 6.2.3

Apply the distributive property.

$2 u^{2} + 1 u - 8 u - 4$

Step 6.2.4

Multiply $u$ by $1$ .

$2 u^{2} + u - 8 u - 4$

Step 6.3

Factor out the greatest common factor from each group.

Tap for more steps...

Step 6.3.1

Group the first two terms and the last two terms.

$(2 u^{2} + u) - 8 u - 4$

Step 6.3.2

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

$u (2 u + 1) - 4 (2 u + 1)$

Step 6.4

Factor the polynomial by factoring out the greatest common factor, $2 u + 1$ .

$(2 u + 1) (u - 4)$

Step 7

Replace all occurrences of $u$ with $x$ .

$(2 x + 1) (x - 4)$