Pre-Algebra Examples

$2 x^{2} - 5 x + 2$ , $2 x^{2} + x - 1$

Step 1

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

$4 x^{2} - 5 x + 2 + x - 1$

Step 2

Add $- 5 x$ and $x$ .

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

Step 3

Subtract $1$ from $2$ .

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

Step 4

Factor using the perfect square rule.

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Step 4.1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Step 4.2

Rewrite $1$ as $1^{2}$ .

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

Step 4.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot (2 x) \cdot 1$

Step 4.4

Rewrite the polynomial.

${(2 x)}^{2} - 2 \cdot (2 x) \cdot 1 + 1^{2}$

Step 4.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 x$ and $b = 1$ .

${(2 x - 1)}^{2}$

Step 5

Since there are no common prime factors, the GCF is $1$ .

$1$