Factor x^2-7x+12+(x-3)^2

$x^{2} - 7 x + 12 + {(x - 3)}^{2}$

Regroup terms.

$- 7 x + x^{2} + 12 + {(x - 3)}^{2}$

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$- 7 x + x^{2} + 12 + (x - 3) (x - 3)$

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$- 7 x + x^{2} + 12 + x (x - 3) - 3 (x - 3)$

Apply the distributive property.

$- 7 x + x^{2} + 12 + x \cdot x + x \cdot - 3 - 3 (x - 3)$

Apply the distributive property.

$- 7 x + x^{2} + 12 + x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$- 7 x + x^{2} + 12 + x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3$

Move $- 3$ to the left of $x$ .

$- 7 x + x^{2} + 12 + x^{2} - 3 x - 3 x - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$- 7 x + x^{2} + 12 + x^{2} - 3 x - 3 x + 9$

Subtract $3 x$ from $- 3 x$ .

$- 7 x + x^{2} + 12 + x^{2} - 6 x + 9$

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

$- 7 x + 2 x^{2} + 12 - 6 x + 9$

Add $12$ and $9$ .

$- 7 x + 2 x^{2} - 6 x + 21$

Reorder terms.

$2 x^{2} - 6 x - 7 x + 21$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 6 x) - 7 x + 21$

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

$2 x (x - 3) - 7 (x - 3)$

Factor the polynomial by factoring out the greatest common factor, $x - 3$ .

$(x - 3) (2 x - 7)$