Answer
The factors for the equation ${{x}^{2}}-5x+6$is $\left( x-3 \right)\left( x-2 \right)$.
Work Step by Step
The expression is ${{x}^{2}}-5x+6$.
Following steps to be followed while method of factorization.
Rule1: Arrange the expression in the decreasing order of power of\[x\] as:
${{x}^{2}}-5x+6$
Rule 2: Split the middle term(that is term of\[x\]) as sum or difference of two terms and the product of these two terms is equal to product of constant and the first term (${{x}^{2}}$).
${{x}^{2}}-2x-3x+6$
Rule 3: Taking the x common in first two terms and a constant number common in second two terms as:
$x\left( x-2 \right)-3\left( x-2 \right)$
Rule 4: Rearranging the terms as:
$\left( x-3 \right)\left( x-2 \right)$
These are the factors for the equation.
The factors for the equation ${{x}^{2}}-5x+6$is $\left( x-3 \right)\left( x-2 \right)$.
