factoring quadratics with a common factor\nfactor completely.\n$2x^{2}-18x + 36=$

Answer:

$2(x - 3)(x - 6)$

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the coefficients 2, - 18, and 36. The GCF of 2, - 18, and 36 is 2. So, $2x^{2}-18x + 36=2(x^{2}-9x + 18)$.

Step2: Factor the quadratic inside

We need to factor $x^{2}-9x + 18$. We look for two numbers that multiply to 18 and add up to - 9. The numbers are - 3 and - 6 since $(-3)\times(-6)=18$ and $-3+( - 6)=-9$. So, $x^{2}-9x + 18=(x - 3)(x - 6)$.

Step3: Write the final factored form

Combining the results of Step1 and Step2, we get $2x^{2}-18x + 36=2(x - 3)(x - 6)$.