Simplify (8x^2-44x+60)/(6x^2+18x-108)

Factor ${\displaystyle 2}$ out of ${\displaystyle 6x^2}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 18x}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2\left(3x^2\right)+2\left(9x\right)}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle -108}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2(3x^2+9x)+2(-54)}$.

Cancel the common factor.

Rewrite the expression.

Factor ${\displaystyle 2}$ out of ${\displaystyle 4x^2}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle -22x}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 30}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2\left(2x^2\right)+2(-11x)}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2(2x^2-11x)+2\left(15\right)}$.

For a polynomial of the form ${\displaystyle a{x}^2+bx+c}$, rewrite the middle term as a sum of two terms whose product is ${\displaystyle a\cdot c=2\cdot 15=30}$ and whose sum is ${\displaystyle b=-11}$.

Factor out the greatest common factor from each group.

Factor the polynomial by factoring out the greatest common factor, ${\displaystyle 2x-5}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3x^2}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 9x}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle -54}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3x^2+3\left(3x\right)}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3(x^2+3x)+3\cdot -18}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -18}$ and whose sum is ${\displaystyle 3}$.

Write the factored form using these integers.