## Algebra 1

Given the volume $2 \pi x^{3}$ + $12 \pi x^{2}$ + $18 \pi x$ We see that the three terms have a common factor of $2 \pi x^{3}$ so we factor out a $2 \pi x^{3}$. $2 \pi x(x^{2}$ + 6x + 9) *** We break of the middle term into two factors that add to give +6 and multiply to give +9. The two numbers are +3 and +3. $2 \pi x(x^{2}$ + 3x + 3x + 9) We take the GCD of the first two and the GCD of the last two terms. $2 \pi x(x(x+3) + 3(x+3))$ We take (x+3) and factor it out which gives us. $2 \pi x(x+3)(x+3)$ The formula for volume = $\pi r^{2} h$ So we multiply the to the bracket and get $\pi x^{2} (2x+6)$ According to the formula r= x and h = (2x+6)