\(x^2+5x=x(x+5)\)

\(6a^2-27a=3a(2a-9)\)

\(12ab+27a=3a(4b+9)\)

\(6xy+8xz=2x(3y+4z)\)

\(8pqr+36pq=4pq(2r+9)\)

\(10x^3+45x^4=5x^3(2+9x)\)

\(4x-5x^3+x^6=x(4-5x^2+x^5)\)

\(20a^4b^2+24a^5b^3=4a^4b^2(5+6ab)\)

\(p^2-49=(p-7)(p+7)\)

\(49a^2-121=(7a-11)(7a+11)\)

\(9-16p^2=(3-4p)(3+4p)\)

\(9a^4-121=(3a^2-11)(3a^2+11)\)

\(50a^2-2=2(25a^2-1)=2(5a-1)(5a+1)\)

\(50x^3-2x=2x(25x^2-1)=2x(5x-1)(5x+1)\)

\(x^{12}-16=(x^6-4)(x^6+4)=(x^3-2)(x^3+2)(x^6+4)\)

\(3a^6-243a^2=3a^2(a^4-81)=3a^2(a^2-9)(a^2+9)=3a^2(a-3)(a+3)(a^2+9)\)

\(a^{10}b^2-64c^{10}=(a^5b-8c^5)(a^5b+8c^5)\)

\(p^2+11p+24=(p+8)(p+3)\)

\(x^2+3x-10=(x+5)(x-2)\)

\(x^2-12x+32=(x-8)(x-4)\)

\(a^2+14a+49=(a+7)(a+7)\)

\(a^4+a^3-2a^2=a^2(a^2+a-2)=a^2(a+2)(a-1)\)

\(p^8-8p^4+7=(p^4-1)(p^4-7)\)

\(x^2-8x=(x-4)^2-16\)

\(x^2-19x+20=(x-9\frac{1}{2})^2-90\frac{1}{4}+20\)

\(\text{}=(x-9\frac{1}{2})^2-70\frac{1}{4}\)

\(-5x^2-10x-11=-5(x^2+2x)-11\)

\(\text{}=-5((x+1)^2-1)-11\)

\(\text{}=-5(x+1)^2+5-11\)
\(\text{}=-5(x+1)^2-6\)