Question

find all real zero's of f(x) = 2x^3+x^2-5x+2 by facoring

Answer 1

\[2x^3+x^2-5x+2=2x^3-2x^2+3x^2-3x-2x+2=\]\[=2x^2(x-1)+3x(x-1)-2(x-1)=(x-1)(2x^2+3x-2)=\]\[=(x-1)(2x^2-x+4x-2)=(x-1)(x(2x-1)+2(2x-1))=\]\[=(x-1)(2x-1)(x+2)\]