Drag things and watch what changes, then test yourself with challenges.
Why do we factor? A farm model
A farm's yield depends on rain, sunlight and the farmer. Multiply them and the zeros of the whole are the zeros of each part.
Drag the three dots along the axis. Watch where the red yield curve touches zero.
r(x)s(x)f(x)A(x)
r(x)=x−2,s(x)=10−x,f(x)=x−4A(x)=10r(x)⋅s(x)⋅f(x)=101(x−2)(10−x)(x−4)
Yield is 0 at x=2,4,10: each is where one factor is 0. Expanded, A(x)=−0.1x3+1.6x2−6.8x+8, where the zeros are hidden. Factoring puts them back in view.