how to factor ac+xc=aw2+xw2

Question

     ac+xc+aw²=xw²

Answer 1

Rita,

 

Is this one problem or two?  You show two different polynomials which will result in two different solutions. I'll do both since it may help you.

 

(1) Factor ac + xc = aw² + xw²

ac - aw²  +  xc - xw² = 0

a(c - w²) + x(c - w²) = 0

(a + x)(c - w²) = 0

(a + x)(c^0.5 + w)(c^0.5 - w) = 0    , where c^0.5 is just a way of writing the square root of c

 

(2) Factor ac + xc + aw² = xw²

ac  +  aw²  +  xc - xw²  = 0

a (c + w²)  + x(c - w²) = 0

a(c + w²)  + x(c^0.5 + w)(c^0.5 - w) = 0   since (c + w²) can't be factored using real numbers

.5