Hey GMAT Fam,
Question from the OG 16 on Solving Equations by Factoring:
In the section 4.2.6 they state that some equations can be solved by factoring. First add or subtract expressions to bring one side to 0 and the other side contains all of the expressions. Then factor out the nonzero side into factors and each factor can be set to 0 (Real Numbers 4.1.4 property (7). So the equations is as follows:
x^3 - 2x^2 + 5 = -5(x-1)^2
X^3 - 2x^2 +x + 5(x-1)^2 = 0
x(x^2-2x+1) + 5(x-1)^2 = 0
x(x-1)^2 +5(x-1)^2 = 0
(x+5)(x-1)^2 = 0
X+5 = 0 or (x-1)^2 = 0
x=-5 or x=1
The part I'm not understanding is how to go from x(x-1)^2 +5(x-1)^2 = 0 to (x+5)(x-1)^2 = 0? Did I miss something in the explanation? Any help provided is greatly appreciated.
Thanks!
Question from the OG 16 on Solving Equations by Factoring:
In the section 4.2.6 they state that some equations can be solved by factoring. First add or subtract expressions to bring one side to 0 and the other side contains all of the expressions. Then factor out the nonzero side into factors and each factor can be set to 0 (Real Numbers 4.1.4 property (7). So the equations is as follows:
x^3 - 2x^2 + 5 = -5(x-1)^2
X^3 - 2x^2 +x + 5(x-1)^2 = 0
x(x^2-2x+1) + 5(x-1)^2 = 0
x(x-1)^2 +5(x-1)^2 = 0
(x+5)(x-1)^2 = 0
X+5 = 0 or (x-1)^2 = 0
x=-5 or x=1
The part I'm not understanding is how to go from x(x-1)^2 +5(x-1)^2 = 0 to (x+5)(x-1)^2 = 0? Did I miss something in the explanation? Any help provided is greatly appreciated.
Thanks!
