Polynomial Factoring Question

[whitedreams]

Hi there, the instructions are to "factor completely, relative to the integers:

\(\displaystyle 2x(x\, +\, 1)^4\, +\, 4x^2(x\, +\, 1)^3\)

\(\displaystyle =\, 2x(x\, +\, 1)^3\left[(x\, +\, 1)\, +\, 2x\right]\)

\(\displaystyle =\, 2x(x\, +\, 1)^3\, (3x\, +\, 1)\)

I do not understand how the final solution was reached. They seem to be doing some type of weird grouping but I cannot figure it out. Any help/explanation is much appreciated thank you

 

[Deleted member 4993]

Hi there, the instructions are to "factor completely, relative to the integers:

\(\displaystyle 2x(x\, +\, 1)^4\, +\, 4x^2(x\, +\, 1)^3\)

\(\displaystyle =\, 2x(x\, +\, 1)^3\left[(x\, +\, 1)\, +\, 2x\right]\)

\(\displaystyle =\, 2x(x\, +\, 1)^3\, (3x\, +\, 1)\)

I do not understand how the final solution was reached. They seem to be doing some type of weird grouping but I cannot figure it out. Any help/explanation is much appreciated thank you

2x(x+1)⁴ + 4x²(x+1)³

= 2x(x+1)(x+1)³ + 2*2x*x(x+1)³ → common factors are 2x and (x+1)³

= 2x(x+1)³[(x+1) + 2*x] ................now continue..................