How do i factor by grouping? (please help!)?

Question

for example 2^3+4x^2+x+2
tell me how step by step

thanks in advance

Answer 1

Grouping is pretty much factoring out twice, here:

First of all to do the first factor you'll have to place parentheses around the terms like this:

(2x^3 + 4x^2) + (x + 2)

Now factor out the two groups like normal:

2x^2(x+2) + (x+2)

Now factor out the now revealed common factor:

(2x^2 + 1)(x+2) >>> That 1 was there before, it's just that math people are lazy

And there you go.

Answer 2

2^3+4x^2+x+2
the first 2 terms have 2 & x^2 as a common factor so:
2x^2 (x+2) + x+2
Now the x+2 term becomes common to the first term and the remainder of the expression so:
(x+2)[2x^2 + 1]
is the simplest form

Answer 3

2x^3+4x^2+x+2
= 2x^2(x+2)+(x+2)
= (2x^2+1)(x+2)

Answer 4

2x³ + 4x² + x + 2
2x² (x + 2) + (x + 2)
(x + 2) (2x² + 1)

Answer 5

2x^2(x +2) + (x + 2)
=(2x^2 +1)(x+2)