Question

Factor completely: 2x3 + 6x2 + 2x + 6
2[(x + 3)(x2 + 1)]

(2x + 6)(x2 + 1)

(x + 3)(2x2 + 2)

2(x3 + 3x2 + x + 3)

Answer 1

@dpasingh

Answer 2

Note the pattern of the coefficients 2,6,2,6 which helps us factorize by grouping:
\( 2x^3+6x^2+2x+6\\
=2(x^3+3x^2+x+3)\\
=2[x^2(x+3)+(x+3)]
\)
Can you continue with the factorization?

Answer 3

Thank you lots.

Answer 4

You're welcome!

Answer 5

Actually that happens to not be an answer choice can it be wrote differently?

Answer 6

@calculusxy

Answer 7

\[2x^3 + 6x^2 + 2x + 6\]First factor out your 2 \[2 (x^3+3 x^2+x+3)\]\[2 (x^2+1)(x+3)\] (x^2+1) Got it from here?

Answer 8

Dont mind that "(x^2+1)" at the bottom

Answer 9

Thank I was confused about the first answer so how do I work out these kinds of problems?

Answer 10

This is how you can work it out for similar problems:

Note the pattern of the coefficients 2,6,2,6 which helps us factorize by grouping.
First factor out the common factor 2
\(2x^3 +6x^2 +2x+6 =2(x^3 +3x^2\ \ +\ \ x+3) \)
Now factor out x+3 in each of the two groups:
\( 2[ x^2(x+3)+(x+3)] \)
Notice that (x+3) is now a common factor, so we will factor it out to get
\( 2x^2(x+3)(x^2+1) \)
as the final answer.