Question

I really need help! I do not understand this.

Question: choose one of the factors of 6x^3+6

a) x-1
b) x+1
c) x^2 -2x+1
d) x^2 + x+ 1

can you put the steps? I tried and I got x^3 + 3^3 = (x+3) (x^2 -3x+3^2) None of the two are in the answer choices so I know it's wrong! Help please.

Answer 1

if you factor out the 6 you get
6(x^3 + 1)
both x^3 and 1^3 are cubes (notice we can say 1= 1^3)

see http://www.purplemath.com/modules/specfact2.htm
for how to factor a sum of cubes

Answer 2

I got as far as 6(x^3 + 1)

but I get mixed up when plugging the terms in to a^3 +b^3 = (a+b) (a^2 -ab+6^2)

Answer 3

its b) x=1

Answer 4

to use this formula
a^3 +b^3
match it with
x^3 + 1^3
the a matches x and b matches 1

the formula says
a^3 +b^3 = (a+b) (a^2 -ab+b^2)
replace a with x, and b with 1
x^3 + 1^3 = (x+1)(x^2 -x*1 + 1^2)
x*1 is just x, and 1^2 is 1*1 = 1
so we can simplify it to

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

I would say (x+1) is the answer.