Question

x^6 + 26x^3 - 27 is it equal to : (x^3 + 27)(x^3 - 1) ?

Answer 1

lets check
x^6 +27x^3-x^3-27 = 0
x^3 (x^3+27) -1 (x^3+27) =0
(x^3+27)(x^3-1) = 0
correct! but both of these can be further factorized, do you know the relations ?

Answer 2

How can I factorize it further? :)

Answer 3

\(\large a^3+b^3 = (a+b)(a^2-ab+b^2) \\ \large a^3-b^3 = (a-b)(a^2+ab+b^2)\)

Answer 4

Oh. Thankyou! :)

Answer 5

So it will be (x+3)(x^2-3x+9) ?

Answer 6

correct for x^3+27
what about x^3-1 ??

Answer 7

I'm still trying to figure it out :))

Answer 8

\( \\ \large a^3-b^3 = (a-b)(a^2+ab+b^2) \\a=x, b=1 \\ \large x^3-1^3=...?\)

Answer 9

will it be (x-1)(x^2-x+1) ?

Answer 10

in the term x^2-x+1
will it be -x or +x ?
take a look at the formula...

Answer 11

Oh. yeah XD sorry. My mistake. Thankyouuuuu!!!

Answer 12

welcome ^_^