Question

Which of the following is a factor of 512x3 − 125?

A) 8x + 5
B) 64x2 + 80x + 25
C) 64x2 + 40x + 25
D) None of the above

Answer 1

The correct answer option is C) 64x^2 + 40x + 25.

Explanation:

We are given the following expression:

`512x^3 - 125`

which can also be written in the form of
`x^3-y^3` as:

`\left(8x\right)^3-5^3`

Now we will apply the difference of cubes Formula:

`x^3-y^3=(x-y)(x^2+xy+y^2)`

`(8x)^3-5^3=(8x-5)(8^2x^2+5*8x+5^2)`

`=\left(8x-5\right)\left(8^2x^2+5\cdot \:8x+5^2\right)`

`=\left(8x-5\right)\left(64x^2+40x+25\right)`

Therefore, from the given answer options we can see that the option C) 64x^2 + 40x + 25 is the factor of the given expression 512x^3 - 125.

Answer 2

C) 64x2 + 40x + 25

Explanation:

we are given

`512x^3-125`

we can also write as

`512=8^3`

`125=5^3`

`512x^3-125=(8x)^3-(5)^3`

we can use factor formula

`a^3-b^3=(a-b)(a^2+ab+b^2)`

we can compare and find 'a' and 'b'

a=8x

b=5

`512x^3-125=(8x-5)((8x)^2+8x* 5+(5)^2)`

now, we can simplify it

`512x^3-125=(8x-5)(64x^2+40x+25)`

so, (64x^2+40x+25) factor matches