Question

Factor the polynomial completely

Answer 1

`\boxed{(7-5x)(49+35x+25x^2)}`

Explanation:

These are the steps you must follow to solve this problem:

Step 1:

We can write
`125=5^3` and
`343=7^3` so:

`343-125x^3=(7^3-5^3x^3)`

Step 2:

We can arrange this as follows:

`343-125x^3=[7^3-(5x)^3]`

Step 3:

So we can use difference of cubes formula:

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

So:

`a=7 \\ \\ b=5x`

Therefore:

`343-125x^3=(7-5x)[(7)^2+(7)(5x)+(5x)^2]`

`343-125x^3=(7-5x)(49+35x+25x^2)`