Question

Factor the polynomial completely

Answer 1

Answer:

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

Step-by-step 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:

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

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