Algbrea 2 Math

Question

Please answer

 

x^3-343= 

 

Or is the polynomial prime??

Answer 1

Hello, thank you for taking the time to post your question!

The expression you’re trying to factor here is a difference of cubes, where

x^3 = (x)^3 and 343 = (7)^3.

That means you can factor it using the general form

a^3 – b^3 = (a – b)(a^2 + ab + b^2)

for this set of values that becomes

(x – 7)(x^2 + 7(x) + 7^2)

= (x – 7)(x^2 + 7x + 49)

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi again David;

x³-343=

These are two cubes...

x³-7³

The equation for adding two cubes...

a³+b³=(a + b)(a²–ab+b²)

a=x

b=-7

So...

x³+(-7)³=[x+(-7)][x²-(-7)(x)+(-7)²]

x³-7³=(x-7)(x³+7x+49)