Factor the polynomial
x*x*x-343
Find the real number solution of the equation
x^3 = 343 -->
x = 7
Put:
[x^3 - 343]/[x-7] = A x^2 + Bx + C -->
x^3 - 343 = [A x^2 + Bx + C]*[x-7]--->
x^3 - 343 = A x^3 +(B-7A)x^2+(C-7B)x-7C
A = 1
B = 7
C = 49
To factor the polynomial x^3 - 343, we recognize that 343 is the cube of 7. Therefore, we can rewrite the polynomial as (x)^3 - (7)^3.
Using the formula for factoring the difference of cubes, we have:
(x - 7)(x^2 + 7x + 49)
So, the factored form of the polynomial is (x - 7)(x^2 + 7x + 49).
Next, to find the real number solutions of the equation x^3 = 343, we can set the equation equal to zero:
x^3 - 343 = 0
We can rearrange this equation as:
x^3 = 343
Taking the cube root of both sides, we get:
x = ∛343
Simplifying, we find that x = 7.
Therefore, the real number solution of the equation x^3 = 343 is x = 7.