Finding the unknown

Question

Solve the equation (X³ +4X² +4X +1= 0) find X

Answer 1

Let's try factoring by grouping:

(x³ + 1) + (4x² + 4x) = 0

(x + 1)(x² - x + 1) + 4x(x + 1) = 0

(x + 1)(x² - x + 1 + 4x) = 0

(x + 1) (x² + 3x + 1) = 0

x = -1 or x = [-3 ± √5] / 2

Answer 2

The first thing I would do is graph it. The graph gives you one of the zeros, or x intercepts of x=-1

The other 2 are decimals. So we need to use synthetic division and the quadratic equation.

Using synthetic division

-1 | 1 4 4 1

-1 -3 -1

----------------------

1 3 1 0

The last term so us remainder is zero, so this is in fact a factor.

The remaining equation is x²+3x+1=0

We can use the quadratic equation to solve what remains

(-3± √3²-4(1)(1))/2

This gives us: (-3± √5)/2 and x=-1 for the 3 zeros