Find all of the zeros of x^3+4x^2+3x-2=0

Answer: x = - 1

x = (5-√17) / 2 = 0.438

x = (5+√17) / 2 = 4.562

Step by step solution:

Step 1:

Equation at the end of step 1:

(((x3) - 22x2) - 3x) + 2 = 0

Step 2:

Checking for a perfect cube:

2.1 x3-4x2-3x+2 is not a perfect cube

Trying to factor by pulling out:

2.2 Factoring: x3-4x2-3x+2

Thoughtfully split the expression at hand into groups, each group having two terms:

Group 1: - 3x+2

Group 2: x3-4x2

Pull out from each group separately:

Group 1: (-3x+2) • (1) = (3x-2) • (-1)

Group 2: (x-4) • (x2)