Answer: the factors are (x - 2)(x + 2)(3x - 1)
Step-by-step explanation:
The given polynomial function is expressed as
f(x) = 3x⁴ - 7x³ - 10x² + 28x - 8
The first step is to test for any value of x that satisfies the polynomial when
3x⁴ - 7x³ - 10x² + 28x - 8 = 0
Assuming x = 2, then
3(2)⁴ - 7(2)³ - 10(2)² + 28 × 2 - 8 = 0
48 - 56 - 40 + 56 - 8 = 0
0 = 0
It means that x - 2 is a factor.
To determine the other factors, we would apply the long division method. The steps are shown in the attached photo. Looking at the photo, we would factorize the quadratic equation which is expressed as
3x² + 5x - 2 = 0
3x² + 6x - x - 2 = 0
3x(x + 2) - 1(x + 2)
(3x - 1)(x + 2) = 0