having trouble with this problem

Question

solve and check the solution,

I want to either factor out the ^ or combine like terms

2x^3-x^2-8x+4=0

Answer 1

You would not factor out the "^"---that is a symbol used to mean "raised to a power"

So this: 2x^3-x^2-8x+4=0

is the same as this: 2x³ - x² - 8x + 4 = 0 (some extra spaces added for clarity)

The first step is to figure out what one of the factors is. In the answer from Paul M., he recognized that 2x - 1 is a factor by looking at the pattern in the pairs of terms. The more general method is to guess the first factor based on the factors of the 1st and last terms. ALL of the factors must have either 1 or 2 for the first coefficient and either 1, 2, or 4 for the last. Suppose we guess that one factor is x - 2: Using long division, divide the expression by x - 2 to get 2x² + 3x - 2. This then factors into 2x - 1, and x + 2.

Try it also by starting with x + 2 as the first factor.

Answer 2

2x³ - x² - 8x+4 = x²(2x-1) - 4 (2x -1) = (x+2)(x-2)(2x-1)

Therefore the roots are 1/2, +2, -2