Final answer:
To check if x-2 is a factor of 2x³-5x²+x-2, you apply the Factor Theorem, substituting 2 into the polynomial, which results in -4. Since the outcome is not zero, x-2 is not a factor of the polynomial.
Step-by-step explanation:
To determine if x-2 is a factor of 2x³-5x²+x-2, you can use the Factor Theorem. The Factor Theorem states that x-c is a factor of a polynomial if the polynomial evaluates to zero when x is substituted with c. In this case, substitute x with 2 in the polynomial 2x³-5x²+x-2 and calculate.
Step 1: Substitute x with 2.
- 2(2)³ - 5(2)² + (2) - 2
- 2(8) - 5(4) + 2 - 2
- 16 - 20 + 2 - 2
- 16 - 20 + 0 = -4
Since the result is not zero, x-2 is not a factor of 2x³-5x²+x-2.