Final answer:
To find the value of p and q in the given expression, divide by x-1 and x² respectively, and solve for x.
Step-by-step explanation:
In the given problem, we are told that both x-1 and x² are factors of 2x³ - x²pxq. We need to find the value of p and q.
Since x-1 is a factor, we can divide the given expression by x-1 using synthetic division to find the quotient.
After performing the synthetic division, we can equate the quotient to 0 and solve for x to find the value of p. To find the value of q, we can divide the expression 2x³ - x²pxq by x² and set the result equal to 0. Solving for x will give us the value of q.