When px^3 – 2px^2 + 3x – p is divided by (x – 1), the remainder is -5. Find p.
To find the value of p, we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by (x - c), then the remainder is equal to f(c).
In this case, we are given that the polynomial px^3 – 2px^2 + 3x – p is divided by (x – 1), and the remainder is -5. So we can set up the equation:
px^3 – 2px^2 + 3x – p = -5
Now, to find p, we need to substitute x = 1 into the equation and solve for p. Let's do that:
p(1)^3 – 2p(1)^2 + 3(1) – p = -5
p – 2p + 3 – p = -5
-p + 3 = -5
Next, we will isolate the variable p:
(-p + 3) - 3 = -5 - 3
-p = -8
Finally, to solve for p, we multiply both sides of the equation by -1:
p = 8
Therefore, the value of p is 8.