When px^3 – 2px^2 + 3x – p is divided by (x – 1), the remainder is -5. Find p.
-1
do the long division
in the last row you get
-3 + 2 p
which has to be -5
To find the value of p, we need to use the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by (x - c) and the remainder is r, then f(c) = r.
In this case, we are given that when px^3 – 2px^2 + 3x – p is divided by (x – 1), the remainder is -5. This means that f(1) = -5.
Let's substitute x = 1 into the given polynomial and equate it to the remainder:
p(1)^3 - 2p(1)^2 + 3(1) - p = -5
p - 2p + 3 - p = -5
-p + 3 = -5
3 - p = -5
Now, rearrange the equation to isolate p:
-p = -5 - 3
-p = -8
p = 8
Therefore, the value of p is 8.