Answer:
D is the operation
Explanation:
P(x)=x^4 + 3x^3 +2x^2 -x+2
Q(x) = (x^3 +2x^2+3) (x^2 -2)
The answer is x^5 +x^4 -5x^3 -3x^2 +x-8
What operation are we doing?
First we need to see what Q(x) is
Q(x) = (x^3 +2x^2+3) (x^2 -2)
Distribute
= x^5 + 2x^4 +3x^2 -2x^3 -4x^2 -6
Simplify
=x^5 + 2 x^4 - 2 x^3 - x^2 - 6
A) P+Q
x^4 + 3x^3 +2x^2 -x+2
x^5 + 2 x^4 - 2 x^3 - x^2 - 6
---------------------------------------
-4
So a cannot be the operation
B) P-Q
x^4 + 3x^3 +2x^2 -x+2
- (x^5 + 2 x^4 - 2 x^3 - x^2 - 6)
---------------------------------------
+8
So B cannot be the operation
C) P* Q
x^4 + 3x^3 +2x^2 -x+2
* x^5 + 2 x^4 - 2 x^3 - x^2 - 6
---------------------------------------
-12
C cannot be the operation
D) Q-P
(x^5 + 2 x^4 - 2 x^3 - x^2 - 6)
- x^4 + 3x^3 +2x^2 -x+2
---------------------------------------
-8
D is the operation