Question

if a polynomial (2x³-3x²+x+1) is divided by x-2 and can be expressed as px/dx=q(x)+rx/dx then what is the value of rx

Answer 1

To divide the polynomial 2x³-3x²+x+1 by x-2, perform polynomial long division. The remainder, rx, is 7x.

Step-by-step explanation:

To divide the polynomial 2x³-3x²+x+1 by x-2, we use polynomial long division. The divisor, x-2, goes into the dividend, 2x³-3x²+x+1, to get a quotient and a remainder. The remainder, rx, is the term with the highest degree of x in the polynomial division. Let's perform the polynomial long division:

2x² + x - 2
_________________________
x - 2 | 2x³ - 3x² + x + 1
- (2x³ - 4x²)
_________________
+ x² + x + 1
- (x² - 2x)
_______________
3x + 1
- (3x - 6)
_______________
7

After performing the polynomial long division, we have a remainder of 7x, which is represented by rx.