Question

The distance covered by an object is governed by the expression x3 + 3x2 + 2x. If the time taken to cover this distance is given by x + 1, what is the expression that governs the speed of the object?

(A). x^2+2x
(B). x^2+2x-1/x+1
(C). x+2
(D). x^2+1/x+1

Answer 1

distanc=speed times time

undistribute or factor
we can factor out x
x(x^2+3x+2)
factor again
(x)(x+2)(x+1)
time=(x+1)
speed=(x)(x+2)=x^2+2x

A is answer

Answer 2

speed = distance / time = x^3 + 3x^2 + 2x / x + 1

x^2 + 2x
_________
x + 1 | x^3 + 3x^2 + 2x
- | x^3 + x^2
|________
| 2x^2 + 2x
- | 2x^2 + 2x

Therefore, speed is x^2 + 2x