if a car moving at a constant rate travel (2x³-x²-4x+3)km in (x²-2x+1) hours what is the rate of the car in km per hour?
I need it asap thanks
check:
(2x+3)(x^2-2x+1)
is
2x(x^2-2x+1)
+
3(x^2-2x+1)
which is
2 x^3 -4x^2 +2x + 3x^2 -6x+3
= 2x^3 - x^2 - 4x +3
remarkable !
so divide
2x^3-x^2-4x+3
---------------------
x^2-2x+1
http://www.wolframalpha.com/input/?i=(2x%5E3-x%5E2-4x%2B3)%2F(x%5E2-2x%2B1)
To find the rate of the car in km per hour, we need to divide the distance traveled by the time taken.
The given expression represents the distance traveled by the car: 2x³ - x² - 4x + 3 km.
The given expression represents the time taken by the car: x² - 2x + 1 hours.
To find the rate, we divide the distance traveled by the time taken:
Rate = (2x³ - x² - 4x + 3) / (x² - 2x + 1)
Let's simplify the expression:
Rate = (2x³ - x² - 4x + 3) / (x² - 2x + 1)
Now, we can factorize the numerator and denominator:
Numerator:
2x³ - x² - 4x + 3 = (2x - 1)(x² + 1) - (4x - 3) = (2x - 1)(x² + 1) - (x - 1)(4x - 3) = (2x - 1)(x² + 1 - 4x + 3)
Denominator:
x² - 2x + 1 = (x - 1)(x - 1) = (x - 1)²
Now, substitute the factored forms back into the expression:
Rate = [(2x - 1)(x² + 1 - 4x + 3)] / [(x - 1)²]
Simplify the numerator:
Rate = (2x - 1)(x² - 4x + 4) / (x - 1)²
Now, cancel out any common factors between the numerator and denominator:
Rate = (2x - 1)(x - 2) / (x - 1)²
The rate of the car in km per hour is given by the expression (2x - 1)(x - 2) / (x - 1)².