(5y^4-23y^3+24y^2-7)/(y-3)
Can you help me if I help you? the temperature of a room during an experiment can be modeled by the function f(x)=23.7 cos (Pi x /60) +18. Where f(x) is the temperature F degrees and x is the number is hours into the experiment. What is the lowest temperature the room reached during the expriement?
I got -5.7 F *
5 y^3-8y^2 with Remainder = -7
http://calc101.com/webMathematica/long-divide.jsp#topdoit
thanks
To simplify the expression (5y^4-23y^3+24y^2-7)/(y-3), you can use a method called polynomial long division. Here's how you can do it step by step:
Step 1: Start by dividing the first term of the numerator (5y^4) by the denominator (y-3). This gives you 5y^3, which you write above a line.
5y^3
_______
y-3 | 5y^4 - 23y^3 + 24y^2 - 7
Step 2: Multiply the divisor (y-3) by the quotient you found in Step 1 (5y^3), and write the result (5y^4 - 15y^3) below the line, aligned with the corresponding terms.
5y^3
_______
y-3 | 5y^4 - 23y^3 + 24y^2 - 7
- (5y^4 - 15y^3)
Step 3: Subtract the result from Step 2 from the numerator (5y^4 - 23y^3 + 24y^2 - 7).
5y^3
_______
y-3 | 5y^4 - 23y^3 + 24y^2 - 7
- (5y^4 - 15y^3)
_______________________
-8y^3 + 24y^2 - 7
Step 4: Bring down the next term from the numerator (24y^2) and continue the process. Divide this term by the denominator (y-3) to find the next term of the quotient.
5y^3 - 8y^2
_______________
y-3 | 5y^4 - 23y^3 + 24y^2 - 7
- (5y^4 - 15y^3)
_______________________
-8y^3 + 24y^2 - 7
- (- 8y^3 + 24y^2)
___________________________
0
Step 5: Since the result of the subtraction in Step 4 is 0, it means there are no more terms left in the numerator to bring down. Therefore, the polynomial long division process is complete.
The quotient is 5y^3 - 8y^2, and since there is no remainder, the simplified expression is 5y^3 - 8y^2.