Find the quotient...Show work.....y^4+y+1/y^2-9
visit calc101 . com where they have a link to polynomial division. It shows the complete solution.
2*49
To find the quotient of the expression (y^4 + y + 1) / (y^2 - 9), we can use long division. Here's how you can work it out:
Step 1: Write out the dividend (y^4 + y + 1) and the divisor (y^2 - 9), and set it up for long division:
_______________________
y^2 - 9 | y^4 + y + 1
Step 2: Divide the highest power of the dividend by the highest power of the divisor. In this case, divide y^4 by y^2, yielding y^2.
y^2
_______________________
y^2 - 9 | y^4 + y + 1
Step 3: Multiply the divisor (y^2 - 9) by the result of the division (y^2). This gives y^4 - 9y^2.
y^2
_______________________
y^2 - 9 | y^4 + y + 1
- (y^4 - 9y^2)
Step 4: Subtract the product (y^4 - 9y^2) from the dividend (y^4 + y + 1). Bring down the next term, which is y.
y^2
_______________________
y^2 - 9 | y^4 + y + 1
- (y^4 - 9y^2)
_______________
10y^2 + y + 1
Step 5: Now, we have to repeat steps 2 to 4 with the new expression that is left: 10y^2 + y + 1.
Step 6: Divide the highest power of the new expression (10y^2) by the highest power of the divisor (y^2). This yields 10.
y^2 + 10
_______________________
y^2 - 9 | y^4 + y + 1
- (y^4 - 9y^2)
_______________
10y^2 + y + 1
- (10y^2 - 90)
_________________
y + 91
Step 7: Subtract the new product (10y^2 - 90) from the remaining expression (y + 91).
y^2 + 10
_______________________
y^2 - 9 | y^4 + y + 1
- (y^4 - 9y^2)
_______________
10y^2 + y + 1
- (10y^2 - 90)
_________________
y + 91
- (y + 9)
________________
82
Step 8: Since we cannot divide further, the remainder is 82. Therefore, the quotient of (y^4 + y + 1) divided by (y^2 - 9) is y^2 + 10, and the remainder is 82.
Final result: (y^4 + y + 1) / (y^2 - 9) = y^2 + 10 + 82 / (y^2 - 9)