need to find the quotient and remainder.
x^3+x^2y-9xy^2-9y^3 / x+y
take a look at calc101 . com
There's a section on polynomial long division, which shows all the intermediate steps involved.
To find the quotient and remainder when dividing the expression (x^3 + x^2y - 9xy^2 - 9y^3) by (x + y), you can use polynomial long division. Here are the steps:
Step 1: Arrange the terms of the dividend and the divisor in descending order of their powers.
Dividend: x^3 + x^2y - 9xy^2 - 9y^3
Divisor: x + y
Step 2: Divide the first term of the dividend by the first term of the divisor and write the result as the first term of the quotient.
Quotient: x^2
Step 3: Multiply the divisor by the quotient obtained in the previous step and subtract it from the dividend.
Partial division: (x + y) * x^2 = x^3 + xy^2
Subtract: (x^3 + x^2y - 9xy^2 - 9y^3) - (x^3 + xy^2) = x^2y - 9xy^2 - 9y^3
Step 4: Repeat steps 2 and 3 with the updated partial division, continuing until the degree of the remainder is less than the degree of the divisor.
1st repeat:
Divide: (x^2y - 9xy^2 - 9y^3) / (x + y)
Divide the first term of the updated partial division by the first term of the divisor:
(x^2y) / (x) = x^2
Multiply: (x + y) * x^2 = x^3 + xy^2
Subtract: (x^2y - 9xy^2 - 9y^3) - (x^3 + xy^2) = -10xy^2 - 9y^3
2nd repeat:
Divide: (-10xy^2 - 9y^3) / (x + y)
Divide the first term of the updated partial division by the first term of the divisor:
(-10xy^2) / (x) = -10y^2
Multiply: (x + y) * -10y^2 = -10xy^2 - 10y^3
Subtract: (-10xy^2 - 9y^3) - (-10xy^2 - 10y^3) = y^3
Step 5: Since the degree of the remainder (y^3) is less than the degree of the divisor (x + y), we have reached the end of the division.
The quotient is x^2 - 10y^2, and the remainder is y^3.