Dividing Polynomials with 2 or More Unknowns
Read this topicExplanations 3
- (Video) Dividing Multivariable Polynomials by Krista King In the video above, by the YouTube channel CalculusExpert.com it is explained how to divide polynomials that have multi…
By Stefan Cuevas, Alex Federspiel, Joshua Siktar, Amy Feraco, Anusha Rahman
- Two or More So we've learned how to use long division to divide polynomials but those were only with one variable. Now it's time for multiple variables. x2−y2x+y\frac{x^2-y^2}{x…
By Alex Federspiel, Joshua Siktar, Anusha Rahman
- Dividing Polynomials with 2+ Variables So far, we've learned polynomial division with just one variable. In this lesson, we're going to learn how to divide polynomials that have…
By Anusha Rahman
Problems 21
- Divide x3−x2−xy+yx^3 - x^2 - xy + yx3−x2−xy+y by x2−yx^2-yx2−y.
- Simplify y4−xy3−x3y+x2y2x2+y2\dfrac{y^4-xy^3 -x^3y+x^2y^2}{x^2+y^2}x2+y2y4−xy3−x3y+x2y2, where x,yx,yx,y are positive real numbers.
- Let U=xy2−yU = xy^2-yU=xy2−y and V=yV = yV=y, and suppose U=V⋅WU = V\cdot WU=V⋅W for some polynomial WWW in xxx and yyy. What is the value of WWW when both x,yx,yx,y are set equ…
- Write the following fraction in simplest form x4−y4x+y.\frac{x^4-y^4}{x+y}.x+yx4−y4.
- Which of the following are multivariable polynomials?
- Polynomial long division is often used by pharmacists to determine the proper amount of elements to add into medicine during its composition. If the elements to add are represen…
- What term needs to be inserted (in the ? box) to complete the long division process?
- Simplify: x2+2x2y−2xy+2xy2−3y2x+y\frac{x^2+2x^2y-2xy+2xy^2-3y^2}{x+y}x+yx2+2x2y−2xy+2xy2−3y2
- What is the next step in solving the polynomial long division above?
- If yyy and zzz are unknown constants, write the algebraic fraction x3−2x2−xyz+2xy+yzx−2\frac{x^3-2x^2-xyz+2xy+yz}{x-2}x−2x3−2x2−xyz+2xy+yz in the form quotient+remainderx−2\tex…
- Is x2−xy+21xy−21y2x^2-xy + 21xy-21y^2x2−xy+21xy−21y2 divisible by x−yx-yx−y? If so, find the quotient.
- Is x2−y2x^2-y^2x2−y2 divisible by x−yx-yx−y? If so, find the quotient.
- Let yyy be a constant. Is x2+y2x^2+y^2x2+y2 divisible by x+yx+yx+y? If so, find the quotient.
- If yyy is a nonzero constant, find the quotient when x−yx-yx−y is divided by xy−1xy-1xy−1.
- If yyy is a nonzero constant, find the remainder when x−yx-yx−y is divided by xy−1xy-1xy−1.
- Find the number of ordered pairs of positive integers (x,y)(x,y)(x,y) such that x+y≤2019x+y \le 2019x+y≤2019 and the rational expression x3−x2y+2x+xy2−y3−2y+1x−y\frac{x^3-x^2y+2…
- Which of the following is equal to x3+y3+z3−3xyzx+y+z?\frac{x^3+y^3+z^3-3xyz}{x+y+z}?x+y+zx3+y3+z3−3xyz?
- For which of the following values of aaa is xa+yax^a+y^axa+ya divisible by x+yx+yx+y?
- Find all integer values of aaa such that the expression x5−x4y2+13x4y−13x3y3+30x3y2−x3y−30x2y4+x2y3−13x2y2+13xy4−30xy3+30y5\begin{align*} &x^5-x^4y^2 + 13x^4y-13x^3y^3+30x^3y^2 …
- Alina is playing a game. She starts with a polynomial x4+a1x3y+a2x2y2+a3x3y+y4.x^4+a_1x^3y+a_2x^2y^2+a_3x^3y + y^4.x4+a1x3y+a2x2y2+a3x3y+y4. She flips a fair coin 333 times. …
- What is 2x3+5x2y+5xy2+2xy+3y3+3y22x+3y?\frac{2x^3+5x^2y+5xy^2+2xy+3y^3+3y^2}{2x+3y}?2x+3y2x3+5x2y+5xy2+2xy+3y3+3y2?