Polynomial Long Division
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- Polynomial Long Division Polynomial division helps break down expressions into factors, consistent with the total number of roots. Let's say that we are trying to divide x2+2x−7…
By Vinitha Ranganeni, Victor Wang, Vatsal Ojha, Joshua Siktar, Evan Fang, Alex Federspiel, Anusha Rahman
- (Video) How to Do Long Division with Polynomials by Nancy Pi In this video by Nancy Pi she explains how to use long division with polynomials. Summary\large{\text{Summary}}Summa…
By Stefan Cuevas, Alex Federspiel, Amy Feraco, Anusha Rahman
- (Video) Long Division of Polynomials by PatrickJMT In this video, Patrick looks at a more challenging example of long division with polynomials. Summary\large{\text{Summary}}Sum…
By Ben Ferrara, Alex Federspiel, Amy Feraco, Anusha Rahman
- (Video) Dividing Polynomials by yaymath Here's a video by yaymath showing you how to divide polynomials with long division. Summary\large{\text{Summary}}Summary The steps are: S…
By Alex Federspiel, Amy Feraco, Anusha Rahman
- Polynomial long division isn't too different from integer long division. And like integer long division, it can be a pain. Therefore, it's best to use this new tool when you can…
By Alex Federspiel, Anusha Rahman
- Polynomial Long Division Polynomial long division is a method for dividing one polynomial by another. It works a lot like regular long division with numbers, but instead of digi…
By Anusha Rahman
Problems 73
- Which method would allow you to divide x4+x3+x2+10xx^4 + x^3 + x^2 + 10xx4+x3+x2+10x by x2+1x^2+1x2+1?
- Find the quotient when x3−2x2+2x−4x^3 - 2x^2 + 2x -4x3−2x2+2x−4 is divided by x−2x-2x−2.
- Find the quotient when x4+5x3+8x2+49x+45x^4 + 5x^3 + 8x^2+49x+45x4+5x3+8x2+49x+45 is divided by x3+8x+9,x^3 +8x+9,x3+8x+9, using long division.
- Find the quotient when 5x2−x5x^2-x5x2−x is divided by −x-x−x.
- Which of the following expressions equal x2x2−2x\frac{x^2}{x^2-2x}x2−2xx2 when x2−2x≠0x^2-2x\ne0x2−2x=0?
- Find a polynomial Q(x)Q(x)Q(x) such that −11x2+x3−45+39x-11x^2+x^3-45 +39x−11x2+x3−45+39x equals the product of Q(x)Q(x)Q(x) with −8x+x2+15-8x+x^2 + 15−8x+x2+15.
- Rewrite the following polynomial into standard form: x2+5x+3x5+100,000x9−50,000x20−80,000x2010,x^2 + 5x + 3x^5 + 100,000x^9 - 50,000 x^{20}-80,000x^\frac{20}{10},x2+5x+3x5+100,0…
- Find the quotient when x4−12x2+20x^4 - 12x^2+20x4−12x2+20 is divided by x2−10x^2 -10x2−10.
- Find a polynomial Q(x)Q(x)Q(x) such that x3−10x2−2x+20=(x2−2)Q(x)x^3 - 10x^2 - 2x+20 = (x^2 -2)Q(x)x3−10x2−2x+20=(x2−2)Q(x).
- Using long division, find the quotient when x4−2x3−10x2+20xx^4 -2x^3-10x^2+20xx4−2x3−10x2+20x is divided by x2−10x^2 -10x2−10.
- What zero coefficient term should be inserted into the following polynomial if we want to use long division, and it is a dividend? 5x5−3x3+x2−x−105x^5 - 3x^3 + x^2 - x - 105x5−3…
- What term is missing in the following polynomial if we want to use long division, and it is a dividend? x4+x2−2x+1x^4 + x^2 - 2x + 1x4+x2−2x+1
- What would the degree of the zero coefficient term be in the dividend of the following expression? x4−2x3+x−2x−2\frac{x^4 - 2x^3+x-2}{x-2}x−2x4−2x3+x−2
- Divide 4x2+4x4−5x3+50−45x4x^2 + 4x^4 - 5x^3 + 50 - 45x4x2+4x4−5x3+50−45x by 4x−54x - 54x−5.
- Rewrite the following polynomial in standard form (for a long division problem): x2−7x3+4−4xx^2 - 7x^3+4 -4xx2−7x3+4−4x.
- Simplify the following expression: x3+3x2+2xx+1\frac{x^3 + 3x^2 + 2x}{x+1}x+1x3+3x2+2x.
- Find the remainder when the polynomial x2+x+1x^2+x+1x2+x+1 is divided by the polynomial xxx.
- The total number of visitors who came to the Washington Theatre from May 1 to May 31 can be modeled by the function F(x)=126x3+279x2+90x+450F(x)=126x^3+279x^2+90x+450F(x)=126x3+…
- Using the information above, determine the average price per gallon of gas in 2012.
- Which of the following expressions is another way to represent the polynomial long division problem pictured below?
- Which of the following is the correct way of showing polynomial long division with a remainder, in fraction form? DividendDivisor=?\frac{\text{Dividend}}{\text{Divisor}} = ?Divi…
- How can we check to see if our answer is correct for polynomial long division?
- Perform long division on the fraction 6x2+3x+22x+1.\frac{6x^2+3x+2}{2x+1}.2x+16x2+3x+2.
- Divide 2x3+7x2−4x+72x^3+7x^2-4x+72x3+7x2−4x+7 by x2+2x−1.x^2+2x-1.x2+2x−1. Express the remainder (if any) using fractions.
- Perform long division on the rational expression x2+4x+1x+1.\frac{x^2+4x+1}{x+1}.x+1x2+4x+1. If there is a remainder, represent it using fractions.
- The area and length of this uninteresting and generic rectangle are pictured above. Find its length.
- The total number of notebooks sold from 2010 to 2015 at Charlie's store is given by the function N(x)=40x3+8x2+14824x+33000N(x) = 40x^3 + 8x^2 + 14824x + 33000N(x)=40x3+8x2+1482…
- The total number of passengers who left the train station from 6am and 11am is shown by the function P(x)P(x)P(x). The number of trains that left the station from 6am and 11am i…
- Divide 6x2+2x+16x^2+2x+16x2+2x+1 by x+3.x+3.x+3. Express the remainder (if any) using fractions.
- Rearrange the steps for the long division problem (4x3−13x2+2x−7)÷(x2+3x−2)(4x^3-13x^2+2x-7)\div (x^2+3x-2)(4x3−13x2+2x−7)÷(x2+3x−2) in correct order. A. Multiply 4x4x4x by x2+3…
- Simplify 2x3+8x2−3x−12x+4.\frac{2x^3+8x^2-3x-12}{x+4}.x+42x3+8x2−3x−12.
- In the polynomial x4−x2+x−1x^4-x^2+x-1x4−x2+x−1, we are missing a term of what degree?
- Re-write the numerator of 4x3−2x+82x+1\frac{4x^3-2x+8}{2x+1}2x+14x3−2x+8 to include all the degrees, and then find the quotient of the given polynomials.
- 6x5−7x4+4x3+2x−142x3−x2+2=?\frac{6x^5-7x^4+4x^3+2x-14}{2x^3-x^2+2} = ?2x3−x2+26x5−7x4+4x3+2x−14=?
- The top panel of the pizza box above has an area of 10x7+5x5+3x2+x+210x^7+5x^5+3x^2+x+210x7+5x5+3x2+x+2 square inches and a width of x−1x-1x−1 inches. Find the polynomial that r…
- What are the zero coefficient terms of the numerator of the fraction 17x4+15x2+3x+9?\frac{17x^4+15x^2+3}{x+9}?x+917x4+15x2+3?
- What zero coefficient terms should be inserted into the following polynomial if it is a dividend in a long division problem? 8x7+5x4+4x2+38x^7+5x^4+4x^2+38x7+5x4+4x2+3
- What is the sum of the degrees of the zero coefficients of the dividend in the following polynomial expression? 6x5−5x3+2x2+4x+3\frac{6x^5-5x^3+2x^2+4}{x+3}x+36x5−5x3+2x2+4
- 4x3+x2+2x+1=?\frac{4x^3+x^2+2}{x+1} = ?x+14x3+x2+2=?
- What are the zero coefficient terms of 7x7+4x6+8x4+3x3+2x+1?7x^7+4x^6+8x^4+3x^3+2x+1?7x7+4x6+8x4+3x3+2x+1?
- Cara is designing a wall hanging arrangement full of photos. The area of the arrangement is represented by 4x5+2x2+34x^5+2x^2+34x5+2x2+3 square feet and the width of the arrange…
- Find the length of the flag.
- Rearrange the terms in the following polynomial so that the powers are in descending order. Note: for this problem, interpret the letters eee and iii as variables rather than an…
- −x2+1+3x4+2xx+1=?\frac{-x^2+1+3x^4+2x}{x+1} = ?x+1−x2+1+3x4+2x=?
- Reorder the terms above so that the polynomial can be used in long division. Write your answer as a polynomial in standard form.
- Rewrite the polynomial in standard form.
- 5x+3+x3+x2x−2=?\frac{5x+3+x^3+x^2}{x-2} = ?x−25x+3+x3+x2=?
- Candice is assembling a gift box for her friend, Jane. She is looking for enough wrapping paper to cover the length of the blue rectangular section of the box. Using the measure…
- 2x−x2+x4−3+6x3x−3=?\frac{2x-x^2+x^4-3+6x^3}{x-3} = ?x−32x−x2+x4−3+6x3=?
- Evaluate x3x−1.\frac{x^3}{x-1}.x−1x3. (Hint: Treating xxx as a variable, use polynomial long division to rewrite x3x−1=quotient+remainderx−1.)\frac{x^3}{x-1} = \text{quotient} …
- Evaluate x3x+1.\frac{x^3}{x+1}.x+1x3. (Hint: Treating xxx as a variable, use polynomial long division to rewrite x3x+1=quotient+remainderx+1.)\frac{x^3}{x+1} = \text{quotient} …
- Find the remainder when (1+x)4(1+x)^4(1+x)4 is divided by 1+x21+x^21+x2.
- Find the remainder when (1+x)2(1+x)^2(1+x)2 is divided by 1+x21+x^21+x2.
- Find the quotient when 1+x1+x1+x is divided by 1+x21+x^21+x2.
- Find the remainder when (1+x)3(1+x)^3(1+x)3 is divided by 1+x21+x^21+x2.
- Is x2−y2x^2-y^2x2−y2 divisible by x−yx-yx−y? If so, find the quotient.
- Find the quotient when (1+x)2(1+x)^2(1+x)2 is divided by 1+x21+x^21+x2.
- Find the quotient when (1+x)3(1+x)^3(1+x)3 is divided by 1+x21+x^21+x2.
- Tim the 8th nods along. He wants to guess c=8c = 8c=8, because the other Tims have guessed different values of ccc. If Tim is correct that c=8c=8c=8, at most how many of the rem…
- The process described above is most similar to...
- Apply long division on x2+4x+4x+2.\frac{x^2 + 4x + 4}{x+2}.x+2x2+4x+4.
- Apply long division on x4+7x+6x3\frac{x^4 + 7x + 6}{x^3}x3x4+7x+6
- Find the largest integer nnn such that n−2016n-2016n−2016 divides n2−2016n^2-2016n2−2016. Source: Lexington Math Tournament.
- Simplify: 42x2−337x+7\frac{42x^2 - 33}{7x + 7}7x+742x2−33
- Determine the remainder when dividing x2−2x^2-2x2−2 from x4−x3+3x−1x^4-x^3+3x-1x4−x3+3x−1.
- Find the quotient when dividing x3−x+7x^3-x+7x3−x+7 from x5−x4+2x2−3x+5x^5-x^4+2x^2-3x+5x5−x4+2x2−3x+5.
- Find the remainder when dividing x2−6x+6x^2-6x+6x2−6x+6 by x−1x-1x−1.
- Suppose Q(x)Q(x)Q(x) is a polynomial such that x3+7x2+2x+14=(x+7)Q(x)x^3+7x^2+2x+14 = (x+7)Q(x)x3+7x2+2x+14=(x+7)Q(x). Which of the following is Q(0)Q(0)Q(0)?
- A statistician was researching for a college / university and was wondering on average, how many students are enrolled in a college / university. The total number of enrolled co…
- The total number of passengers at the 30th30^{\text{th}}30th Street Station in Philadelphia on January 555 from 6:006:006:00am to 8:008:008:00pm can be modeled by the function f…
- A new movie was released on Sunday at 8:008:008:00am. The total number of viewers who watched the movie on Sunday from 8:008:008:00am to 11:0011:0011:00pm can be expressed as th…
- A high school student was at a soccer game and wanted to figure out how many people, per average, came to watch the high school soccer games. The total number of people who watc…
- Determine the remainder after dividing x−7x-7x−7 from 7x2+18x−207x^{2}+18x-207x2+18x−20. Express your answer in fractional form.