DIVIDE POLYNOMIAL BY MONOMIAL HELP?
i will attempt to respond to this despite if it quite is going to in all threat seem very messy and annoying to stick to on exhibit.In phrases you divide 3x into 6(x)^3 to get 2(x)^2 . you presently multiply (3x -2 ) by 2(x)^2 which provides 6(x)^3 - 4(x)^2. Now subtract this from 6(x)^3 - sixteen(x)^2 to offer - 12(x)^2 convey down 17x and now divide -12(x)^2 by 3x and proceed the technique to crowning glory.i will attempt to set it out for you . 2(x)^2 - 4x + 3 ................................... 3x - 2) 6(x)^3 - sixteen(x)^2 + 17x - 6 6(x)^3 - 4(x)^2 " - 12(x)^2 + 17x -12(x)^2 + 8x " 9x - 6 9x - 6 " " desire this helps, it seems messy as a results of way the positioning units it out.
DIVIDING POLYNOMIALS BY MONOMIALS?
16x^3y-20x^2 -------------------- 4xy same as 16x^3y - 20x^2 ---------- -------- 4xy 4xy Simplify variables and numbers 5x 4x^2 - ------------ 4y
Dividing a monomial by a binomial?
Yes, it can be simplified. In simpler terms, it will be x^2/2(x^2+3). In tough, its answer will be an infinite term expansion which is 1/2-3/2x^2+18/4x^4-108/8x^6+648/16x^8...... where we should multiply the first term by -6/2x^2 and multiply the product got and then again by the product got and so on. This answer will de obtained by 'long division method'.
Help dividing a polynomial by a monomial (6x^2+13x+8)/(2x+1)?
The best way is to use the method of polynomial long division, though it will be hard to display here and there are other methods but i'll show it. ........______________ 2x+1 | 6x² + 13x + 8 How many times does 2x go into 6x²? it goes 3x times. Write 3x in the first degree of x column and times the expression by 3x then take away from the top as done below. ................... 3x ........ ______________ 2x+1 | 6x² + 13x + 8 ......... 6x² + 3x .......... 0 + 10x Now you ask how many times does 2x go into 10x? the answer is 5. ...................3x + 5 .........______________ 2x+1 | 6x² + 13x + 8 ......... 6x² + 3x ............0 + 10x ....................10x + 5 .......................0 + 3 The remainder is 3. If it was 6x² + 13x + 5 the answer would just be 3x+5.
Multiplying and Dividing a Polynomial by a Monomial?
Jenny There may be different ways to do a problem, but there is only one right answer! So the fact that you and your teacher do it differently shouldn't make any difference. That said, I know it's confusing when you and you and your teacher do things differently. A lot of times, the teacher may teach one particular way because it works on different kinds of problems you'll get in the future. You can't know that, but she/he does. If your concern is truly to resolve the differences between what your teacher does and what you do I'd suggest two possible actions. (1) Talk to your teacher, demonstrate that both ways produce the same answer to a few problems. Ask (nicely) what is the difference and why you need to learn the new way. (The answer in my school more than 50 years ago would have been "Because that's the way we do it!" I understand teachers are less arbitrary now.) (2) Put up a question on Answers, pick a problem and describe what you do and what your teacher does. (maybe it could be a survey if you don't tell people which is which.) Ask people to comment on the pros and cons of each approach. Or you could do both. You'll learn something good in any event!
Dividing polynomials.. algebra 2?
the two numbers interior the numerator are divided by utilising 2 so the respond could be 5c + 3 enable me supply you some extra examples : 6+8 / 2 = 3+4 10x+12y / 2 = 5x+6y while there is an including or subtracting equation then the full equation is split by utilising 2, each term is split by utilising 2 seperately like the examples above
The Long Division learned in grade school can be easily adapted for polynomials as follows.You want to divide [math]3x^4–4x^3–3x-1[/math] by [math]x-1[/math]. The first question is, exactly what monomial do you multiply the divisor by, so that its leading term matches the dividend’s leading term? The answer is [math]3x^3[/math], as can be seen by dividing the coefficients and subtracting the degrees of the leading terms.We put the [math]3x^3[/math] above the dividend’s [math]x^3[/math] term and division bar, (just like putting down the digit in the Long Division learned in grade school). Then, multiply the divisor by this monomial: [math]3x^3(x-1)=3x^4–3x^3[/math]. Subtract it from the [math]x^4[/math] and [math]x^3[/math] terms of the dividend, and then bring down the [math]x^2[/math] term, which this dividend happens to not have. You now have [math]-x^3-3x-1[/math] in your hands (the [math]-3x-1[/math] part need not be rewritten though).Dividing [math]-x^3–3x-1[/math] by [math]x-1[/math], we again see by dividing the leading terms that the next term in the quotient is [math]-x^2[/math]. Put that down, multiply by [math]x-1[/math] and subtract: [math](-x^3–3x-1) - (-x^2)(x-1) = -x^2-3x-1[/math]. (Only the [math]-3x[/math] part needs to be rewritten, though.)Similarly, dividing [math]-x^2–3x-1[/math] by [math]x-1[/math], the next monomial in the quotient is [math]-x[/math], and multiplying that through and subtracting yields [math]-4x-1[/math]. Finally, the constant term of the quotient is [math]\frac{-4x}{x}=-4[/math], and subtracting [math]-4(x-1)[/math] yields [math]-5[/math]. Since [math]-5[/math] has degree less than that of [math]x-1[/math], it is the (unique) remainder.Thus the quotient is [math]3x^3-x^2-x-4[/math], and the remainder is[math] -5[/math], as illustrated below.
Yes, a monomial is a polynomial.In ordinary English, “mono” and “poly” have opposite meanings, as in monogamy vs. polygamy, monotheism vs. polytheism, monolingual vs. polylingual, etc.However, mathematicians have their own language and, at least in this case, every monomial is also considered a polynomial.In this situation it makes things much simpler to consider monomials as polynomials. For example, if you wanted to make a statement about all polynomials, you would have to instead make that statement about all monomials and all polynomials, so you would have to give two proofs, one that worked for all monomials and another that worked for all polynomials that weren’t monomials. That’s extra work, and mathematicians would not be fond of it.A similar example: Are squares also rectangles? You could argue it either way. But if all squares are considered rectangles, then if you’re proving a theorem about all rectangles, you would avoid having two separate cases — one for squares and another for rectangles that are not squares. So in the mathematical world, all squares are rectangles (at least in English).Another example of how words have a different definition in mathematics than in ordinary speech: When you are asked for a definition of a term, you look in the dictionary and there are multiple ways of defining that term. In mathematics, however, each term must have a single definition. So the word “definition” is different in mathematics than it is in ordinary speech.
Is there a way to do polynomial long division with a graphing calculator such as a TI-83?
The program TI-Assistant v0.6 claims to be able to 'synthetically divide polynomials up to the fifth power'. Also, the program 'Synthetic Division' claims to 'take the coefficients of a polynomial and a binomial and divides the polynomial by the binomial with them' Synthetic division is a simpler way of doing long division. See links for relevant theory, examples, and where to get the software, etc. In addition, Ultimate V2.3, claims to do polynomial long division, as well. In case you don't have a cable or software to transfer the application to your calculator, see the last two links. The software is free, the cable should be no more than $20.
Monomial is a expression with 1 termBinomial is a expression with 2 termsTrinomial is a expression with 3 termsPolynomial is an expression with 4 or more termsThey are just named for different types of expressions but there are different ways you multiply and divide multiple monomials, binomial, or trinomial for each one. For 2 binomials you can use FOIL, and for multiple trinomials and/or monomials just multiply each term by each other term in the other trinomial or binomial. If you haven't learned this in Algebra you will soon.