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degree of polynomial degree of polynomial the number i.e the highest power in the polynomial is known as the degree or sometimes the order of the polynomial for example is a degree 4 polynomial certain degrees have names and are often written using certain letters for the coefficients when they are unknown degree 0 constant or degree 1 linear or degree 2 quadratic degree 3 cubic degree 4 quartic notation most of the polynomials on this page are written in terms of for example although polynomials can be written with other letters,for example is called a polynomial in.it is conventional to write polynomials in descending powers for clarity although a polynomial may have the powers in any order.by writing polynomials in descending powers it is possible to see what the degree of the polynomial is simply by looking at the first term performing operations with two or more polynomials are also much simpler when the powers are in order,since like powers are usually grouped during calculations.indeed,you may lose marks in your exam if you don t simplify things like know more about division with remainders math.edurite.com page 1/3

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p. 2

operations with polynomials addition to add polynomials you simply add the co-efficients of each term if that sounds confusing don t worry as you will probably already know how to do this it is basically the same as collecting like terms you add the co-efficients of together the co-efficients of together and so on.notice that and some find it helpful to write this out like numerical addition.when using this method it is essential that terms with to the same power are lined up leaving spaces if necessary as in the example above subtraction for subtraction of polynomials it is possible to use the same method as above except subtracting instead of adding it may get confusing when there are negative terms involved so it is preferred to reverse the signs in the second row and then add the two polynomials together this method is desirable in the exam because subtracting negative numbers may cause confusion and mistakes may be overlooked in the pressure of the exam multiplication to multiply polynomials you simply multiply all the terms in one by all the terms in the other and then sum the results this method is known as the foil method it stands for first outer inner last.multiply the first terms together,then multiply the outer terms together.then multiply the inner terms together.then multiply the last terms together.then we add the results together to give us written in descending powers as you become confident with the process you ll be able to do the entire multiplication in one go without splitting it up division division of polynomials can be done just like regular long division however you will need to be quite adept at addition subtraction and multiplication of polynomials to divide 1 divide the first term of the dividend by the highest term of the divisor place the result above the bar x3 ÷ x x2 2 multiply the divisor by the result you just obtained the first term of the eventual quotient write the result under the first two terms of the dividend x2 x-3 x3 3x2 3 subtract the product you just obtained from the appropriate terms of the original dividend and write the result underneath this can be tricky at times because of the sign x3-12x2 x3-3x2 -12x2 3x2 -9x2 then pull down the next term from the dividend 4 repeat the last three steps except this time use the two terms that you have just written as the dividend read more about 2 digit subtraction with regrouping math.edurite.com page 2/3

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p. 3

thank you math.edurite.com

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