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1、Unit 1:Polynomial FunctionsLesson 3:Dividing PolynomialsLong Division Do you remember long division?Lets review it by dividing 589 by 33 58931289271961813 will go in to 5 once3 will go in to 28 nine times3 will go in to 19 six timesBring down the 8Bring down the 9So,589 3=196 with a remainder of 1(3
2、1=3)with 2 left over with 1 left over(39=27)with 1 left over(36=18)Long Division RecapIn the previous example:The dividend was 589 What is being divided The divisor was 3 What is dividing into the dividend The quotient was 196 The answer The remainder was 1 Whats left overDivision formula:i.e.589=31
3、96+1Dividing Polynomials by Binomials Polynomials are algebraic expressions with many terms x3+2x2 x+5 x4-6x3 4x2+3x 10 Binomials are algebraic expressions with two terms x 7 2x+1 We can divide a polynomial by a binomial using the same long division process we use for numbersExample 1 Divide-3x2+2x3
4、+8x 12 by x 1 Before we begin,write the polynomial in order of descending powers:2x3 3x2+8x 12Example 1:Solution321 23812xxxxDivide 2x3 by x to get 2x22x2Multiply x 1 by 2x2 to get 2x3 2x22x3 2x 2Subtract.Bring down the next term x 2+8xDivide x2 by x to get-xMultiply x 1 by-x to get x2+xSubtract.Bri
5、ng down the next term x x2 +x 7x 12 Divide 7x by x to get 7Multiply x 1 by 7 to get 7x 7Subtract.The remainder is-57+7x 75 Example 1:Solution Based on the division formula:5 2x3 3x2+8x 12(x 1)(2x2 x+7)=Example 2 Divide 4x3+9x 12 by 2x+1 Notice that theres no x2 term Before we begin,write in 0 x2 as
6、a placeholder 4x3+0 x2+9x 12Example 2:Solution3221 40912xxxxDivide 4x3 by 2x to get 2x22x2Multiply 2x+1 by 2x2 to get 4x3+2x2 4x3+2x 2Subtract.Bring down the next term 2x 2+9xDivide 2x2 by 2x to get-xMultiply 2x+1 by-x to get-2x2-xSubtract.Bring down the next term x 2x2 x 10 x 12 Divide 10 x by 2x t
7、o get 5Multiply 2x+1 by 5 to get 10 x+5Subtract.The remainder is-175+10 x+5 17 Example 1:Solution Based on the division formula:17 4x3+9x 12(2x+1)(2x2 x+5)=The Remainder Theorem When a Polynomial Function P(x)is divided by a binomial ax b,the remainder is a cannot be zero a and b are integersbPaExam
8、ple 3 Verify the remainder theorem using Examples 1&2Example 3:SolutionIn Example 1 we divided-3x2+2x3+8x 12 by x 1ThereforeAnd we want to find P(1)Our remainder was 5.3223812P xxxx 3212 13 18 112P238 12 5 Example 3:SolutionIn Example 2 we divided 4x3+9x 12 by 2x+1ThereforeAnd we want to find Our re
9、mainder was 17.34912P xxx31114912222P194128217 12PSummary Polynomials can be divided by binomial using the long division technique we use for numbers Before dividing write the polynomial in order of descending powers(see Example 1)put a zero in front of any missing terms(see Example 2)When a Polynom
10、ial Function P(x)is divided by a binomial ax b,the remainder is P(b/a)known as the Remainder TheoremPractice Problems P.91-92#1-3a,7-9bc,10 Note:For#1-3a,do not express your answer in quotient form.I want you to write your answers like I did in Examples 1&2(using the division formula).So,when you check your answers in the back of the text,check the answer for part c(not part a)
高三(国际部)数学复习ppt课件：1.3多项式函数的因式分解
