章节大纲

  • Section 6.2 Polynomial Functions
    ::第6.2节 多元函数

    Review
    ::回顾

    1. Standard form: x 2 + 3 x 1 2 + 3 ; degree: 2; lead term: x 2 ; lead coefficient: 1; constant term: 3.
      ::标准窗体: x2+3x12+3; 度: 2; 铅值: x2; 铅系数: 1; 恒定值: 3。
    2. Standard form: 1 3 x 2 y 9 y 2 4 ; degree: 2; lead term: 1 3 x 2 y ; lead coefficient: 1 3 ; constant term: -4.
      ::标准表: 13x2y-9y2-4; 度: 2; 铅期: 13x2y; 铅系数: 13; 恒定期: - 4。
    3. Standard form: 3 x - 3 ; degree: -3; lead term: 3 x - 3 ; lead coefficient: 3; constant term: 0.
      ::标准表: 3x-3; 度: -3; 铅值: 3x-3; 铅系数: 3; 恒定值: 0。
    4. Standard form: 2 3 t 2 t - 2 ; degree: 2; lead term: 2 3 t 2 ; lead coefficient: 1 3 ; constant term: 0.
      ::标准表:23t2-t-2;度:2;铅期:23t2;铅系数:13;恒定期:0。
    5. Standard form: - 2 x + x 1 2 1 ;   degree: 1; lead term: - 2 x ; lead coefficient: -1; constant term: -1.
      ::标准窗体: -2x+x12-1; 度:1; 牵头条件: -2x; 牵头系数: -1; 恒定条件: -1。
    6. Standard form: x 3 + 5 ; degree: 3; lead term: x 3 ; lead coefficient: 1; constant term: 5.
      ::标准表: x3+5; 度: 3; 铅值: x3; 铅系数: 1; 恒定值: 5。
    7. Standard form: - 2 x + 3 ; degree: 1; lead term: - 2 x ; lead coefficient: -2; constant term: 3.
      ::标准窗体: - 2x+3; 度: 1; 牵头条件: - 2x; 牵头系数: - 2; 恒定条件: 3。
    8. Standard form: x + x - 2 + 5 ; degree: 1; lead term: x ; lead coefficient: 1; constant term: 5.
      ::标准表: x+x-2+5; 度:1; 铅值: x; 铅系数:1; 恒定值: 5。
    9. Standard form: 8 x 4 + x 3 + 14 x 2 15 x 20 ; degree: 4; lead term: 8 x 4 ; lead coefficient: 8; constant term: -20.
      ::标准表: 8x4+x3+14x2-15x-20; 度: 4; 铅期: 8x4; 铅系数: 8; 恒定期: - 20。
    10. Standard form: x 3 + 8 ; degree: 3; lead term: x 3 ; lead coefficient: 1; constant term: 8.
      ::标准表: x3+8; 度: 3; 铅值: x3; 铅系数: 1; 恒定值: 8。
    11. Standard form: 9 x - 1 + 5 x - 2 + 16 ; degree: -1; lead term: 9 x - 1 ; lead coefficient: 9; constant term: 16.
      ::标准表: 9x-1+5x-2+16; 度: -1; 铅期: 9x-1; 铅系数: 9; 恒定期: 16。
    12. Standard form: 2 x 2 6 x + 10 ; degree: 2; lead term: 2 x 2 ; lead coefficient: 2 ; constant term: 10.
      ::标准表: 2x2-6x+10; 度: 2; 铅值: 2x2; 铅系数: 2; 恒定值: 10。
    13. Standard form: 1 3 x 4 + 8 3 x 2 + 4 ; degree: 4; lead term: 1 3 x 4 ; lead coefficient: 1 3 ; constant term: 4.
      ::标准表: 13x4+83x2+4; 度: 4; 铅期: 13x4; 铅系数: 13; 恒定期: 4。
    14. Standard form: x 4 x - 1 ; degree: 1; lead term: x ; lead coefficient: 1; constant term: 0.
      ::标准表: x-4x-1; 度: 1; 铅值: x; 铅系数: 1; 恒定值: 0。
    15. Standard form: - 10 x 6 + 7 x 5 6 x 3 + 19 x 2 3 x + 41 ; degree: 6; lead term: - 10 x 6 ; lead coefficient: -10; constant term: 41.
      ::标准窗体: - 10x6+7x5 - 6x3+19x2 - 3x+41; 度: 6; 牵头条件: - 10x6; 铅系数: - 10; 恒定条件: 41。
    Explore More
    1. Answers will vary. Example: x 3 9 .
      ::答复将有所不同。例如: x3-9。
    2. f ( 0 ) = 8 ; g ( 0 ) = - 7 , h ( 0 ) = 0 . The y-intercept for each of these polynomials is equal to the constant term.
      ::f( 0) = 8; g( 0) = 7, h( 0) = 0。 这些多元值中每个值的 Y 拦截值等于常数 。
    3. Program 3
      ::方案3
       

    Section 6.3 Adding and Subtracting Polynomials
    ::第6.3节 增添和减减多面体

    Review
    ::回顾

    1. 4 x 3 + 3 x 2 19 x + 20  
      ::4x3+3x2-19x+20
    2. - 6 x 4 + 8 x 3 2 x 2 12 x + 7  
      ::-6x4+8x3-2x2-12x+7
    3. x 4 + 7 x 3 + 7 x 2 3 x + 19  
      ::x4+7x3+7x2-3x+19
    4. - 6 x 4 3 x 3 3 x 2 4  
      ::-6x4-3x3-3-3x2-4
    5. 3 x 3 + 15 x 2 11 x 11  
      ::3x3+15x2-11x-11
    6. 2 x 5 4 x 4 + 3 x 3 + 30 x 2 3 x 17  
      ::2x5 - 4x4+3x3+30x2 - 3x- 17
    7. 0.56 x 5 + 1.29 x 4 1.87 x 3 + 1.59 x 2  
      ::0.56x5+1.29x4 - 1.87x3+ 1.59x2
    8. - 3 8 x 3 13 9 x 2 + 8 15 x  
      ::-38x3-139x2+815x
    9. 7 x 3 12 x 2 + 20 x 12  
      ::7x3-12x2+20x-12
    10. - 2 x 5 + 14 x 4 10 x 3 + 30  
      ::-2x5+14x4-10x3+30
    Explore More
    1. - 4 x 2 + 12 x + 35 , 000  is the total, and 2 x 2 2 x + 5 , 000  is the difference.
      ::-4x2+12x+35,000是总数,2x2-2x+5000是差额。
    2. P e r i m e t e r = 10 x 2  
      ::周边=10x-2
    3. - 5 t 2 + 10 t  
      ::-5t2+10t

    Section 6.4 Multiplying by a Monomial and the FOIL Method
    ::第6.4节 单体和FIL方法的乘数

    Review
    ::回顾

    1. 5 x 3 30 x 2 + 40 x  
      ::5x3-30x2+40x
    2. - 8 x 5 + 11 x 3 20 x 2  
      ::-8x5+11x3-20x2
    3. 21 x 6 7 x 5 + 112 x 4 + 70 x 3  
      ::21x6-7x5+112x4+70x3
    4. x 3 5 x 2 + 4 x 20  
      ::x3 - 5x2+4x- 20
    5. 6 x 3 21 x 2 8 x + 28  
      ::6x3-21x2-8x+28
    6. - x 3 2 x 2 + 9 x + 18  
      ::-x3-2x2+9x+18
    7. 25 x 2 120 x + 144  
      ::25x2 - 120x+144
    8. 16 x 2 + 72 x + 81  
      ::16x2+72x+81
    9. - 6 x 7 33 x 6 + 2 x 5 + 11 x 4  
      ::-6x7-33x6+2x5+11x4
    10. 18 x 6 + 17 x 5 15 x 4  
      ::18x6+17x5-15x4 18x6+17x5-15x4

    Explore More
    ::探索更多

    1. 3 x 3 + 18 x 2 + 24 x  
      ::3x3+18x2+24x
    2. 2 x 3 + 5 x 2 + 2 x  
      ::2x3+5x2+2x
    3. ( w + 100 ) ( u + 20 ) = w u + 20 w + 100 u + 2 , 000  
      :伤心w+100(u+20)=wu+20w+100u+2 000)

     

    Section 6.5 Multiplying Polynomials
    ::第6.5节 乘数聚合体

    Review
    ::回顾

    1. x 4 2 x 3 2 x + 1  
      ::x4 - 2x3 - 2x+1
    2. 5 x 4 x 3 + 40 x 2 68 x + 12  
      ::5x4-x3+40x2-68x+12
    3. 3 x 4 25 x 3 + 36 x 2 41 x 105  
      ::3x4-25x3+36x2-41x-105
    4. 8 x 5 6 x 4 + 25 x 3 12 x 2 + 3 x 18  
      ::8x5- 6x4+25x3- 12x2+3x- 18
    5. 2 x 3 + 9 x 2 51 x + 40  
      ::2x3+9x2 - 51x+40
    6. 2 x 5 + 8 x 4 + x 3 + 4 x 2 10 x 40  
      ::2x5+8x4+x3+4x2-10x-40
    7. 9 x 4 25 x 2 + 16  
      ::9x4-25x2+16
    8. 10 x 5 26 x 4 15 x 3 + 61 x 2 + 10 x 28  
      ::10x5 - 26x4 - 15x3+61x2+10x- 28
    9. x 5 4 x 4 15 x 3 + 29 x 2 51 x 90  
      ::x5 - 4x4 - 15x3+29x2 - 51x- 90
    10. - 12 x 5 + 22 x 4 7 x 3 77 x 2 + 148 x 110  
      ::-12x5+22x4-7x3-77x2+148x-110

    Explore More
    ::探索更多

    1. x 3 13 x + 12  
      ::x3 - 13x+12
    2. x 4 4 x 3 8 x 2 16 x 48  
      ::x4 - 4x3 - 8x2 - 16x- 48
    3. x 3 4 x 2 11 x + 30  
      ::x3 - 4x2 - 11x+30

     

    Section 6.6 Long Division of Polynomials
    ::第6.6节 一夫多妻制长分割法

    Review
    ::回顾

    1. 2 x 2 + 3 x 10 + 4 x + 1  
      ::2x2+3x-10+4x+1
    2. x 3 5 x 2 25 x 110 580 x 5  
      ::x3 - 5x2 - 25x - 110 - 580x - 5
    3. 2 x 2 8 x + 6 + - 19 x + 5 x 2 1  
      ::2x2-8x+6+19x+5x2-1
    4. x 2 2 x + 3 8 3 x + 2  
      ::x2-2x+3-83x+2
    5. 3 x 3 + 7 x 2 + 7 x 2  
      ::3x3+7x2+7x-2
    6. x 3 4 x + 3 + - 3 x + 11 2 x 2 + 3  
      ::x3-4x+3+3+3x+112x2+3
    7. x 2 14 x + 97 500 x + 5  
      ::x2 - 14x+97 - 500x+5
    8. x 2 9  
      ::x2- 9
    9. 2 x 2 + 11 x + 15  
      ::2x2+11x+15
    10. 5 x 2 + 6 x 27 + - 18 x + 78 x 2 + 3  
      ::5x2+6x-27+-18x+78x2+3

    Explore More
    ::探索更多

    1. x 4 + 3 x 3 8 x 2 9 = ( x 2 ) ( x 3 + 5 x 2 + 2 x + 4 ) 1  
      ::x4+3x3-8x2-9=(x-2)(x3+5x2+2x4)-1
    2. x 3 4 x 2 + 9 x 13 x 2 = 4 x 2 + 2 x 3 + - 1 x 2   and f ( 2 ) = - 1  
      ::x3-4x2+9x-13x-2=4x2+2x-3+-1x-2和f(2)=-1
    3. y = 4 x 11  
      ::y=4x- 11 y=4x- 11

     

    Section 6.7 Synthetic Division of Polynomials
    ::第6.7节 多元体合成司

    Review
    ::回顾

    1. x 2 + 4 x 1 + 12 x + 2  
      ::x2+4x- 1+12x+2
    2. 4 x 2 + 17 x + 16  
      ::4x2+17x+16
    3. 2 x 1 + - 4 2 x + 1  
      ::2 - 1+-42x+1
    4. 2 x 3 33 x 2 + 267 x 2 , 423 + 21 , 849 x + 9  
      ::2x3-33x2+267x-2,423+21,849x+9
    5. x 2 + 2 x 1  
      ::x2+2x- 1
    6. 3 x 4 + 3 x 3 + 7 x 2 + 7 x + 6 + 4 x 1  
      ::3x4+3x3+7x2+7x6+6+4x-1
    7. 12 x 2 + 40 x 13 + 19 x + 3  
      ::12x2+40x-13+19x+3
    8. x 2 7 x + 12 + - 14 x + 2  
      ::x2-7x+12+-14x+2
    9. 6 x 2 + 7 x + 39 + 154 x 4  
      ::6x2+7x+39+154x-4
    10. x 3 + 3 x 2 6 x 8  
      ::x3+3x2 - 6x-8

    Explore More
    ::探索更多

    1. Yes, since 2 x 3 + 5 x 2 x 6 2 x + 3 = x 2 + x 2 . Therefore, the three sides have side lengths of 2 x + 3 , x + 2 , and x 1 .
      ::是,因为2x3+5x2-x-62-62x+3=x2+x-2。 因此,三边的侧长为2x+3、x+2和x-1。
    2. a. f ( - 2 ) = - 14  
      ::a. f( 2) =-14
             b. 2 x 4 5 x 3 10 x 2 + 21 x 4 x + 2 = 2 x 3 9 x 2 + 8 x + 5 + - 14 x + 2 .  The remainder is f ( - 2 ) .
     
       3. lead term: x 3 ;  constant term: 16. 

     

    Section 6.8 Operations with Functions
    ::第6.8节 具有职能的业务

    Review
    ::回顾

    1. x 2 + 5 x + 6  
      ::x2+5x+6
    2. 5 x + 1 3 x 5  
      ::5x+1-3x-5
    3. 9 x 45  
      ::9-45岁
    4. x 5 ( x 2 + 5 ) 3 x 15  
      ::x-5(x2+5)3x-15
    5. 5 x 3 + x 2 + 25 x + 5  
      ::5x3+x2+25x5+5
    6. x  
      ::x x
    7. 25
    8. 26 x 5  
      ::26x5 26x5
    9. x 3 2 25 5 x  
      ::x32-255x
    10. x 6 125  
      ::x6125

    Explore More
    ::探索更多

    1. w i d t h = 2 x 2 x + 3 ,  with the restriction that x - 3 .
      ::宽度=2x2x+3, 限制为 x-3 。
    2.  Profit function is 60 x 2 , 500 , and the break-even point is 41.67.
      ::利润函数为60x-2,500,平衡点为41.67。
    3.  They are not equal:  f 2 ( x ) = [ f ( x ) ] 2 = ( x + 4 ) 2 = x 2 + 8 x + 16 f ( x 2 ) = [ ( x 2 ) + 4 ] = x 2 + 4  
      ::它们不等于: f2( x) =[f( x) 2=( x+4) 2=( x+4) 2=x2+8x+16f( x2) =[( x2)+4) =x2+4

    Section 6.9 Composition of Functions
    ::第6.9节 职能的组成

    Review
    ::回顾

    1. 9 x 40  
      ::9-40岁
    2. 5 x 2 + 26  
      ::5x2+26
    3. 3 | x |  
      ::3x___________________________________________________________________________________________________________________________________________________
    4. 3 5 x 4  
      ::35x-4
    5. 45 x 31  
      ::45x-31岁
    6. x x , x > 0  
      ::xx,xx>0
    7. 5 x , x 0 or 5 | x |  
      ::5x 5x0Oor5x
    8. 5 x , x 0 or 5 | x |  
      ::5x 5x0Oor5x
    9. 25 x , x > 0 or 25 | x |  
      ::25x,x>0or25x
    10. 25 x x , x > 0  
      ::25xxx >0

     

    Explore More
    ::探索更多

    1. 30% off: d = 0.7 x ; $10 coupon: d = x 10 ; two ways to get the discount: d = 0.7 x 10  and d = 0.7 x 7 . The last equation gives the better discount.
      ::30%下调:d=0.7x;10张优惠券:d=x-10;两种折扣方式:d=0.7x-10和d=0.7x-7。
    2. A = P ( 1 + r ) 3  
      ::A=P(1+r)3
    3. V = 256 3 π t 3  
      ::V=2563t3

     

    Section 6.10 Connections: Impact of the Deepwater Horizon Oil Spill
    ::第6.10节 连接:深海地平线石油泄漏的影响

    Review
    ::回顾

    1. A = π ( 0.13 t ) 2  
      ::A(0.13t)2
    2. 619.3 square miles
      ::619.3平方英里
    3. A = π ( 0.175 t 4.9 ) 2  
      ::A(0.175t-4.9)2
    4. 3,848.45 square miles
      ::3,848.45平方英里
    5. About 40.3 days
      ::约40.3天

     

    Section 6.11 Connections: Protecting Your Data
    ::第6.11节连接:保护数据

    Review
    ::回顾

    1. x 2 + 1 + - 1 x + 1  
      ::x2+1+1+-1x+1
    2. No, the check values do not agree.
      ::不,检查值并不一致。
    3. No, the check values do agree.
      ::不,检查值是一致的。
    4. Answers will vary.
      ::答案将各有不同。