X y 2 differences and sum of cubes x y x 2 xy y 2 x 3

This preview shows page 39 - 51 out of 69 pages.

x - y ) 2 Differences and Sum of Cubes ( x + y )( x 2 - xy + y 2 ) = x 3 + y 3 ( x - y )( x 2 + xy + y 2 ) = x 3 - y 3 MBA501: Math and Stat for Business 41 / 71
Image of page 39

Subscribe to view the full document.

§ 1.4 Rational Expressions Rational Expressions Expression that can be written as the quotient of two polynomials x + 1 x 2 + 3 MBA501: Math and Stat for Business 42 / 71
Image of page 40
§ 1.4 Rational Expressions Rational Expressions Expression that can be written as the quotient of two polynomials x + 1 x 2 + 3 Operations of Rational Expressions Cancellation Property PS QS = P Q Multiplication Rule P Q · R S = PR QS Division Rule P Q ÷ R S = P Q · S R MBA501: Math and Stat for Business 43 / 71
Image of page 41

Subscribe to view the full document.

§ 1.4 Rational Expressions Multiply, divide, add or subtract 21) 15 p - 3 6 ÷ 10 p - 2 3 27) k 2 - k - 6 k 2 + k - 12 · k 2 + 3 k - 4 k 2 + 2 k - 3 39) 7 ( b + 2 ) + 2 5 ( b + 2 ) MBA501: Math and Stat for Business 44 / 71
Image of page 42
§ 1.5 Exponents and Radicals What We Know a n = a · a · a · · · a n real number a is the base natural number n is the exponent Extension Expand the definition of exponent to include negative exponents and rational-number exponents ( - 2 ) - 2 , 8 1 / 3 MBA501: Math and Stat for Business 45 / 71
Image of page 43

Subscribe to view the full document.

§ 1.5 Exponents and Radicals Negative Exponent If n is a natural number, and if a = 0, then: a - n = 1 a n . Inversion Property ( a b ) - n = ( b a ) n . MBA501: Math and Stat for Business 46 / 71
Image of page 44
§ 1.5 Exponents and Radicals Exercises ( 1 3 ) - 2 ( rs ) 3 r 4 2 MBA501: Math and Stat for Business 47 / 71
Image of page 45

Subscribe to view the full document.

§ 1.5 Exponents and Radicals Roots Definition If a is a real number and n is a positive integer, then a 1 / n is defined to be the n th root of a (if it exists). Note if a is negative and n is even, then n th root of a does NOT exist. If n is even, then n th root of a is the positive real number whose n th power is a 0 . 4 = 16 = ( 16 ) 1 / 2 ⇐⇒ 4 2 = 16 If n is odd, then n th root of a is the real number whose n th power is a . 2 = ( 8 ) 1 / 3 , - 2 = ( - 8 ) 1 / 3 MBA501: Math and Stat for Business 48 / 71
Image of page 46
§ 1.5 Exponents and Radicals Radicals If any real number a and natural number n , is an even and a 0, or if n is an odd natural number, a 1 / n = n a . For all rational numbers m / n and all real numbers a for which n a exists, a m / n = ( n a ) m , or a m / n = ( n a m ) MBA501: Math and Stat for Business 49 / 71
Image of page 47

Subscribe to view the full document.

§ 1.6 First-Degree Equations Equations An equation is a statement that two mathematical expressions are equal 2 x - 1 = 3 x - 2 MBA501: Math and Stat for Business 50 / 71
Image of page 48
§ 1.6 First-Degree Equations Equations An equation is a statement that two mathematical expressions are equal 2 x - 1 = 3 x - 2 First-Degree Equations An equation involve only constant and first power of the variable. 2 x + 1 = 3 MBA501: Math and Stat for Business 51 / 71
Image of page 49

Subscribe to view the full document.

§ 1.6 First-Degree Equations Equations An equation is a statement that two mathematical expressions are equal 2 x - 1 = 3 x - 2 First-Degree Equations An equation involve only constant and first power of the variable. 2 x + 1 = 3 Solution of an Equation An number that can be substituted for the variable to make the equation true.
Image of page 50
Image of page 51
  • Spring '13
  • AnBotao
  • Math, Business, Quadratic equations, Quadratic equation

{[ snackBarMessage ]}

Get FREE access by uploading your study materials

Upload your study materials now and get free access to over 25 million documents.

Upload now for FREE access Or pay now for instant access
Christopher Reinemann
"Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

Ask a question for free

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern