Exponents and Polynomials - XYZ Custom Plus

Chapter 12 SummaryNOT FOR SALE. Copyright XYZtextbooks Last reEXAMPLEs1. a. 2 3 = 2 ⋅ 2 ⋅ 2 = 8b. x 5 ⋅ x 3 = x 5 + 3 = x 8_ xc.5x = x 5 − 3 = x 23d. (3x) 2 = 3 2 ⋅ x 2 = 9x 2e. ​ 2 _3​ 3 = 23_3 = _ 83 27f. (x 5 ) 3 = x 5⋅3 = x 15g. 3 −2 _= 1 3 = _ 12 92. (5x 2 )(3x 4 ) = 15x 63.12x 9_4x 5 = 3x 44. 768,000 = 7.68 × 10 50.00039 = 3.9 × 10 −45. (3x 2 − 2x + 1) + (2x 2 + 7x − 3)= 5x 2 + 5x − 26. (3x + 5) − (4x − 3)= 3x + 5 − 4x + 3= −x + 87. a. 2a 2 (5a 2 + 3a − 2)= 10a 4 + 6a 3 − 4a 2b. (x + 2)(3x − 1)= 3x 2 − x + 6x − 2= 3x 2 + 5x − 2c. 2x 2 − 3x + 4× 3x − 26x 3 − 9x 2 + 12x+ − 4x 2 + 6x − 86x 3 − 13x 2 + 18x − 8Exponents: Definition and Properties [12.1, 12.2]Integer exponents indicate repeated multiplications.Product Property a r ⋅ a s = a r + s To multiply with the same base,you add exponents.Quotient Property_ a ra = s ar − s To divide with the same base,you subtract exponents.Distributive PropertyExpanded Distributive Property​(ab) r = a r ⋅ b r Exponents distribute over multiplication.​​​ a _b​r_= arb rExponents distribute over division.Power Property (a r ) s = a r ∙ s A power of a power is the product of the powers.Negative Exponent Propertya −r = 1 _a rMultiplication of Monomials [12.3]Negative exponents imply reciprocals.To multiply two monomials, multiply coefficients and add exponents.Division of Monomials [12.3]To divide two monomials, divide coefficients and subtract exponents.scientific notation [12.1, 12.2, 12.3]A number is in scientific notation when it is written as the product of a number between1 and 10 and an integer power of 10.Addition of Polynomials [12.4]To add two polynomials, add coefficients of similar terms.subtraction of Polynomials [12.4]To subtract one polynomial from another, add the opposite of the second to the first.Multiplication of Polynomials [12.5]To multiply a polynomial by a monomial, we apply the distributive property. To multiplytwo binomials, we use the FOIL method. In other situations we use the Column method.Each method achieves the same result: To multiply any two polynomials, we multiplyeach term in the first polynomial by each term in the second polynomial.Chapter 12 Summary819