2One of the topics in this section is finding the cube or cube root of a number. A cubed number is the solution when a number is multiplied by itself three times.A cube root “undos” the cubing operation just like a square root would.
3Calculator Function – How to take the cube root of a number To take the cube root of a number, press MATH, then select option 4.Example: What is ?24
4Solving Polynomials by Graphing We start getting into more interesting equations now . . .Ex: x3 + 3x2 = x + 3Problem: Solve the equation above, using a graphing calculator
5Solving Polynomials by Graphing What about something like this???Ex: x3 + 3x2 + x = 10Use the same principal; plug the first part of the equation in for Y1; the solution (10) for Y2; then find the intersection of the two graphs.
6FACTORING AND ROOTS CUBIC FACTORING Difference of Cubesa³ - b³ = (a - b)(a² + ab + b²)Sum of Cubesa³ + b³ = (a + b)(a² - ab + b²)Question: if we are solving for x, how many possible answers can we expect?3 because it is a cubic!
7CUBIC FACTORING EX- factor and solve a³ - b³ = (a - b)(a² + ab + b²)8x³ - 27 = (2x - 3)((2x)² + (2x)3 + 3²)(2x - 3)(4x² + 6x + 9)=0X= 3/2Quadratic Formula
8CUBIC FACTORING EX- factor and solve a³ + b³ = (a + b)(a² - ab + b²)x³ = (x + 7)(x² - 7x + 7²)(x + 7)(x² - 7x + 49)=0X= -7Quadratic Formula
13Factor by Using a Quadratic Form Ex: x4-2x2-8= (x2)2 – 2(x2) – 8Substitute a in for x2= a2 – 2a – 8This is something that we can factor(a-4)(a+2)Now, substitute x2 back in for a(x2-4)(x2+2)(x2-4) can factor, so we rewrite it as (x-2)(x+2)Since this equation has the form of a quadratic expression, we can factor it like one. We will make temporary substitutions for the variablesSo, x4-2x2-8 will factor to (x-2)(x+2)(x2+2)