Chapter 5

What is a relative max and min?

*remember, find only y value for mas/min*

What does rational include?

ONLY whole numbers and fractions Number must be able to be expressed as a ratio No square roots and no imaginaries

What is a zero?

The x-intercept

State the number and type of root given a sum of cubes

Use quadratic formula to solve for the trinomial

What are critical points?

X and y intercepts Turning points (max and min)

How do you graph cubics, quartics, and quintics

if you factor something like (x²-6x+9) and you get (x-3)(x-3), ALWAYS write it as (x-3)²

What is multiplicity?

multiplicity = degree

Sum of cubes

Note, to solve sum of cubes, you may have to use the quadratic formula

What are the two exceptions?

1) Fill in 0 for mussing variables (ex. x^3+X+2) 2) In synthetic division, leading coefficient must be 1 divide all equation by the a from ax Remainder is over the new divisor

Synthetic Division

1) drop, multiply, add

Given a graph, find the factors of the function

1. Determine the roots: -2, 3 2. Using synthetic division, make L number -2 3. Re-write answer 4. Using synthetic division, make L number 3 and divide the new answer 5. Final answer is the third factor (x+2) and (x-3) are the other two

Factor Theorem: Determine/Find the remaining factors of 2x⁴ - 5x² + 8x - 7/x+3

1. Divide using synthetic division 2. If the remainder is zero, x+3 is a factor 3. Re-write answer multiplied by x+3 4. factor the trinomial to get the other factors of 5x² + 8x - 7

Remainder Theorem: Find f(2) for f(x) =2x⁴ - 5x² + 8x - 7

1. Using synthetic division, make the L number 2 2. Solve, and the remainder should be the answer to f(2)

What does value (+ or -) of the leading coefficient mean?

It describes the direction of the far right arrow on on a function Ex. cubic graph has a positive leading coefficient because the far right arrow is up