Chp 5 Math

x^a • x^b

x^a+b

x^a/x^b

x^a-b

x^-a =

1/x^a

1/x^-a

x^a

(xy)^a

x^ay^b

(x^a)^b

x^ab

(x/y)^a

x^a/y^a

_____ divided by the _____ = ______

Dividend, divisor, quotient

Do we put placeholders in final answers?

No

In synthetic division, the divisors number (Ex: x - 4) would come out to be …

4, or the opposite of the divisor's constant term.

Do we add or subtract in synthetic division?

Add

Do we add or subtract in long division?

Subtract

The last number in both long divisions are ??? & go where?

the remainder & on top of the of the divisor

2 equations for sum & differences of perfect squares

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

3 rules for s & d of perfect squares

Dont Double

NEVER FACTORABLE

What are the 3 way that will be used to solve a quadratic?

Factoring, Quadratic formula, completing squares

What are the 4 way that will be used to factor?

Pull out GCF, S&D of Perfect Cubes, Grouping, Quadratic Form

What can the degree of a solution tell you?

How many solutions there could possibly be.

End Behavior

Does the graph rise or fall in the right and left direction?

Even Degree

x²,x⁴,x⁶

Odd Degree

x³,x⁵,x⁷

Even Degree → + LC →

2 increases

Even Degree → - LC →

2 decreases

Odd Degree → + LC →

Up, down

Odd Degree → - LC →

Down, up

Even Degree → + LC → 2 increases

As x → - ∞. f(x) → + ∞

As x → + ∞. f(x) → + ∞

Even Degree → - LC → 2 decreases

As x → - ∞. f(x) → - ∞

As x → + ∞. f(x) → - ∞

Odd Degree → + LC → Down, up

As x → - ∞. f(x) → - ∞

As x → + ∞. f(x) → + ∞

Odd Degree → + LC → Up, down

As x → - ∞. f(x) → + ∞

As x → + ∞. f(x) → - ∞

Do we factor or simplify when plugging into f(x² + 2)?

NOOOOO

WHAT MUST U REMEMBER TO ADD WHEN MAKING POLYNOMIALS

F(X) AND IF ITS NEGATTIVE OR NOT

Will your final answer in exponents be perfect?

No, sometimes it requires a 1/wsiofhofihsd.

2x^-2y²z^-2

Convert to fraction

Multiplicity even

it touches the x-axis (not crossing it)

Odd multiplicity

it crosses the x-axis at the point of intersection.