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22 Cards in this Set

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The order of a polynomial is determined by?

The highest power of x

Powers

The coefficient proceeding the highest power of x is known as?

The lead coefficient

Follow the...

Any coefficient can take any value save for this exception.

The lead coefficient can not be 0

Lead coefficient

A positive or negative lead coefficient corresponds with the polynomial being classified as?

Positive or negative respectively

Reread the question

How are polynomials added or subtracted?

By adding or subtracting like terms (same order of x)

X and x

How are polynomials multiplied?

Each term of the first polynomial is multiplied by each term of the second. The products are then added to combine like terms.

Think dot product

When are two polynomials equal?

They share the same coefficients and the same orders of x.

Identity property?

The remainder theorem says that

when f(x) is divided by (x-p) the remainder is given by f(p)

The factor theorem says that

if f(p)=0 then (x-p) is a factor

f(x) divided by g(x) can be written using a quotient and a remainder as

f(x)/g(x) = q(x) + r/g(x)

To solve any polynomial you need to

factorize and set the function equal to zero



LISA stands for

Label, Intercepts, Stationary points, Asymptotes

A turning point

location of a local maximum or minimum

The maximum number of turning points of a polynomial is

one less than the degree

A repeated root is means there is less turning points than the maximum number. A repeated root is represented as

a flattening of the 'vertex' in an even repeated root, a flattening of the 'inflection' point in an odd repeated root.

To find the equation of a polynomial from its graph don't forget this at the front of the factored form

a as the coefficient of the lead term. You would divide zero by this when solving so we must remember that it is there when we go backwards

b^2-4ac

discriminant

If discriminant is more than zero

quadratic function has two real roots

If discriminant is equal to zero

quadratic function has one repeated root

If a quadratic function has no real roots, the discriminant is

negative

If a quadratic is positive for all x then the discriminant is

negative

If a quadratic is negative for all x then the discriminant is

negative