What does a discriminate of more than 0 mean?

Two real and distinct roots.

What is the discriminat?

The b² -4ac part of a quadratic equation.

What does a discriminate equal to 0 mean?

There are two repeated roots.

What does a discriminate of less than 0 mean?

No real solutions.

What is a factor of a polynomial ?

An algebraic expression that divides the polynomial and leaves no remainder.

If f(x) is the polynomial and p(x) is the root then what is the quotient?

F(x)÷P(x) = q(x)

What is the order of a polynomial?

The highest power of X.

The no. of turning points is always one less than the highest power.

How are axes intercept of a polynomial found?

Substitute 0 as Y and X. When Y is 0 each bracket should equal 0.

What is the factor therem?

If f(a) = 0 then x-a is a factor. The converse is also true.

What is the remainder theorem ?

If x-a isn’t a factor of F(x) then f(a) =r which is the remainder.

When 2x³ +3x² + kx-6 is divided by x+1 the remainder is 7. How would you go about finding K?

F(-1)=7.

Replace x with -1 to get an expression with a K in it. It should equal 7 and so solve.

K=-12

What do you do when a polynomial has 2 unknowns and two different remainders are given?

Calculate the two equations by using on remainder in each. Then add the two equations together to find one of unknows.

What would y=f(x-a)+b do to a graph of y=f(x)?

A translation of a units right, along the X axis and B units up along the Y axis.

What would writing an equation in complete the square form mean?

Re arrange it so it is X plus a value in squared bracket and add something to the side.

How would you transform a graph of y=x²-4 by 2 to the right?

It would by y=f(x-2) so where you have an x, it becomes x-2.

(X-2)²-4