Chapter 4 Flashcards
(12 cards)
What is a polynomial?
Function made up of a sum of terms which has non-negative integer powers of an unknown e.g. x.
What is the degree of a polynomial?
The highest power of an unknown occurring in the function.
Give an example of a constant function and state it’s degree.
f(x) = a.
0.
What is a coefficient.
Number before an unknown e.g. a in ax.
Define leading coefficient.
Coefficient of the highest power in the function.
Define leading order term.
Term containing highest x power.
How do you perform polynomial division?
.Divide LOT in numerator by LOT in denominator.
.Multiply this by whole denominator and subtract this from numerator.
.repeat until all terms accounted for.
What is the factor theorem?
(x-a) is a factor of f(x) if and only if f(a) = 0 or (ax-b) is a factor if and only if f(b/a) = 0
How many roots for a quadratic, cubic and quartic graph?
.0,1,2.
.1,2,3.
.0,1,2,3,4.
What happens if there is (x-a), (x-a)^2 and (x-a)^3?
.Passes straight through.
.Touches the axis.
.Flattens as it passes through.
How do you sketch a graph of a polynomial?
.Basic shape.
.Find y-intercept.
.Factorised form if possible.
.X-intercepts.
.How curve meets x-axis.
.Draw in a smooth curve.
How do you find the equation from a graph?
.Write down factors.
.Use other points given for the constant factor.
