Graphs
Sketching Polynomials
● Factorise the expression as much as possible to give the x-intercepts
● Set x equal to 0 and find the y-intercept
● Consider what happens as x tends towards ±∞
● Make sure the graph is the right way up
Finding the Equation of a Polynomial Curve
● Often given roots
● Write equation in factorised form using roots
● Expand to give final equation of curve
● Same goes for looking at graph → find the roots and write equation in
factorised form
Factor Theorem
● If (x – a) is a factor of f(x) then f(a) = 0 and x = a is a root of the equation
f(x) = 0
● We can use this to deduce solutions for polynomial equations
● If given a number to test to see if it is a root, plug number into function and
if this gives zero then that number is a root
● Special instance of remainder theorem → the answer to f(a) is the
remainder of dividing the polynomial by (x – a)