2. Polynomials and the binomial theorem

missing curve sketching

degree of a polynomial

highest power

steps to proving that x-1 is a factor of f(x) = 0

1) state if x-1 is a factor then f(1) = 0

2) show substitution of f(1)

3) calculate f(1)

4) state as f(1) = 0 , x-1 must be a factor of f(x)=0

remainder theorem

if polynomial P(x) is divided by x-a then the remander is P(a)

nCr =

n!/((n-r)! x r!)

in formula book

describe what nCr gives

the possible different combinations of choosing r things out of n things

eg how many different ways can a football team of r be picked from n players

identify the quotient and remainder and equate to original equation

quotient = x² + x + 3

remainder = 5

x³ - 2x² - 4 = (x- 3)(x² + x + 3) + 5

+ive odd degree polynomial starts in which quadrant

negative x and negative y

+ive even degree polynomial starts in which quadrant

negative x and positive y

describe the transformation y = f(x) + a

translation by vector

(0)

(a)

describe the transformation y = f(x+a)

translation by vector

(-a)

(0)

describe the transformation y = af(x)

stretch parallel to the y axis scale factor a

describe the transformation y = f(ax)

stretch parallel to the x axis scale factor 1/a