polynomials (y1)

polynomials

finite expressions with positive whole number indices (powers)

polynomials: 2x²+3, 8xy-x+6

not polynomials: √5, x^-2, 4/x, 5/3

dividing polynomials

the use of long division to divide polynomials by (x±k)

-ensure the polynomial is arranged in descending order of degree of power

-divide the first term of the polynomial by x, append this to the solution

-multiply the result by (x±k)

-subtract the result from the original polynomial

-repeat this until the original polynomial is reduced to 0 or an integer remainder which is appended to the solution

expanding brackets

when mutiple polynomials in brackets are multiplied together, each term must be multiplied by each term in the other bracket(s)

factor theorem

for a polynomial f(x), if f(p) = 0, then (x-p) is a factor of f(x)

factorising polynomials

you can factorise a cubic polynomial by finding p where f(p) = 0 and dividing f(x) by (x-p)

the result of this should be factorised further if possible