polynomials

Polynomials have exponents which are _________

whole numbers

If a polynomial has a degree n, and n is even, then the polynomial can have _______ intersection points with the x-axis and will have a maximum of _______ turning points

0 to n, n-1

If a polynomial has a degree n, and n is odd, then the polynomial can have _______ intersection points with the x-axis and will have a maximum of _______ turning points

1 to n, n-1

If a solution is repeated ___ times it is said to have a multiplicity of ___

n, n

x = a is a _____, _______, ______ of the function f(x)

solution, zero, root

(x-a) is a ______ of the function f(x)

factor

(a, 0) is a ______ of the function f(x)

x-intercept

Remainder Theorem

If P(x) is divided by (x-a), then the remainder is P(a)

Factor Theorem

• P(x) has a factor by (x-a) if, and only if, P(a) = 0

• If P(a) = 0 then (x-a) is a factor

• If (x-a) is a factor then P(a) = 0

Rational Roots Theorem

± factors of constant term / ± factors of lead coefficient

Explain the behaviour/role of a & e:
y = ax⁴ + bx³ + cx² + dx + e

• a is the coefficient of the polynomial, it also determines if it’s negative or positive

• e is the y-intercept, it determines where the polynomial starts on the y-axi