POLYNOMIALS

POLYNOMIALS

1. DEFINITION: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

2. TYPES: MONOMIAL, BINOMIAL, TRINOMIAL

3. ZERO OF A POLYNOMIAL: A zero or root of a polynomial function is a number that, when plugged in for the variable, makes the function equal to zero

4. THEOREMS:

   • REMAINDER THEOREM: The remainder theorem is based on synthetic division, which is the process of dividing a polynomial f(x) by a polynomial D(x) and finding the remainder.
     • FACTOR THEOREM:The theorem states that isa factor of a polynomial f(x)if ;that is, r is a root of f(x). ... If , then the remainder is 0 and , showing that is a factor of f(x).

5. IDENTITIES: (a+b)2 = a^2 + 2ab + b^2 2. (a-b)2 = a^2 - 2ab + b^2 3. (a+b) (a-b) = a^2 -b^2 4. (x + a)(x + b) = x^2 + (a + b) x + ab 5.(a + b)^3 = a^3 + b^3 +3ab (a + b) 6. (a - b)^3 = a^3 - b^3 - 3ab (a - b) 7.(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy +2yz + 2xz 8. x^3 + y^3 + z^3 - 3xyz = (x + y + z) (x^2 + y^2 + z^2 - xy - yz -xz) 9. x^3 + y^3 = (x + y) ( x^2 - xy + y^2) 10. x^3 - y^3 = (x - y) ( x^2 + xy + y^2) 11.