Math 112 Polynomials Notes

Variable

A symbol that we can assign values to

→ x, y, z, t, w

Expressions with both variables & constants

→ ex: ax²

• a = constant (fixed)

• x = variable (changing)

constants: a,b,c,d

Monomial

Is an expression of the form a^n

• a = real number

• n = non negative whole number

example: 1 * x^0 = 1, 4*x², 75x^100

Binomial

Is two monomial terms added together

example: x+5, 3x² +2x

Polynomial

is an expression made up on finitely many constants and integer powers of a variable

Example: 7x^4 + 3x³ +7, 5x³+70x

Degree of Polynomial

Is the highest power that appears in the expression

Example → 3x^4 + 3x² (4 is the highest power)

Coefficients

Constants multiplying the powers of the variable

Leading Coefficients

Is the coefficients corresponding to the highest power

Constant Term

Is a coefficient with no powers of variable

ex: 3x²+x

Adding Polynomials

Combining like terms

Multiplying Polynomial

Two distributions of the terms of each polynomial then add like terms

Difference of squares

(A + B)(A-B) = A²-B²

Square of a sum

A²+2AB+B²

Square of a difference

(A-B)(A-B)=A²-2AB+B²