Add & Subtract Polynomials Math Notebook & Pencil

Monomial Number, a variable, or the product of a number and one or variables with whole number exponents. The degree of a monomial is the sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0. The constant 0 does not have a degree.

Examples MonomialDegree 100 3x1 3x^22 3x^1010

Not a Monomial Reason 5 + xA sum is not a monomial 2/nCannot have a variable in denominator 4^aCannot have a variable exponent

Polynomial A monomial or a sum of monomials, each called a term of the polynomial. The degree of a polynomial is the greatest degree of its terms.

Leading Coefficient When a polynomial is written so that the exponents of a variable decrease from left to right, the coefficient of the term is called a leading coefficient 2x^3 + x^2 -5x +12 Leading coefficient

Re-writing a Polynomial Write 15x-x^3 + 3 so that the exponents decrease from left to right. Label your leading coefficient, degree and constant.

Classifying Polynomials A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial.

Examples Is this a polynomial? What degree? Let’s look at 6n^4 -8^n

Adding Polynomials (2x^3 – 5x^2 + x) + (2x^2 + x^3 - 1) Solution: Vertical Format: If a particular power of a the variable appears in one polynomial but not the other, leave a space in that column, or write the term with a coefficient of 0

Degree and Leading Coefficient Write 5y-2y^2 +9 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.

Let’s Try (3x^2 +x-6) + (x^2 +4x + 10)

Let’s Try (4n^2 +5) – (-2n^2 +2n -4)

Let’s Try (4x^2 -3x+5) – (3x^2 –x- 8)