MTH 100
Introduction to Polynomial Functions
Objectives
1. Find the Degree and Coefficient of a
Monomial
2. Find the Degree and Leading Coefficient of a
Polynomial
3. Evaluate a Polynomial Function for a Given
Value
4. Add Polynomials
5. Subtract Polynomials
Objective 1
• 3x4 is a monomial. The degree is 4 and the
coefficient is 3.
• -6x is a monomial. The degree is (understood
to be) 1 and the coefficient is -6.
• 13 is a monomial. The degree is 0 and the
coefficient is 13 (a term without a variable is
called a constant term.
Objective 2
• 18 – 6x is a binomial. The degree is 1 and the
lead coefficient is -6.
• 6 – 3m3 + m4 – 7m2 – 5m6 is a polynomial. The
degree is 6 and the lead coefficient is -5.
• 20 + 5s + 4s5 is a trinomial. The degree is 5 and
the lead coefficient is 4.
Objective 3
• Recall that evaluating a function requires that
we substitute a given value from the domain
into the function rule.
• Find Q(-1) for Q(t) = t5 + 4t4 – 6t3 – 9t2 + t - 18
Objective 4
• Adding polynomials requires us to add
coefficients of terms that have the same
exponent:
(12p3 – 3p2 – 6p – 7) + (-6p3 + p2 + 2p – 5)
• When you add like terms, do not add the
exponents.
Objective 5
• To subtract polynomials, apply “keep-changechange”—that is, keep the first polynomial,
change the subtraction sign to addition,
change all the signs in the second
polynomial—then add.
(12y3 – 2y + 9) – (-5y3 – 5y2 + 3y – 11)