Polynomials
Classifying, Adding, Subtracting,
MultiplyingPolynomialsMonomials in one variableThe product of a
constant and a variable raised to a nonnegative integer power.
2x42 is the coefficientdegree is 4
What does it mean to be raised to a nonnegative integer
power?
The degree of a monomial is found by adding the exponents
together!Monomials:CoefficientDegree6x2Yes 6 33x1/2 Yes 3 1 -(2)
x34x-33-5xx4Like TermsTwo monomials with the same variable raised
to the same power.
2x4 and -5x4 are like terms
Add or subtract like terms using the distributive property.2x4 +
5x4 = (2 + 5)x4 = 7x42x4 - 5x4 = (2 - 5)x4 = -3x4
Polynomial:A monomial or the sum of monomials
Terms are the monomials that make up the polynomial.2x2yone term
monomial2x2y + 5two termsbinomial5x2 3x + 10 three
termstrinomial2x5 + 3x3 -6x + 9four termspolynomial (or more) with
4 termsDegree of a PolynomialThe largest exponent of the polynomial
is the degree if the polynomial has only one variable.5x2 3x +
10degree is 2
The coefficient of the term with the highest exponent is the
leading coefficient.5x2 3x + 10leading coefficient is 5
Name the type of Polynomial.CoefficientsDegree3x2 -5Bi 3 29y3
2y2 + 3 3 Poly. 9 31/xZ5 + (x2+1)/(x+5)5x + 230Zero Polynomial and
Standard FormZero Polynomial: If all the coefficients are zero, the
polynomial is called the zero polynomial.
Standard form: Polynomials are usually written in standard form,
beginning with the nonzero term of highest degree and continuing
with terms in descending order according to degree.2x5 + 4x4 3x3
2x2+ 6x + 9
Adding PolynomialsFind the sum of (8x3 2x2 + 6x 2) and (3x4 2x3
+ x2 + x).
Subtracting PolynomialsFind the difference:(3x4 - 4x3 + 6x2 1)
(2x4 - 8x2 - 6x +5)Multiplying PolynomialsMay use the distributive
property, FOIL, or Box methodFind the product:a. (x + 3)(x + 1) b.
(2x + 1)(3x + 4)
Find the product:c. (2x + 5)(x2 - x + 2) d. (x2 + 5x 4)(x2 3x +
2)Dividing PolynomialsFind the quotient:a. 3x3 4x2 7xb. 4x4 8x3 2x2
- 16 x 2x
a. Answer: 3x2 4x - 7
