4.3 Polynomials

• Monomial: 1 term (axn with n is a non-negative integers)

Ex: 3x, -3, or 4y2

• Binomial: 2 terms

Ex: 3x - 5, or 4y2 + 3y

• Trinomial: 3 terms

Ex: 4x2 + 2x - 3

• Polynomial: is a monomial or sum of monomials

Ex: 4x3 + 4x2 - 2x - 3 or 5x + 2

Identify monomial, binomial, trinomial, or none

None (polynomial)4x3 + 4x2 - 2x - 3

trinomial-2x2 - 2x +1

binomial4 + (1/2)x

monomial3x2

binomial-2x + 4

monomialx4

• Term: each monomial of the polynomial

• Degree: exponents

• Degree of polynomial: highest exponent

• Coefficient: number in front of variables

• Constant term: the term without variable

• Missing term: the term that has 0 as its coefficient 0

• Ex: -3x4 – 4x2 + x – 1Term: -3x4 , – 4x2 , x, – 1Degree 4 2 1 0Coefficient -3 -4 1 -1Degree of this polynomial is 4Constant term: is -1Missing term (s): is x3

• Descending order: exponents decrease from left to right

• Ascending order: exponents increase from left to right

• When working with polynomials, we often use Descending order

• Arrange in descending order using power of x

1) -6x2 – 8x6 + x8 + 3x - 4

= x8– 8x6 - 6x2 + 3x - 4

Missing terms are: x7, x5, x4, x3

2) 5y2 + 4y + 2y4 + 9

= 2y4 + 5y2 + 4y + 9

Missing terms are: y3

Collecting Like Terms

• Like terms:4x and 3x

5xy and -6xy

2x2 and x2

When add or subtract like-term, add or subtract only the coefficients of the terms, keep the same variables

1) -6x4 – 8x3 + 3x - 4 + 5x4 + x3 + 2x2 -7x

= -6x4 + 5x4 – 8x3 + x3 + 2x2 + 3x -7x -4

= -x4 - 7x3 + 2x2 - 4x -4

2) -6x4 – 8x3 + 3x - 4 - 5x4 - x3 - 2x2 +7x

= -6x4 - 5x4 – 8x3 - x3 - 2x2 + 3x +7x - 4

= -11x4 - 9x3 - 2x2 +10x -4