You can ad d or subtract m onom ials by adding or subtracting like term s.Th in k
W ill th e sum o f tw o
monomials always be
a monomial?
No. The m o n o m ia ls m ust
be like terms.
Why do you need to
combine like terms
in p a r t (B)?
To nam e a p o ly n o m ia l
correctly based on its
n u m ber o f term s, you
must first combine all
like terms.
Adding and Subtracting Monomials
What is the sum or difference?
©3x2 + 5x2 = 8x2 Combine like terms. 04x3y - x3y = 3x3y Combine like terms.Go t It? 2. W hat is th e sum —6x4 + l l x 4? W hat is th e difference 2x2y4 — 7x2y4?A polynomial is a m onom ial or a sum of m onom ials. I h e following polynom ial is the
sum of th e m onom ials 3x4 5 x 2 — 7x, an d 1.3x4 + 5x2 - 7x + 1
t T T tDegree o f each monom ial (^42 1 0)
I h e polynom ial show n above is in standard form. Standard form of a polynomial
m ean s th at th e degrees of its m o nom ial term s decrease from left to right. I h e degree
of a polynomial in o n e variable is th e sam e as th e degree of th e m o nom ial w ith the
greatest exponent. I h e degree of 3x4 + 5x2 - 7x + 1 is 4.
You can n am e a polynom ial b ased on its degree or th e n u m b er of m onom ials it contains.
Number
of Terms
5x+ 9
4x2 + 7x + 3
Linear Binomial
Quadratic
2x3 3 Cubic 1 Monomial
8X4 - 2x3 + 3x 4 Fourth degree^3 Trinomial
Trinomial
I C l a s s i f y i n g P o l y n o m i a l s
Write each polynomial in standard form. What is the name of the polynomial based
on its degree and number of terms?
0 3x + 4x2 0 4x - 1 + 5x3 + 7x
4x2 + 3x Place terms in order. 5x3 + 4x + 7x - 1 Place terms in order.
This is a q uadratic binom ial. 5 x 3 + llx — 1 Combine like terms.
This is a cubic trinom ial.
Go t It? 3. a. Write 2x - 3 + 8x2 in stan d ard form. W hat is th e n am e of the
polynom ial b ase d on its degree an d n u m b e r of term s?
b. Reasoning How does writing a polynom ial in stan d ard form help you
n am e th e polynom ial?
c
PowerAlgebra.com Lesso n 8-1 A d d i n g an d Su b t r act in g Po lyno m ials^487