Expressions that are NOT monomials:
A polynomial is a sum of one or more monomials.
GATHERING LIKE TERMS
If the variable part of two monomials is the same, they're called like
terms. 3x and 5x are like terms but 3x and
5y are unlike terms; so are 5ab and
7ab2.
If two terms are "like" then you can add or subtract them. Notice the use
of the Distributive
Law:
3x + 5x = (3 + 5)x = 8x
We can keep the same letter part and add the coefficients (the numbers
in front of the variables).
But unlike terms can't be added: (The symbol ≠ means "not equal to.")
3x + 4y ≠ 7x or 7y or
7xy, and
6 + 5x ≠ 11x (multiply before adding).
This is important when simplifying polynomials.
Example:
6x2 + 5x + 4 – 4x2 +
7x – 8
First, collect the like terms.
= (6x2 – 4x2) + (5x +
7x) + (4 – 8)
Then simplify.
= 2x2 + 12x – 4
Say whether the given expression is a polynomial. If it is a polynomial, classify it as a monomial, binomial, or trinomial.
Say whether the given expression is a polynomial. If it is a polynomial, classify it as a monomial, binomial, or trinomial.
6 + 5x3
Say whether the given expression is a polynomial. If it is a polynomial, classify it as a monomial, binomial, or trinomial.
Say whether the given expression is a polynomial. If it is a polynomial, classify it as a monomial, binomial, or trinomial.
–11ab6 – 11
Say whether the given expression is a polynomial. If it is a polynomial, classify it as a monomial, binomial, or trinomial.
–55
Say whether the given expression is a polynomial. If it is a polynomial, classify it as a monomial, binomial, or trinomial.
–h3 – 4h + 9
What is the degree of the given monomial?
13b6
What is the degree of the given monomial?
–300w5
Express the given polynomial in standard form and identify it by its degree and the number of terms.
40m3
Express the given polynomial in standard form and identify it by its degree and the number of terms.
–11
Express the given polynomial in standard form and identify it by its degree and the number of terms.
–15 + 13y3
Express the given polynomial in standard form and identify it by its degree and the number of terms.
–2b2
+ 8b3
Rearrange the polynomial in descending powers of x, and state the degree.
Rearrange the polynomial in descending powers of x, and state the degree.
Rearrange the polynomial in ascending powers of x, and state the degree.
Fill in the blank with always, sometimes, or never.
Each term of a polynomial is  a monomial.
Fill in the blank with always, sometimes, or never.
The sum of two binomials is  a binomial.
Gather the like terms in 7x4 – 2x4 + 9.
Gather the like terms in 7x3 – 5 – 3x3.
Gather the like terms in 4a4 – 3a + a4 + 3a.
Gather the like terms in 5xy2 + 4x2y + 2x2y
– xy2.
Gather the like terms in 3ab2 + 4ab + 5ab2
– 6a2b.
Write a polynomial for the perimeter of the two given figures. Write the polynomial so obtained in the simplest form by gathering the like terms.
The sum of a number and 3 is multiplied by the number, and then 4 is subtracted from the result. Express the final result as a polynomial.
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