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Chapter 7: Q24. (page 430)

Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial.

4t5+3t2+t

Short Answer

Expert verified

The given expression4t5+3t2+t is a polynomial. The given polynomial4t5+3t2+t is a trinomial.

Step by step solution

01

Step 1. Write the definition of the polynomial.

A monomial is a number, a variable or the product of a number and one or more variables with non-negative integer exponents. The monomial has only one term.

A polynomial is a monomial or the sum of monomials, each called a term of the polynomial.

The polynomial having only one term is called a monomial.

The polynomial having two terms is called a binomial. That is binomial is sum of two monomials.

The polynomial having three terms is called a trinomial. That is trinomial is sum of three monomials.

02

Step 2. Determine whether each expression is a polynomial.

The given expression is4t5+3t2+t.

It can be noticed that each term of the given expression is a variable or the product of a number and one variable with non-negative integer exponents.

Therefore, each term of the given expression is a monomial.

As, the given expression is the sum of the monomials. Therefore, the given expression is a polynomial.

03

 Step 3. Identify the polynomial as a monomial, binomial, or trinomial.

The given expression is a polynomial having three terms that is the given polynomial is sum of three monomials.

Therefore, the given polynomial 4t5+3t2+tis a trinomial.

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Most popular questions from this chapter

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Mickey has 180feet of fencing that she wants to use to enclose a play area for her puppy. She will use her house as one of the sides of the region.

  1. If she makes the play areaxfeet deep as shown in the figure, write a polynomial in standard form to represent the area of the region.
  2. How many square feet of area will the puppy have to play in if Mickey makes it 40 feet deep?

Express the area of a square with sides of length3xy2as a monomial.

Write three different expressions that can be simplified tox6.

Determine whether the given expression is a monomial or not.

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Express each number in standard form.

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