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Chapter 5: Q. 487 (page 564)

For the polynomial 8y4-3y2+1.

(a) Is it a monomial, binomial, or trinomial?

(b) What is its degree?

Short Answer

Expert verified

Part (a) The given polynomial is a trinomial.

Part (b) The degree of the polynomial is 4.

Step by step solution

01

Part (a) Step 1. Given information.

The given polynomial is:

8y4-3y2+1

02

Part (a) Step 2. Determine the type of polynomial.

Monomial: A polynomial with exactly one term is called a monomial.

Binomial: A polynomial with exactly two terms is called a binomial.

Trinomial: A polynomial with exactly three terms is called a trinomial.

The given polynomial has exactly three terms. So, it is a trinomial.

03

Part (a) Step 3. Conclusion.

The given polynomial is a trinomial.

04

Part (b) Step 1. Given information.

The given polynomial is:

8y4-3y2+1

05

Part (b) Step 2. Determine the degree of the polynomial.

The degree of a polynomial is the highest degree of all its terms.

The terms in the given polynomial are 8y4,3y2and 1.

The highest degree of these terms is 4. So, the degree of the polynomial is 4.

06

Part (b) Step 3. Conclusion.

The degree of the polynomial is 4.

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