Question

True or false:

A linear binomial has a degree of 0

A trinomial has a degree of 2

A constant has a degree of 1

A cubic monomial has a degree of 3

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Answer 1

A linear binomial has a degree of 1, not 0. A trinomial can have a degree of 2 if the highest degree of the variable is 2. A constant has a degree of 0 because it does not contain any variable. A cubic monomial has a degree of 3.

Step-by-step explanation:

A linear binomial is a polynomial with two terms. The degree of a term in a polynomial is the exponent of the variable in that term. In a linear binomial, the highest degree of the variable is 1. Therefore, a linear binomial has a degree of 1, not 0.

A trinomial is a polynomial with three terms. The degree of a trinomial is determined by the highest degree of the variable among the terms. So, if the highest degree of the variable is 2, then the trinomial has a degree of 2.

A constant is a polynomial with only one term, and that term does not contain any variable. Since a term with no variable has a degree of 0, a constant has a degree of 0.

A cubic monomial is a polynomial with one term and a degree of 3. The term contains a variable raised to the power of 3, which gives it a degree of 3.

Answer 2

The degree of a binomial is zero. The product of two binomials is not a polynomial. The sum of two polynomials is a polynomial. A monomial containing ^2 has a degree of three

The degree of the polynomial is found by looking at the term with the highest exponent on its variable(s). Examples: 5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.

Names of Degrees

Degree Name Example

0 Constant 7

1 Linear x+3

2 Quadratic x2−x+2

3 Cubic x3−x2+5

The degree of a cubic monomial is three. A quadratic polynomial is a trinomial. The degree of a binomial is two.

Step-by-step explanation: