Question

Which statement is true about the polynomial
–3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified?

It has 3 terms and a degree of 5.
It has 3 terms and a degree of 7.
It has 4 terms and a degree of 5.
It has 4 terms and a degree of 7.

Answer 1

The correct answer among the choices given is the last option. When it has been simplified, it has 4 terms and a degree of 7. For polynomials having to or more variables, degree can be of a term or of the polynomial. The degree of a term is the sum of the exponents in a specific term.

 –3x^4y^3 + 8xy^5 – 3 + 18x^3y^4 – 3xy^5
 –3x^4y^3 + 5xy^5 – 3 + 18x^3y^4

Answer 2

The true statement about the polynomial –3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified will be "It has 4 terms and a degree of 7".

What is a polynomial?

They are mathematical expressions involving variables raised with nonnegative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and nonnegative exponentiation of variables involved.

Example:

x^2 + 3x + 5 is a polynomial.

The simplification is as follows;

 $-3x^4y^3 + 8xy^5 - 3 + 18x^3y^4 - 3xy^5\\\\-3x^4y^3 + 5xy^5 - 3 + 18x^3y^4$

Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.

When it has been simplified, it has 4 terms and a degree of 7. The degree of a term is the sum of the exponents in a specific term.

Therefore, The true statement about the polynomial –3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified will be "It has 4 terms and a degree of 7".

Learn more about polynomials here:

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