Question

Which statement is true about the polynomial

Answer 1

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:

Option D: It has 4 terms and a degree of 7.

Explanation:

The given polynomial is $3x^4y^3+8xy^5-3+18x^3y^4-3xy^5$

We need to simplify the polynomial to determine the number of terms and the degree of the polynomial.

Hence, the simplified polynomial is given by

$3 x^{4} y^{3}+5x y^{5}-3+18 x^{3} y^{4}$

Term of a polynomial:

The term of a polynomial consists of a number multiplied by a variable or it may be a constant.

Thus, the simplified polynomial has 4 terms.

Degree of a polynomial:

The degree of a polynomial is the sum of exponents of the variables in a term.

Thus, the simplified polynomial has a degree of 7.

Hence, the polynomial has 4 terms and a degree of 7.

Therefore, Option D is the correct answer.