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 [tex]3x^4y^3+8xy^5-3+18x^3y^4-3xy^5[/tex]
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
[tex]$3 x^{4} y^{3}+5x y^{5}-3+18 x^{3} y^{4}$[/tex]
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.
