which statement is true about the polynomial $-3x^{4}y^{3}+8xy^{5}-3 + 18x^{3}y^{4}-3xy^{5}$ after it has…
which statement is true about the polynomial $-3x^{4}y^{3}+8xy^{5}-3 + 18x^{3}y^{4}-3xy^{5}$ 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
Explanation:
Step1: Combine like terms
Combine (8xy^{5}-3xy^{5}=(8 - 3)xy^{5}=5xy^{5}). The polynomial becomes (-3x^{4}y^{3}+5xy^{5}-3 + 18x^{3}y^{4}).
Step2: Count the number of terms
The terms are (-3x^{4}y^{3}), (5xy^{5}), (-3), (18x^{3}y^{4}). So there are 4 terms.
Step3: Find the degree of each term
- For the term (-3x^{4}y^{3}), the degree is (4 + 3=7).
- For the term (5xy^{5}), the degree is (1+5 = 6).
- For the term (-3) (a constant term), the degree is (0).
- For the term (18x^{3}y^{4}), the degree is (3 + 4=7).
The highest degree among the terms is (7).
Answer:
It has 4 terms and a degree of 7.