Find the quotient of n(x) = 6x^5y^7 and m(x) = 2x^3y
1 answer:
Answer:
a. Yes
b. Yes
c. Yes
d. Degree 8
Step-by-step explanation:
a. Yes, n(x) is a polynomial of one single term (also called monomial) because it contains variables raised to positive integers.
b. Yes, m(x) is a polynomial of also one single term (also called monomial) because it contains variables raised to positive integers.
c. The quotient of n(x) / m(x) can be reduced to a polynomial of one single term as follows:
which as can be seen, also contains variables raised to positive integers.
d. The degree of the polynomial resultant is the addition of the powers of all variables present (x and y) which results in: 2 + 6 = 8
Therefore the degree of this polynomial is 8.
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Question:
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to .
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
5n = 3d and n - 2 = 2d - 4
5n = 3d and 2n - 4 = d - 2
3n = 5d and 2n - 4 = d - 2
Answer:
5n = 3d and 2n – 4 = d – 2
Solution:
Let n be the numerator of the fraction and d be the denominator of the fraction.
Given the numerator and denominator of a fraction are in the ratio of 3 to 5.
This can be written as n : d = 3 : 5.
⇒ – – – – (1)
Do cross multiplication, we get
⇒ 5n = 3d
When the numerator and denominator are decreased by 2, the fraction is equal to .
⇒
Do cross multiplication, we get
⇒ 2(n –2)=1(d – 2)
⇒ 2n – 4 = d – 2
Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.