can someone correct these also for me..
Which of the following is not a polynomial?
a) 24
b) 4x^3+5x-1
c)2x-(1)/(x)
d)3xy^2+xy
MY answer is: A
Simplify. write your answer with only positive exponents
(y^5)/(y^10)
Possible answers:
a)y^2
b)(1)/(y^2)
c)(1)/(y^5)
d) y^5
My answer: c
all correct.
excellent....thank you bobpursley
To solve the first question, which asks which of the following is not a polynomial, let's start by understanding what a polynomial is. A polynomial is an expression consisting of variables (such as x and y) and constants (like 1, 2, 3) combined using arithmetic operations (addition, subtraction, multiplication) and non-negative whole-number exponents.
a) 24: This is a constant, and a constant can be considered a polynomial since it can be expressed as the sum of powers of x with all coefficients equal to 0 (24 = 0x^2 + 0x + 24). So, this is a polynomial.
b) 4x^3 + 5x - 1: This is a polynomial since it is a combination of terms with non-negative whole-number exponents.
c) 2x - 1/x: This is not a polynomial because it contains a term with a negative exponent (1/x), and negative exponents are not allowed in polynomials.
d) 3xy^2 + xy: This is a polynomial since it is a combination of terms with non-negative whole-number exponents.
Therefore, the correct answer is c) 2x - (1/x).
Moving on to the next question, which asks to simplify (y^5)/(y^10) and write the answer with only positive exponents:
To simplify the division of two exponents with the same base, you subtract the exponent in the denominator from the exponent in the numerator. In this case, we have y^5 divided by y^10.
Subtracting the exponent 10 from 5, we get y^(5-10), which simplifies to y^(-5).
Since we want the answer with positive exponents, we can rewrite y^(-5) as 1/(y^5).
So, the correct answer is c) (1)/(y^5).
I hope this explanation helps you understand the process of solving these questions!