which of the following are not polynomials?
A. x^4+ πx^3+√2x
B. 3x+x^4
C. 4x^3+2x^2+ √x
D. 2x^3/5-x/3+π
E.x/4-5/x+10
To determine which expressions are not polynomials, we need to understand the definition of a polynomial.
A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. The exponents must be non-negative integers.
Now, let's analyze each option:
A. x^4+ πx^3+√2x: This expression is a polynomial because all the exponents are non-negative integers.
B. 3x+x^4: This expression is a polynomial because all the exponents are non-negative integers.
C. 4x^3+2x^2+ √x: This expression is not a polynomial because the exponent in the term √x is not a non-negative integer.
D. 2x^3/5-x/3+π: This expression is not a polynomial because it contains division (2x^3/5, x/3), which is not allowed in polynomials.
E. x/4-5/x+10: This expression is not a polynomial because it contains division (x/4, 5/x), which is not allowed in polynomials.
So, the expressions that are not polynomials are option C (4x^3+2x^2+√x), option D (2x^3/5-x/3+π), and option E (x/4-5/x+10).