Final answer:
a) The degree of the polynomial - 5x ^ 5 - 6x ^ 4 - 8x ^ 2 4 is 5. b) The algebraic expression x^3 + 1/(x^3) - 2x + 1 is a polynomial. c) The polynomial sqrt(x^4) * 4x + 1 is not a quadratic trinomial.
Step-by-step explanation:
a) The degree of polynomial - 5x ^ 5 - 6x ^ 4 - 8x ^ 2 4.
The given polynomial is - 5x^5 - 6x^4 - 8x^2 + 4.
The degree of a polynomial is the highest power of the variable.
In this polynomial, the highest power is 5, so the degree of the polynomial is 5.
b) The algebraic expression is a polynomial. x ^ 3 + 1/(x ^ 3) - 2x + 1
The given algebraic expression is x^3 + 1/(x^3) - 2x + 1.
A polynomial is an algebraic expression with one or more terms, where each term is a constant multiplied by a variable raised to a non-negative integer exponent.
In this expression, all the terms are of the form x^n, where n is a non-negative integer. So, the given algebraic expression is a polynomial.
c) The polynomial is a quadratic trinomial. sqrt(x ^ 4) * 4x + 1
The given polynomial is sqrt(x^4) * 4x + 1.
A quadratic trinomial is a polynomial with three terms and the highest power of the variable is 2.
In this polynomial, the highest power of the variable is 4, not 2. So, the given polynomial is not a quadratic trinomial.