State whether each expression is a polynomial. If the expression is a polynomials, identify it as a monomial,a binomial, or a trinomials.
1.7a^2b+3b^2-a^2b
2.1/5y^3+y^2-9
3.6g^2h^3k
Are these the right answers?
1.Yes-trinomials
2.No
3.Yes- monomials.
To determine whether an expression is a polynomial, we need to check if it meets the criteria of a polynomial. A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with no division by a variable.
Let's break down each expression:
1. 7a^2b + 3b^2 - a^2b
This expression contains variables (a and b) combined with coefficients (7, 3, and 1). We can combine like terms (terms with the same variable and exponent) to simplify it: (7a^2b - a^2b) + 3b^2 = 6a^2b + 3b^2.
This expression is a polynomial. Furthermore, since it contains three terms, it is called a trinomial.
2. 1/5y^3 + y^2 - 9
This expression contains a variable (y) combined with coefficients (1/5 and -9), but it also contains a division by a variable (1/5y^3), which violates the criteria for a polynomial. Therefore, this expression is not a polynomial.
3. 6g^2h^3k
This expression contains variables (g, h, and k) combined with a coefficient (6), but there is no addition, subtraction, or division by a variable. Therefore, it is considered a polynomial. Furthermore, since it contains only one term, it is called a monomial.
So the correct answers are:
1. Yes, trinomial
2. No, not a polynomial
3. Yes, monomial