Question

List all the given equations that are Polynomial? Not Polynomial?

a) 3a - 2 + 10a - 30 is Polynomial.
b) 8w - 30w + 12 is Not Polynomial.
c) 50m + 30m = 100 is Polynomial.
d) 23s^2 + 12s = 0 is Polynomial.
e) 5a + 2 = -3a - 2 is Not Polynomial.

Answer 1

All the equations listed, from a) 3a - 2 + 10a - 30 to e) 5a + 2 = -3a - 2, are polynomial equations upon simplification as they conform to the structure of variables with whole number exponents and numerical coefficients.

Step-by-step explanation:

To determine whether the given equations are polynomial or not, we need to examine their structure. A polynomial equation consists of variables raised to whole number exponents and their coefficients, without division by a variable or negative exponents.

• a) 3a - 2 + 10a - 30 can be simplified to 13a - 32, which is a polynomial because it has a variable 'a' raised to the first power (a whole number) with numerical coefficients.
• b) 8w - 30w + 12 simplifies to -22w + 12, and it is also a polynomial for the same reasons as above.
• c) 50m + 30m = 100 simplifies to 80m = 100, which is a polynomial because it has a variable 'm' raised to the first power.
• d) 23s^2 + 12s = 0 is a polynomial with terms including s squared and s to the first power, both of which are whole number exponents.
• e) 5a + 2 = -3a - 2 can be rewritten as 5a + 3a + 2 + 2 = 0, simplifying to 8a + 4 = 0, which is also a polynomial.

Therefore, all the given equations a) through e) are polynomials based on the definition of a polynomial equation.