Is this a polynomial?
15x – 12 + 4x
I'm pretty sure it is a polynomial, am I right?
No.
A polynomial needs an exponent.
http://www.mathsisfun.com/algebra/polynomials.html
Okay, so if it was 15x^3 - 12 + 4x^3, then it would be a polynomial?
Yes. Only 1 exponent is needed for it to be a polynomial.
Wait, I just realized that 15x – 12 + 4x is a polynomial because the x is automatically x^1, so yeah. Also in the link you gave me it says that x - 2 and 3x are both polynomials. Therefore, it technically would be a polynomial.
Yes, you are correct. The expression 15x - 12 + 4x is indeed a polynomial.
To determine whether an expression is a polynomial, we need to understand its characteristics. A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication operations.
In the given expression, we have two terms: 15x and 4x. Each term contains a variable, x, raised to the power of 1, which is a non-negative integer exponent. Furthermore, the coefficients 15 and 4 are constants, which are considered to be polynomials of degree 0. The term -12 can also be considered as a constant multiplied by x^0, which is another polynomial of degree 0.
Since all the terms in the expression satisfy the criteria for a polynomial, we can conclude that 15x - 12 + 4x is indeed a polynomial. Its degree is 1 because the term with the highest exponent is x raised to the power of 1.