Answer :

The expression [tex]12x^3 + 7x^2 - 4x - 19[/tex] is a polynomial with four terms: [tex]12x^3, 7x^2[/tex], -4x, and -19. Each term is separated by addition or subtraction, and they can be simplified or evaluated individually. Recognizing the number of terms helps in performing operations on the polynomial.

The expression [tex]12x^(3) + 7x^(2) - 4x - 19[/tex]is a polynomial. A polynomial is an algebraic expression consisting of one or more terms. In this case, the expression has four terms:

1. [tex]12x^(3)[/tex] - This term is a monomial because it consists of a coefficient (12) multiplied by a single variable (x) raised to a power (3).
2. [tex]7x^(2)[/tex] - This term is also a monomial, with a coefficient of 7 and a variable (x) raised to the power of 2.
3. -4x - This term is a monomial as well, with a coefficient of -4 and a variable (x) raised to the power of 1 (which is often understood but not written explicitly).
4. -19 - This term is a constant, as it does not contain any variables.

So, there are four terms in the expression [tex]12x^(3) + 7x^(2) - 4x - 19[/tex].

It's important to note that the terms in a polynomial are separated by addition or subtraction symbols, and each term can be simplified or evaluated separately. Understanding the number of terms in an expression helps in performing operations like simplification, addition, and subtraction.

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