The polynomial that represents the sum of the expressions is 3x^2 + 5x – 2.
To arrive at this polynomial, you simply add the like terms of the given expressions. The coefficients of x^2 terms combine, as do the x terms and the constant terms.
For example, if you have two polynomial expressions such as (2x^2 + 5x – 1) and (x^2 + 3x – 1), you add them together. The x^2 terms add up to 3x^2, the x terms to 8x, and the constant terms to -2.
Careful organization is key when adding polynomials. Always align similar terms to avoid confusion. This method ensures that you don’t overlook any part of the equations.
If you encounter more complex polynomials, break them down into smaller parts. It makes addition much easier and reduces the chance of errors.
Remember to simplify your final result. A polynomial is often most useful when it’s expressed in its simplest form.
What are polynomials?
Polynomials are mathematical expressions that consist of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents.
How do you add polynomials?
To add polynomials, align like terms and combine their coefficients. This process follows the basic principles of arithmetic.
What is a like term?
A like term is a term that has the same variables raised to the same powers. For instance, 2x^2 and 3x^2 are like terms.
Can polynomials have negative exponents?
No, polynomials cannot have negative exponents. They must only include non-negative integer exponents.
What is the degree of a polynomial?
The degree of a polynomial is the highest exponent of the variable in the expression. For example, in 4x^3 + 2x^2, the degree is 3.
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