Adding Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What are the degrees of the polynomials in the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

The degrees of the polynomials are 3 for 4a^3 and 7a^3, 2 for -4a^2, and 1 for -8a and -6a.

Front

How do you combine like terms in a polynomial?

Back

To combine like terms, identify terms that have the same variable raised to the same power and add or subtract their coefficients.

Front

What is the result of adding the polynomials (-3x + 4) and (8x - 5)?

Back

The result is 5x - 1.

Front

What is the process for adding two polynomials?

Back

To add two polynomials, align like terms and combine their coefficients.

Front

What is the degree of the polynomial 4x^3 - 6x^2 + 4x + 2?

Back

The degree of the polynomial is 3, which is the highest exponent of the variable x.

Front

What is the simplified form of the expression (x³-2x²+3)+(2x³+3x²-1)?

Back

The simplified form is 3x³ + x² + 2.

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degrees.

Front

What is the coefficient of the term 7n^3 in the polynomial 7n^3 + 6?

Back

The coefficient of the term 7n^3 is 7.

Front

How do you identify the leading term of a polynomial?

Back

The leading term of a polynomial is the term with the highest degree when the polynomial is in standard form.