Adding and Subtracting 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 polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = (3 + 4)x^2 + 2x + 5 = 7x^2 + 2x + 5.

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

What is the process for subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 2x) - (x^2 + 5) = (3x^2 - x^2) + 2x - 5 = 2x^2 + 2x - 5.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

Front

How do you simplify the expression -4(9 + 3x) - 4(x - 2)?

Back

Distribute the -4: -36 - 12x - 4x + 8 = -16x - 28.

Front

What is the result of adding (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

Combine like terms: (4x^4 + 7x^4) + (-3x^2 + 5x^2) + (6x + 8x) = 11x^4 + 2x^2 + 14x.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors. For example, x^2 - 9 can be factored as (x - 3)(x + 3).