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 does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions to form a new polynomial.

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 and 5x are like terms.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part unchanged.

Front

What is the degree of a polynomial?

Back

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

Front

What is the sum of (x - 2) and (x^2 + 3)?

Back

The sum is x^2 + x + 1.

Front

How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

The simplified expression is 11a^3 - 4a^2 - 14a - 7.

Front

What is the result of adding (2x + 5y - z) and (-6x - 4y + 7z)?

Back

The result is -4x + y + 6z.

Front

What is the sum of (4a + 6ab - b) and (-2a - ab + 3b)?

Back

The sum is 2a + 5ab + 2b.

Front

What does distributing a negative sign mean in polynomials?

Back

Distributing a negative sign means to multiply each term inside the parentheses by -1. For example, -3(x - 4) becomes -3x + 12.