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 a polynomial?

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 find the perimeter of a rectangle?

Back

The perimeter of a rectangle is found by adding the lengths of all four sides, or using the formula P = 2(length + width).

Front

What is the formula for the perimeter of a rectangle with width w and length l?

Back

P = 2(w + l) or P = 2l + 2w.

Front

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

Back

Combine like terms: 4a^3 + 7a^3 = 11a^3, -4a^2 remains, -8a - 6a = -14a, and -7 remains. The simplified expression is 11a^3 - 4a^2 - 14a - 7.

Front

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

Back

The result is 2a + 5ab + 2b after combining like terms.

Front

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

Back

The result is -4x + y + 6z after combining like terms.

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 3x^2 + 2x + 1, the degree is 2.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 5x^2, 5 is the coefficient.