Adding Polynomials

Front

What are like terms?

Back

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

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable. For example, 3x + 5x = (3+5)x = 8x.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 is a polynomial.

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 - x, the degree is 3.

Front

What is the sum of two polynomials?

Back

The sum of two polynomials is found by combining like terms from both polynomials. For example, (2x^2 + 3x) + (4x^2 + 5) = (2+4)x^2 + 3x + 5 = 6x^2 + 3x + 5.

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, and 3x + 2 is a polynomial.

Front

How do you simplify the expression (5x + 2) + (4x + 5)?

Back

Combine like terms: (5x + 4x) + (2 + 5) = 9x + 7.

Front

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

Back

Combine like terms: (4x^3 - 2x^3) + (-5x^2 - x^2) + (3x + 6x) = 2x^3 - 6x^2 + 9x.

Front

What is the perimeter of a rectangle with length x and width 8?

Back

The perimeter P is given by P = 2(length + width) = 2(x + 8) = 2x + 16.

Front

How do you combine the terms 3w - 8k + 12w + w - 5k?

Back

Combine like terms: (3w + 12w + w) + (-8k - 5k) = 16w - 13k.