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. For example, 3x^2 + 2x + 1 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. Like terms have the same variable raised to the same power.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same exponent. For example, 2x^2 and 3x^2 are like terms.

Front

How do you add the polynomials (3x^2 + 2x + 1) and (2x^2 - 4x - 5)?

Back

Combine like terms: (3x^2 + 2x + 1) + (2x^2 - 4x - 5) = (3x^2 + 2x^2) + (2x - 4x) + (1 - 5) = 5x^2 - 2x - 4.

Front

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

Back

Combine like terms: (3x^3 + x^3) + (3x^2 - 2x^2) + (-4x + x) + (5 - 4) = 4x^3 + 1x^2 - 3x + 1.

Front

What is the perimeter of a triangle with sides represented by polynomials?

Back

The perimeter is the sum of the lengths of all sides. If the sides are represented by polynomials, add them together.

Front

How do you subtract polynomials?

Back

To subtract polynomials, change the sign of the polynomial being subtracted and then combine like terms.

Front

What is the result of subtracting (2a^2 + 5a + 3) from (a^2 - 3a - 4)?

Back

Change the sign of the second polynomial: (a^2 - 3a - 4) - (2a^2 + 5a + 3) = a^2 - 3a - 4 - 2a^2 - 5a - 3 = -a^2 - 8a - 7.

Front

What is the sum of (2x + 5y) and (3x - 2y)?

Back

Combine like terms: (2x + 3x) + (5y - 2y) = 5x + 3y.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^3, 4 is the coefficient.