Adding, Subtracting and Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What is the process of subtracting polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the result of (x - 7)(x + 7)?

Back

The result is x^2 - 49, which is a difference of squares.

Front

How do you find the difference of two polynomials?

Back

To find the difference, subtract the second polynomial from the first by changing the signs of the second polynomial and then combining like terms.

Front

What is the simplified form of (3 - 2x + 2x^2) - (4x - 5 + 3x^2)?

Back

The simplified form is -x^2 - 6x + 8.

Front

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

Back

The result is 2x^3 - 6x^2 + 9x.

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to combine like terms and reduce the expression to its simplest form.

Front

What is the simplified form of (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

The simplified form is -8n^2 - 8n + 3.