Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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 simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form by combining like terms and eliminating unnecessary parentheses.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What is the process of grouping in factoring?

Back

Grouping is a method of factoring where terms are grouped in pairs or sets to factor out common factors from each group.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression of the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

Front

What is the difference between adding and subtracting polynomials?

Back

Adding polynomials involves combining like terms, while subtracting polynomials requires distributing a negative sign and then combining like terms.

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you factor by grouping?

Back

To factor by grouping, rearrange the terms, group them into pairs, factor out the common factor from each pair, and then factor out the common binomial.