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 consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers or expressions.

Front

How do you factor the expression x^4 - 9x^2?

Back

Factor out the GCF first: x^2(x^2 - 9), then recognize x^2 - 9 as a difference of squares: x^2(x + 3)(x - 3).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a + b)(a - b).

Front

How do you factor the expression 3x^2 + 18x + 15?

Back

First, factor out the GCF: 3(x^2 + 6x + 5), then factor the quadratic: 3(x + 5)(x + 1).

Front

What is the first step in factoring a polynomial?

Back

The first step is to check if there is a GCF (Greatest Common Factor) among the terms.

Front

How do you factor the expression 81m^2 - 1?

Back

Recognize it as a difference of squares: (9m - 1)(9m + 1).

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c, where a, b, and c are constants.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in graphing functions.