Factoring Polynomials and GCF

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 the Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that two or more numbers have in common. It is used to simplify fractions and factor polynomials.

Front

Factor the polynomial: x² + 7x - 30

Back

(x + 10)(x - 3)

Front

Factor completely: 5x² - 7x + 2

Back

(5x - 2)(x - 1)

Front

Factor completely: 2x² + 22x + 60

Back

2(x + 5)(x + 6)

Front

Factor out the GCF: 10x³ - 15x

Back

5x(2x² - 3)

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 it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means breaking it down into irreducible factors, which cannot be factored further over the set of real numbers.

Front

Factor: k² + 7k + 10

Back

(k + 2)(k + 5)

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get back to the original expression.