Factoring Polynomials Using the GCF

What is the primary focus of factoring in algebra?

• To solve quadratic equations

• To graph polynomial functions

• To find the Greatest Common Factor (GCF)

• To simplify expressions to their simplest form

What does factoring a number like 10 involve?

• Subtracting two numbers to get 10

• Finding two numbers that multiply to get 10

• Dividing 10 by another number

• Adding two numbers to get 10

Why is mastering factoring important in algebra?

• It is necessary for solving all types of equations

• It simplifies expressions, making other operations easier

• It is the only way to solve polynomial equations

• It helps in graphing functions accurately

How can factoring be described in a simple way?

• Graphing a function based on its degree

• Solving an equation for its roots

• Writing a polynomial as the product of its factors

• Breaking down a number into its prime factors

What is the Greatest Common Factor (GCF) of 4x^3, -2x^2, and 6x?

• 6x

• 2x

• 2x^2

• 4x^3

How do you determine the GCF of a polynomial's terms?

• By multiplying the coefficients of the terms

• By finding the highest exponent in the terms

• By adding the coefficients of the terms

• By identifying the largest factor common to all terms

What is the first step in factoring a polynomial?

• Writing the polynomial in standard form

• Dividing each term by the leading coefficient

• Finding the GCF of its terms

• Identifying the variable

What role does the GCF play in factoring polynomials?

• It determines the number of terms in the polynomial

• It is factored out to simplify the polynomial

• It is the highest degree of any term in the polynomial

• It is subtracted from each term

After factoring out the GCF, what is the next step?

• Calculate the derivative

• Solve for x

• Write the remaining terms inside parentheses

• Graph the polynomial

What does the distributive property allow us to do in factoring?

• Find the derivative of the polynomial

• Multiply a common factor by terms inside parentheses to get the original polynomial

• Divide each term by a common factor

• Combine like terms