Factoring Polynomials Using the GCF

This video tutorial introduces the concept of factoring polynomials, focusing on the greatest common factor (GCF). It explains how to identify the GCF in a polynomial by examining coefficients and variables, and provides step-by-step examples to demonstrate the process. The tutorial covers several example problems, illustrating how to factor polynomials using the GCF method and verifying the results through distribution.

What is the process of rewriting a polynomial as a product of two or more polynomials called?

• Division

• Factoring

• Simplification

• Multiplication

What does GCF stand for?

• General Common Factor

• Greatest Calculated Figure

• General Calculus Function

• Greatest Common Factor

If a polynomial cannot be factored, what is it called?

• Undefined

• Prime

• Infinite

• Composite

How do you find the GCF of numerical coefficients?

• Find the smallest number

• Add them together

• Multiply them

• Find the largest number that divides into each term

What must a variable do to be considered part of the GCF in a polynomial?

• Have the highest exponent

• Be present in all terms

• Have the lowest coefficient

• Be the first variable alphabetically

In the expression 9y to the third plus 21y squared, what is the GCF?

• 3y

• 9y

• 3y squared

• 21y squared

After finding the GCF, what is the next step in factoring a polynomial?

• Add the GCF to each term

• Subtract the GCF from each term

• Divide each term by the GCF

• Multiply each term by the GCF

What is the factored form of 12x squared plus 6x?

• 3x(4x + 2)

• 6x(2x + 1)

• 2x(6x + 3)

• 4x(3x + 1.5)

How can you check if you have factored a polynomial correctly using the GCF?

• By adding the GCF to the polynomial

• By dividing the polynomial by the GCF

• By multiplying the factored form by the GCF

• By subtracting the GCF from the polynomial

What is the GCF of the terms 32x squared, -8x, and 16?

• 16

• 8x

• 16x

• 8