Factoring Polynomials: GCF Techniques

The video tutorial covers the process of factoring polynomials using the greatest common factor (GCF). It begins with an introduction to the concept, followed by detailed examples and explanations of how to identify and factor out the GCF from polynomial expressions. The tutorial includes practice problems to reinforce learning and concludes with advanced techniques for more complex factoring scenarios.

What is the first step in factoring polynomials using the greatest common factor?

• Identify the highest exponent

• Determine the coefficients

• Find common factors in the terms

• Multiply the terms together

When factoring a polynomial with a negative coefficient, what must you consider?

• Change all negatives to positives before factoring

• Only factor out positive numbers

• Factor out the negative as part of the greatest common factor

• Ignore the negative signs

What defines a prime polynomial?

• A polynomial that is derived from prime numbers only

• A polynomial with only one variable

• A polynomial that can be factored into two prime numbers

• A polynomial that cannot be factored further

How do you find the greatest common factor of a polynomial?

• By identifying common factors in the coefficients and variables

• By finding the lowest common multiple

• By adding all the coefficients

• By dividing each term by the smallest coefficient

In the expression 4a^2 + 8a, what is the greatest common factor?

• 2a

• 4a

• 12a

• 8a

What is left in the polynomial 3x + 12 after factoring out the greatest common factor?

• 3 + 4x

• 3x + 4

• x + 4

• x + 12

If a polynomial has different variables in its terms, what can you factor out?

• Nothing, it is prime

• Only the numerical coefficients

• All variables present

• The most common variable

What do you do if you can only factor out a '1' from a polynomial?

• Multiply all terms by 1

• None of the above

• Factor out the 1 and simplify

• Leave it as it is, it's prime

In the expression 2xy + 4xy^2 - 8xy, what common factors can be factored out?

• 2xy

• 4xy

• 2x

• 2y

After factoring out the greatest common factor from 35a^2 - 20ab + 15a, what is the simplified expression?

• 5a(7 - 4b + 3)

• 7a - 4b + 3

• 5a(7a - 4b + 3)

• 5(7a^2 - 4ab + 3a)