Factoring Polynomials and Expressions

The video tutorial explains how to factor a polynomial expression completely. It begins by identifying the greatest common factor (GCF) and factoring it out. The tutorial then demonstrates the factor by grouping technique, dividing the polynomial into two halves and factoring each half separately. Finally, it combines the factors to achieve the complete factorization of the polynomial, emphasizing the importance of recognizing common binomial factors.

What is the first step in any factoring problem?

• Factor out the greatest common factor

• Combine like terms

• Complete the square

• Use the quadratic formula

What is the greatest common factor of the terms 12y², 24y, 20y, and 40?

• 5

• 4

• 3

• 2

After factoring out the greatest common factor, what is the next step in factor by grouping?

• Use the quadratic formula

• Divide the polynomial into two halves

• Simplify the expression

• Combine all terms

What is the greatest common factor of the first half of the polynomial 3y² + 6y?

• y

• 6

• 3

• 3y

What is the common binomial factor in the expression after grouping?

• y + 4

• y + 3

• y + 2

• y + 1

What do you do after identifying the common binomial factor in factor by grouping?

• Divide the factors

• Multiply the factors

• Factor out the common binomial factor

• Add the factors

What is the result of factoring out 5 from the terms 5y and 10?

• y + 1

• y + 3

• y + 4

• y + 2

What is the final expression after completely factoring the polynomial?

• 4(y + 2)(3y + 4)

• 4(y + 3)(3y + 5)

• 4(y + 2)(3y + 5)

• 4(y + 1)(3y + 5)

Why are the brackets not needed in the final expression?

• Because the expression is simplified

• Because the expression is not factored

• Because the expression is incorrect

• Because the expression is too complex

What technique is used to factor a polynomial with four terms?

• Quadratic formula

• Synthetic division

• Completing the square

• Factor by grouping