Factoring Polynomials and Common Factors

This video tutorial explains the technique of factoring by grouping, a method used when dealing with polynomials that have an even number of terms. The video emphasizes the importance of first factoring out the greatest common factor before applying the grouping technique. Two examples are provided: the first demonstrates the basic steps of factoring by grouping, while the second example deals with factoring when the polynomial includes negative terms. The video concludes with the final factored forms of the given expressions.

What is the first step in any factoring problem?

• Multiply all terms by a constant

• Divide the polynomial into halves

• Factor out the greatest common factor

• Add like terms

Why can't factor by grouping be used when there is an odd number of terms?

• It requires a common factor

• It requires an even number of terms to divide into pairs

• Odd terms are harder to factor

• It only works with polynomials

In the first example, what is the greatest common factor of the four terms?

• 10y

• 3y

• 2y

• 5y

What is the result of factoring out 2y from 10y cubed?

• 5y

• 5y squared

• 10y

• 10y squared

What is the common polynomial factor found in the first example?

• 5y + 3

• y + 3

• y + 2

• 2y + 5

What is the purpose of dividing the polynomial into halves during factor by grouping?

• To eliminate terms

• To simplify the expression

• To make it easier to factor out common terms

• To find the greatest common factor

Why is it important to factor out a negative greatest common factor when the first term is negative?

• To make the polynomial even

• To eliminate negative terms

• To change the sign of each term

• To simplify the expression

What is the greatest common factor of the terms in the second example?

• 4x

• Negative 4x

• 5x

• Negative 5x

In the second example, what is the common binomial factor?

• x + 4

• x + 3

• 5x + 3

• 4x + 5

What is the final factored form of the second example?

• Negative 4x times (x + 4) times (5x + 3)

• 4x times (x + 4) times (5x + 3)

• Negative 4x times (x + 3) times (5x + 4)

• 4x times (x + 3) times (5x + 4)