Mastering Factor by Grouping Techniques

This video tutorial explains the factor by grouping technique, a method used for factoring polynomials with an even number of terms, typically four or six. The video emphasizes the importance of first factoring out the greatest common factor (GCF) before applying the grouping method. Two examples are provided: the first uses 2y as the GCF, and the second uses -4x. Each example is broken down into steps, demonstrating how to group terms, factor out the GCF from each group, and finally factor out the common polynomial factor to achieve the completely factored form.

What is the first step in any factoring problem?

• Divide the polynomial into halves

• Apply the quadratic formula

• Factor out the greatest common factor

• Combine like terms

Why can't we use factor by grouping when we have an odd number of terms?

• It makes the calculation too complex

• It is not a valid mathematical technique

• Factor by grouping requires an even number of terms

• It leads to incorrect results

What is the greatest common factor (GCF) of the terms 10y^3, 20y^2, 6y^2, and 12y?

• 4y

• 2

• y

• 2y

After factoring out the GCF of 2y, what is the next step in factor by grouping?

• Simplify the expression

• Apply the quadratic formula

• Divide the polynomial into halves

• Combine like terms

What is the common polynomial factor in the first example after applying factor by grouping?

• 2y

• 3y + 6

• y + 2

• 5y + 3

In the second example, why do we factor out negative 4x instead of positive 4x?

• To avoid negative coefficients

• To simplify the expression

• To make the calculation easier

• To change the sign of each term

What is the GCF of the terms -20x^3, -80x^2, -12x^2, and -48x?

• 12x

• 8x

• 4x

• Negative 4x

After factoring out the GCF of -4x, what is the next step in factor by grouping?

• Apply the quadratic formula

• Simplify the expression

• Divide the polynomial into halves

• Combine like terms

What is the common polynomial factor in the second example after applying factor by grouping?

• 3x + 12

• 4x

• x + 4

• 5x + 3

What is the final factored form of the second example?

• Negative 4x times (x + 2) times (5x + 3)

• 4x times (x + 4) times (5x + 3)

• 4x times (x + 2) times (5x + 3)

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