Factoring Expressions and GCF

The video tutorial explains how to factor the expression 5x^2 y + 15x y - 35 x^2 - 105x by first identifying the greatest common factor (GCF) and then using the grouping method. The process involves splitting the expression into two groups, factoring out the GCF from each group, and verifying the solution by multiplying the factors back together. The tutorial emphasizes the importance of checking the solution to ensure accuracy.

What is the first step to consider when attempting to factor an expression?

• Check for the greatest common factor

• Apply the quadratic formula

• Use the difference of squares

• Perform polynomial long division

What is the greatest common factor in the expression 5x^2y + 15xy - 35x^2 - 105x?

• 5x

• x

• 5

• y

After factoring out the GCF, what expression is left?

• x^2 + 3x - 7x - 21

• 5xy + 15y - 35x - 105

• xy + 3y - 7x - 21

• x^2y + 3xy - 7x^2 - 21x

How many terms are there in the expression after factoring out the GCF?

• 3

• 2

• 5

• 4

What method is used to factor an expression with four terms?

• Difference of squares

• Synthetic division

• Quadratic formula

• Grouping

What is the GCF of the left group in the expression xy + 3y?

• xy

• x

• y

• 3

What is the GCF of the right group in the expression -7x - 21?

• -21

• 21

• x

• -7

What common binomial factor is found in both groups after grouping?

• x - 7

• y - 7

• y + 3

• x + 3

What is the final factored form of the expression?

• 5x(x + 3)(y - 7)

• 5x(x - 3)(y + 7)

• 5x(x + 7)(y - 3)

• 5x(x - 7)(y + 3)

What is the purpose of verifying the solution by multiplying the factors?

• To ensure the factors are correct

• To convert it into a quadratic equation

• To find the roots of the equation

• To simplify the expression