Factoring Expressions and GCF

This video tutorial covers various methods of factoring algebraic expressions, including trinomials, difference of squares, sum and difference of cubes, and factoring by grouping. It provides step-by-step examples to help students understand and master these techniques, emphasizing the importance of identifying the greatest common factor and using appropriate formulas for different types of expressions.

What is the first step in factoring the expression 3x^2 + 21x + 30?

• Complete the square

• Factor out the greatest common factor (GCF)

• Find two numbers that multiply to 30 and add to 21

• Rewrite the expression in vertex form

After factoring out the GCF in the expression 3x^2 + 21x + 30, what is the resulting trinomial?

• x^2 + 7x + 10

• 3x^2 + 7x + 10

• x^2 + 21x + 30

• 3x^2 + 21x + 10

When factoring the trinomial 30x^2 - 5x - 60, what is the GCF that should be factored out first?

• 5

• 2

• 3

• 6

In the expression 30x^2 - 5x - 60, after factoring out the GCF, what is the next step?

• Complete the square

• Factor by grouping

• Multiply the leading coefficient by the constant term

• Find two numbers that multiply to -60 and add to -5

What is the GCF of the expression 3y^5 - 48y?

• 3

• y

• 3y

• 48

In the expression 2x^8 - 128x^2, what is the first step in factoring?

• Rewrite in vertex form

• Factor by grouping

• Factor out the GCF

• Complete the square

When factoring the expression 3x^3 + 6x^2 - 12x - 24, what indicates that you should use factoring by grouping?

• The coefficients of the first two terms have the same ratio as the last two terms

• The expression is a perfect square trinomial

• The expression is a difference of squares

• The leading coefficient is 1

In the expression x^2 - 10x + 25 - 64y^2, what is the first step in factoring?

• Factor by grouping

• Factor out the GCF

• Complete the square

• Recognize it as a perfect square trinomial

When factoring the expression y(2x + 5)^(1/2) - 3(2x + 5)^(3/2), what is the GCF?

• y

• 3

• (2x + 5)^(3/2)

• (2x + 5)^(1/2)

In the expression x^2(x + 3)^(-2) - 4(x + 3)^(-1), what is the GCF?

• (x + 3)^(-2)

• (x + 3)^(-1)

• 4

• x^2