Factoring Quadratics: A Comprehensive Review

This video tutorial covers various techniques for factoring algebraic expressions, focusing on quadratics, trinomials, and binomials. It begins with identifying the greatest common factor and progresses to more advanced methods like trial and error, factoring by grouping, and recognizing perfect squares and cubes. The tutorial provides step-by-step examples to illustrate each method, ensuring a comprehensive understanding of factoring.

What is the greatest common factor used to simplify the expression 3x^3 - 21x^2 - 27x?

• x

• 3

• 3x

• 21

When factoring the expression x^2 - 7x - 9, why can't it be factored further?

• The discriminant is negative.

• The terms do not have a common factor.

• Factors of 9 do not have a sum of 7.

• It is already in its simplest form.

What is the correct factorization of x^2 - 21x + 110?

• x - 10 and x - 11

• x + 10 and x + 11

• Cannot be factored

• x - 5 and x - 22

In the expression 4x^2 + 36x + 72, what is the greatest common factor?

• 4

• 12

• 36

• 72

How is the trinomial 4x^2 + 36x + 72 factored after pulling out the greatest common factor?

• Cannot be factored further

• 4(x + 6)(x + 3)

• 4(x + 3)^2

• 4(x^2 + 9x + 18)

Which expression shows the use of the difference of squares?

• Both B and C

• x^2 - 64

• 64x^2 - 49

• 8x - 7 and 8x + 7

What method is used to factor the expression 3x^2y^2 + 6x^2 + 12y^2 + 24?

• None of the above

• Synthetic division

• Using the quadratic formula

• Factoring by grouping

Which is a factor of the expression 15x^2 - 14x - 8?

• x - 4

• x + 2

• 5x + 2

• 3x - 4

What is the correct factorization of 18x^2 + 3x - 6?

• 3(6x^2 + x - 2)

• 3(2x + 3)(3x - 1)

• 3(6x - 1)(x + 2)

• Cannot be factored

What is the factored form of 512x^3 - 125?

• (8x - 5)(64x^2 + 40x + 25)

• Cannot be factored

• (8x + 5)(64x^2 - 40x + 25)

• (8x - 5)(64x^2 - 40x + 25)