Factoring GCF and Quadratics Mastery

This video tutorial covers a comprehensive review of factoring techniques, including factoring out the greatest common factor (GCF), factoring by difference of squares, and factoring trinomials. It also explains how to solve equations using the zero product property and applies these techniques to solve word problems involving areas, volumes, and projectile motion. The tutorial provides step-by-step examples to illustrate each method, ensuring a clear understanding of the concepts.

What is the first step in factoring out a monomial from a polynomial?

• Add the terms

• Multiply the terms

• Distribute the terms

• Divide out the GCF

In the expression a^2b + 2ab, what is the GCF?

• b

• a

• ab

• a^2

What is the pattern for factoring a difference of squares?

• a^2 + b^2

• a^2 - b^2

• a^2 + 2ab + b^2

• a^2 - 2ab + b^2

How do you determine the terms of the binomials when factoring a difference of squares?

• Add the terms

• Subtract the terms

• Square root the first and second term

• Multiply the terms

What is the first step in factoring trinomials?

• Multiply the first and last terms

• Group the terms

• Write in descending order

• Check for a GCF

When factoring trinomials, what do you do after finding the two numbers that multiply to the first and last terms and add to the middle term?

• Distribute the terms

• Rewrite the problem with four terms

• Solve the equation

• Factor out the GCF

What property is used when solving equations by factoring?

• Associative property

• Commutative property

• Zero product property

• Distributive property

In the equation 3x^2 + 7x - 6 = 0, what are the solutions after factoring?

• x = 3 and x = 2/3

• x = -3 and x = -2/3

• x = 3 and x = -2/3

• x = -3 and x = 2/3

What are the dimensions of a rectangle if its area is given by 10w^2 - 19w - 15?

• w + 5 and 2w - 3

• w - 5 and 2w + 3

• 2w - 5 and 5w + 3

• 2w + 5 and 5w - 3

How long does it take for a projectile launched upward at 32 feet per second from a height of 128 feet to hit the ground?

• 2 seconds

• 8 seconds

• 4 seconds

• 6 seconds