Factoring Quadratic Expressions

This video tutorial explains how to factor quadratic expressions using the factor by grouping method. It begins by identifying the coefficients and constants in the expression, then finds factors of the product ac that add to b. The expression is rewritten using these factors, grouped, and factored by extracting common factors. The tutorial concludes with a verification of the factorization and introduces a quicker method for cases where the leading coefficient is one.

What is the main goal of the video tutorial?

• To learn about polynomial division

• To factor quadratic expressions using grouping

• To understand the quadratic formula

• To solve linear equations

In the expression x^2 - 11x + 28, what is the value of 'a'?

• 0

• 28

• 11

• 1

Tags

CCSS.HSA-REI.B.4B

Which two numbers multiply to 28 and add to -11?

• 4 and 7

• -4 and -7

• -2 and -14

• 2 and 14

Tags

CCSS.7.EE.A.1

How is the term -11x rewritten using the factors found?

• -4x - 7x

• -4x + 7x

• 4x - 7x

• 7x - 4x

What is the greatest common factor of the first group in the expression x^2 - 4x - 7x + 28?

• x

• 4

• 1

• 7

What is the final factored form of x^2 - 11x + 28?

• (x + 4)(x + 7)

• (x - 4)(x - 7)

• (x + 4)(x - 7)

• (x - 4)(x + 7)

Tags

CCSS.HSA.APR.A.1

What property allows us to write (x - 4)(x - 7) as (x - 7)(x - 4)?

• Associative Property

• Distributive Property

• Commutative Property

• Identity Property

What is the first term in each binomial factor when the leading coefficient is one?

• c

• x

• a

• b

What is the quicker method for factoring when the leading coefficient is one?

• Completing the square

• Finding factors of c that add to b

• Using synthetic division

• Using the quadratic formula

Which of the following is a benefit of the quicker method for factoring?

• It is more complex

• It requires solving a system of equations

• It is faster and easier

• It involves calculus