Algebra II: Quadratic Equations - Factoring (Level 9 of 10)

The video tutorial covers solving quadratic equations with negative coefficients using two methods: trial and error, and decomposition and grouping. It explains the steps involved in each method and highlights the advantages of decomposition and grouping over trial and error. The tutorial also discusses how to identify non-factorable quadratic equations.

What is the sign of the constant term in the quadratic equation discussed in the introduction?

• Positive

• Negative

• Zero

• Undefined

In the trial and error method, why must one factor be negative and the other positive?

• Because the equation is not factorable

• Because the quadratic term is positive

• Because the linear term is positive

• Because the constant term is negative

In the trial and error method, what is the purpose of switching the signs of R and S?

• To find the GCF

• To make the equation factorable

• To ensure one factor is negative and one is positive

• To simplify the equation

What is the first step in the decomposition and grouping method?

• Multiply the quadratic and constant terms

• Find the GCF of the equation

• Divide the equation by the quadratic term

• Add the linear and constant terms

When using decomposition and grouping, what do you do after finding the pair of factors?

• Add the factors

• Decompose the linear term

• Solve for x directly

• Multiply the factors

Why is the decomposition and grouping method preferred over trial and error?

• It is the only method that works

• It is more accurate

• It requires fewer steps

• It is faster and requires testing fewer factors

What is the result of applying the zero product property to the factors 2X + 1 and 3X - 2?

• X = 0 and X = 1

• X = 2 and X = -1/3

• X = -1/2 and X = 2/3

• X = 1 and X = -2

What indicates that a quadratic equation is not factorable over the integers?

• The constant term is zero

• The linear term is positive

• The sum of factor pairs does not match the linear term

• The GCF is greater than 1

What is the GCF of the quadratic equation 5X^2 - 5X - 2?

• 2

• 5

• 0

• 1

What is the main advantage of using the decomposition and grouping method?

• It requires fewer calculations

• It is more intuitive

• It is the only method that works for all equations

• It is faster and more efficient