Factoring Quadratic Equations Using the AC Method

What is the first step in the process of factoring by grouping?

• Factor out the greatest common factor (GCF).

• Rewrite the middle term as two separate values.

• Identify the factors of the constant term.

• Apply the zero product property.

How do you determine the factors of a*c that add up to the middle term?

• Multiply a*c and select any two factors randomly.

• Divide a*c by the middle term.

• List all factors of a*c and select the pair that adds up to the middle term.

• Use the quadratic formula.

What is the significance of the signs of the factors when adding to a negative middle term?

• Both factors must be positive.

• The negative factor must be larger in absolute value.

• Both factors must be negative.

• The positive factor must be larger in absolute value.

How do you start finding factors of a given number?

• By dividing the number by 2.

• By listing multiples of the number.

• By starting with the number times one.

• By using a calculator.

Tags

CCSS.4.OA.B.4

Why is the negative factor larger in absolute value when the sum is negative?

• To ensure the sum of the factors is negative.

• To ensure the product is positive.

• To balance the equation.

• To make the equation easier to solve.

Tags

CCSS.HSA-REI.B.4B

After rewriting the equation with identified factors, what is the next step?

• Apply the quadratic formula.

• Factor by grouping.

• Graph the equation.

• Solve for x.

Tags

CCSS.HSA-REI.B.4B

What do you do if the expressions you're trying to factor by grouping don't have a common factor?

• Factor out a positive or negative one.

• Skip the step and move to solving.

• There is always a common factor; find it.

• Multiply the expressions.

What is the purpose of rewriting the middle term in two parts?

• To simplify the equation.

• To prepare for factoring by grouping.

• To find the discriminant.

• To apply the quadratic formula.

What does factoring out the GCF from each group achieve?

• It reveals a common factor between the groups.

• It simplifies the equation for graphing.

• It completes the factoring process.

• It prepares the equation for the quadratic formula.

What property is applied after factoring by grouping?

• Commutative property

• Zero product property

• Distributive property

• Associative property

Tags

CCSS.HSA-REI.B.4B