Factoring Quadratics Using the AC Method

The video tutorial explains how to factor a quadratic equation with a leading coefficient greater than one using the AC method. It begins by introducing the concept and then explains the steps involved in the AC method, including multiplying the 'a' and 'c' terms, finding factors that multiply to the product and add to the middle term, rewriting the quadratic equation, and using grouping to factor the expression. The tutorial provides a detailed walkthrough of each step, ensuring a clear understanding of the process.

What is the first step in factoring a quadratic with a leading coefficient greater than one using the AC method?

• Rewrite the quadratic in standard form.

• Find the greatest common factor.

• Identify the middle term.

• Multiply the a and c terms.

Why is it necessary to multiply the a and c terms in the AC method?

• To find the greatest common factor.

• To simplify the quadratic equation.

• To determine the product needed for factor listing.

• To eliminate the middle term.

What is the product of the a and c terms in the given example?

• -28

• 28

• 8

• -8

Which pair of factors of -28 adds up to the middle term of the quadratic?

• -2 and -14

• 2 and 14

• 4 and -7

• -4 and 7

How is the middle term of the quadratic expression rewritten using the identified pair of factors?

• As a single term.

• As two separate terms.

• As a product of two terms.

• As a sum of three terms.

What is the purpose of grouping terms in the rewritten quadratic expression?

• To simplify the expression.

• To identify common factors.

• To eliminate terms.

• To rearrange terms.

What common factor is identified in the first group of terms?

• 2Z

• Z

• 7

• Z-2

What common factor is identified in the second group of terms?

• 7

• Z-2

• 2Z

• Z

What is the final factored expression of the quadratic?

• (Z + 2)(2Z - 7)

• (Z - 2)(2Z + 7)

• (2Z - 7)(Z + 2)

• (2Z + 7)(Z - 2)

What is the significance of the common factor Z-2 in the final step?

• It is eliminated from the expression.

• It is used to rearrange terms.

• It is used to complete the factorization.

• It simplifies the expression.