Factoring Trinomials with a Common Factor

The video tutorial explains how to factor the expression 8k^2 - 24k - 144. It begins by identifying that all terms are divisible by 8, simplifying the expression to 8(k^2 - 3k - 18). The tutorial then focuses on factoring the quadratic expression by finding two numbers whose sum is -3 and product is -18, which are 3 and -6. The expression is further simplified using grouping, resulting in the final factored form: 8(k + 3)(k - 6).

What is the greatest common factor of the terms in the expression 8k^2 - 24k - 144?

• 2

• 4

• 24

• 8

After factoring out the greatest common factor, what is the simplified form of the expression?

• k^2 - 3k - 18

• 8(k^2 - 3k - 18)

• 8(k^2 - 3k + 18)

• k^2 - 3k + 18

Which operation is performed to simplify the expression 8(k^2 - 3k - 18)?

• Multiplication

• Subtraction

• Addition

• Division

Which pair of numbers has a sum of -3 and a product of -18?

• 3 and 6

• -3 and 6

• -3 and -6

• 3 and -6

In the context of factoring by grouping, which term is used to split the middle term of the quadratic expression?

• 3k - 6k

• 3k + 6k

• -3k + 6k

• -3k - 6k

What is the factored form of the expression inside the brackets after applying the grouping method?

• (k - 6)(k + 3)

• (k + 3)(k - 6)

• (k - 3)(k + 6)

• (k + 6)(k - 3)

What common factor is factored out from the grouped terms in the expression?

• k + 6

• k - 6

• k - 3

• k + 3

What is the coefficient of k in the simplified expression inside the brackets?

• 1

• -1

• 6

• -6

What is the final factored form of the quadratic expression?

• 8(k + 3)(k - 6)

• 8(k - 3)(k + 6)

• (k + 3)(k - 6)

• (k - 3)(k + 6)

Which of the following is a correct step in the process of factoring by grouping?

• Applying the quadratic formula

• Combining like terms

• Solving for k

• Factoring out a common term from each group