Factoring Quadratic Expressions

The video tutorial explains how to factor the quadratic expression -12f^2 - 38f + 22. It begins by identifying a common factor and factoring out -2, simplifying the expression to 6f^2 + 19f - 11. The tutorial then demonstrates factoring by grouping, finding two numbers whose product is -66 and sum is 19, leading to the factors 22 and -3. The expression is rewritten and grouped, factoring out common terms to achieve the final factored form: -2(2f - 1)(3f + 11).

What is the first step in simplifying the expression -12f^2 - 38f + 22?

• Factor out -2

• Divide by 2

• Multiply by -1

• Add 2 to each term

What is the coefficient of f^2 in the simplified expression before grouping?

• 12

• 6

• -12

• -6

What is the product of the two numbers needed for factoring by grouping?

• 66

• -66

• 19

• -19

Which two numbers are chosen to rewrite the middle term 19f?

• 18 and 1

• 20 and -1

• 21 and -2

• 22 and -3

Why is the number 22 placed with -11 during the grouping process?

• They have a common factor of 2

• They have a common factor of 11

• They are both even numbers

• They are both negative

What is factored out from the first group in the expression 6f^2 - 3f?

• f

• -3f

• 3f

• 2f

What is the common factor in the second group 22f - 11?

• 2f

• 11

• f

• -11

What is the final factored form of the expression -12f^2 - 38f + 22?

• -2(2f - 1)(3f + 11)

• 2(3f - 1)(2f + 11)

• -2(3f - 1)(2f + 11)

• 2(2f - 1)(3f + 11)

What property is used to factor out the common term in the final step?

• Associative Property

• Distributive Property

• Reverse Distributive Property

• Commutative Property

What is the purpose of factoring by grouping in this context?

• To simplify the expression

• To change the sign of the expression

• To eliminate the variable

• To find the roots of the equation