Factoring Quadratic Expressions by Grouping

This video tutorial demonstrates how to factor a quadratic expression using the factor by grouping method. It begins by identifying the coefficients and constant in the expression, then finds the factors of the product of the first and last coefficients that add up to the middle coefficient. The expression is rewritten using these factors, allowing the application of the factor by grouping technique. The process involves grouping terms, factoring out the greatest common factor from each group, and identifying a common binomial factor. The tutorial concludes by verifying the factored form through multiplication.

What is the main goal of the video tutorial?

• To factor quadratic expressions using grouping

• To solve linear equations

• To understand the quadratic formula

• To learn about polynomial division

What is the product of a and c in the expression 6x^2 + 7x - 5?

• -30

• 11

• 35

• 30

Which pair of factors of -30 adds up to 7?

• -2 and 15

• -3 and 10

• -1 and 30

• -5 and 6

How is the term 7x rewritten using the factors found?

• As 6x + x

• As 5x + 2x

• As -3x + 10x

• As 3x + 4x

What is the greatest common factor of the first two terms in the expression 6x^2 - 3x?

• 3x

• 2x

• 6x

• x

What is the greatest common factor of the last two terms in the expression 10x - 5?

• 10

• 5

• x

• 2

What is the common binomial factor in the expression after grouping?

• x - 5

• x + 1

• 2x - 1

• 3x + 5

What is the second factor in the factored form of the expression?

• x - 1

• 2x - 1

• 3x + 5

• x + 5

What is the result of multiplying 2x by 3x?

• 5x^2

• 5x

• 6x

• 6x^2

What is the final expression after combining like terms?

• 6x^2 + 7x - 5

• 6x^2 + 10x - 5

• 6x^2 + 8x - 5

• 6x^2 + 5x - 5