Factoring Quadratic Expressions

This video tutorial demonstrates how to factor a quadratic expression using the technique of factor by grouping. It begins with identifying the coefficients and constants in the expression, followed by finding factors of the product of the first and last coefficients that add up to the middle coefficient. The expression is then rewritten using these factors, grouped, and factored by extracting common factors. The final step involves verifying the factored expression by expanding it back to its original form.

What is the main goal of using the factor by grouping technique?

• To factor quadratic expressions

• To find the roots of linear equations

• To simplify linear equations

• To solve cubic equations

In the expression 3x² - 17x + 24, what is the product of coefficients a and c?

• 51

• 17

• 24

• 72

Which pair of factors of 72 adds up to -17?

• -6 and -12

• -8 and -9

• -3 and -24

• -1 and -72

How is the term -17x rewritten using the factors found in step one?

• As 8x + 9x

• As -8x - 9x

• As -9x + 8x

• As 9x - 8x

What is the greatest common factor of the first two terms in the expression 3x² - 8x?

• 3

• 1

• x

• 8

Why do we factor out -3 instead of 3 from the second group of terms?

• To make the binomial factors identical

• To change the sign of the terms

• To eliminate the constant term

• To simplify the expression

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

• 3x - 8

• 3x + 8

• x + 3

• x - 3

What is the factored form of the quadratic expression 3x² - 17x + 24?

• (3x + 8)(x - 3)

• (3x - 8)(x - 3)

• (3x - 8)(x + 3)

• (3x + 8)(x + 3)

What is the result of expanding the expression (3x - 8)(x - 3)?

• 3x² - 7x + 24

• 3x² + 17x - 24

• 3x² - 17x + 24

• 3x² + 7x - 24

How can you verify that the quadratic expression has been factored correctly?

• By comparing with a different expression

• By solving for x

• By expanding the factored form

• By checking the coefficients