Factoring and Solving Equations

The video tutorial covers Section 85, focusing on solving even-numbered problems by factoring polynomials. It begins with identifying the greatest common factor and factoring polynomials, followed by combining like terms. The tutorial then demonstrates solving equations by setting factors to zero and checking solutions. The instructor provides step-by-step guidance and checks solutions to ensure accuracy.

What is the first step in factoring a polynomial?

• Dividing by the smallest coefficient

• Adding all terms

• Finding the greatest common factor

• Multiplying all terms

Which number is the greatest common factor of 8m and -6?

• 4

• 3

• 2

• 1

When factoring b² + b - 6, what two numbers multiply to -6 and add to 1?

• -3 and 2

• -2 and 3

• 1 and -6

• 3 and -1

What is the factored form of b² + b - 6?

• (b - 2)(b + 3)

• (b + 2)(b - 3)

• (b - 1)(b + 6)

• (b + 1)(b - 6)

What does it mean when two factors of an equation equal zero?

• Both factors must be positive

• At least one factor must be zero

• Both factors must be negative

• The equation has no solution

If a - 9 = 0, what is the value of a?

• 9

• 0

• 1

• -9

What is the solution for 2a + 1 = 0?

• a = 1

• a = -1

• a = -0.5

• a = 0.5

How can you verify if a solution to an equation is correct?

• By checking if the solution satisfies the original equation

• By subtracting the solution from the equation

• By multiplying the solution by zero

• By adding the solution to the equation

What is the result of substituting a = 9 into the equation a - 9?

• 18

• 0

• 9

• -9

What is the result of substituting a = -2 into the equation 2a + 1?

• 0

• 1

• -1

• -3