Factoring Quadratics: Day 3B Insights

The video tutorial covers factoring quadratic equations where the leading coefficient is not one. It emphasizes finding the greatest common factor (GCF) first. Two examples are provided: factoring 6x^2 - 51x + 90 and 30x^2 + 65x - 40. Each example is broken down into steps, including identifying the GCF, adjusting the quadratic equation, and verifying the results using the FOIL method. The tutorial concludes with a reminder to include all steps in the solution.

What is the first step in factoring a quadratic equation when the leading coefficient is not 1?

• Applying the quadratic formula

• Extracting the Greatest Common Factor (GCF)

• Finding two numbers that multiply to AC and add to B

• Dividing each term by the leading coefficient

What is the GCF of the quadratic equation 6x^2 - 51x + 90?

• 3

• 6

• 2

• 9

After extracting the GCF, what is the simplified form of 6x^2 - 51x + 90?

• 2x^2 - 17x + 30

• x^2 - 17x + 30

• 3x^2 - 17x + 30

• 2x^2 - 51x + 90

Which pair of numbers multiplies to 60 and adds up to -17?

• 6 and 10

• -6 and -10

• 5 and 12

• -5 and -12

What is the GCF of the quadratic equation 30x^2 + 65x - 40?

• 5

• 10

• 15

• 20

After extracting the GCF from 30x^2 + 65x - 40, what is the coefficient of x^2 in the simplified form?

• 5

• 13

• 6

• 3

Which pair of numbers multiplies to -48 and adds up to 13?

• -3 and 16

• 3 and -16

• 4 and -12

• -4 and 12

What is the simplified form of the factor (6x - 3) after dividing by the GCF?

• x - 1

• 2x - 1

• 3x - 1

• 2x - 3

What is the final factored form of 30x^2 + 65x - 40?

• 5(x - 1)(x + 8)

• 5(2x + 1)(3x - 8)

• 5(3x - 1)(2x + 8)

• 5(2x - 1)(3x + 8)

What is the purpose of checking the factored form by foiling?

• To ensure it simplifies back to the original equation

• To find the GCF of the original equation

• To determine the values of x

• To calculate the discriminant