Slip and Slide Factoring Techniques for Trinomials

The video tutorial introduces the slip and slide factoring method for polynomials of the form ax^2 + bx + c. It provides a detailed explanation of the method through three examples, demonstrating how to factor polynomials by multiplying the leading coefficient with the constant term, simplifying fractions, and rearranging terms. The tutorial emphasizes the importance of checking the results using the FOIL method to ensure accuracy.

What is the first step in the slip and slide factoring method when given a polynomial like 3x^2 + 17x + 10?

• Multiply the coefficient of x^2 by the constant term.

• Add the coefficients of x^2 and x.

• Divide the coefficient of x by the constant term.

• Subtract the constant term from the coefficient of x.

After adjusting the polynomial, what should the new form look like if the original was 3x^2 + 17x + 10?

• x^2 + 51x + 10

• x^2 + 17x + 30

• 3x^2 + 51x + 30

• 3x^2 + 17x + 3

Which pair of numbers multiplies to 30 and adds up to 17?

• 2 and 15

• 3 and 10

• 5 and 6

• 1 and 30

How is the fraction 15/3 simplified in the context of the slip and slide method?

• 5/1

• 3/15

• 1/5

• 5

What is the final factored form of the polynomial 3x^2 + 17x + 10 using the slip and slide method?

• (3x + 5)(x + 2)

• (x + 5)(x + 2)

• (3x + 2)(x + 5)

• (3x + 10)(x + 17)

In the second example, what is the product of the coefficient of x^2 and the constant term initially?

• 48

• 16

• 12

• 4

Which pair of numbers multiplies to -48 and adds up to 13 in the second example?

• -4 and 12

• 3 and 16

• 4 and -12

• -3 and 16

What is the simplified form of the fraction 16/12 in the context of the slip and slide method?

• 4/3

• 3/4

• 8/6

• 12/16

What is the final factored form of the polynomial 12x^2 + 13x - 4 using the slip and slide method?

• (x - 1)(x + 4)

• (4x - 1)(3x + 4)

• (12x - 4)(x + 3)

• (4x + 1)(3x - 4)

What new challenge polynomial is introduced for practice in the slip and slide method?

• x^2 - 22x + 40

• 5x^2 - 22x + 8

• x^2 + 22x - 40

• 5x^2 + 22x + 8