Understanding Adding and Subtracting Rational Expressions

The video tutorial covers various methods for factoring quadratic equations, starting with an introduction to factoring and the importance of the greatest common factor (GCF). It then explores techniques for factoring trinomials, including the x method and slide and divide method for cases where the leading coefficient is greater than one. The tutorial concludes with a section on factoring using the difference of squares, providing examples and practice problems throughout.

What is the greatest common factor (GCF) of 40x^8y and 64x^4y?

• 8x^8y

• 16x^4y

• 4x^4y

• 8x^4y

Which pair of numbers multiplies to 26 and adds to -15?

• 13 and 2

• 13 and -2

• -13 and -2

• -13 and 2

In the X-method for factoring trinomials, what do the numbers in the X represent?

• Numbers that multiply to 'ac' and add to 'b'

• Numbers that add to 'ac' and multiply to 'b'

• Numbers that subtract from 'a' and 'c'

• Numbers that divide 'a' by 'c'

What is the factored form of w^2 - 15w + 26?

• (w + 13)(w - 2)

• (w - 13)(w + 2)

• (w + 13)(w + 2)

• (w - 13)(w - 2)

What is the factored form of x^2 + 14x + 45?

• (x - 45)(x - 14)

• (x + 45)(x + 14)

• (x - 9)(x - 5)

• (x + 9)(x + 5)

What is the result of applying the 'slide and divide' method to 5p^2 + 22p - 48?

• (p + 30)(p - 8)

• 5(p + 6)(p - 8)

• 5(p + 30)(p - 8)

• (p + 6)(5p - 8)

How do you factor a trinomial where the leading coefficient is greater than one?

• By applying the difference of squares

• By using the X-method only

• By finding the GCF only

• By using the slide and divide method

What does the 'difference of squares' formula factor into?

• a^2 - b^2 = (a - b)^2

• a^2 + b^2 = (a + b)(a - b)

• a^2 + b^2 = (a + b)^2

• a^2 - b^2 = (a + b)(a - b)

What is the factored form of y^2 - 81?

• (y + 9)(y - 9)

• (y - 9)^2

• (y + 81)(y - 81)

• (y + 9)^2

What is the factored form of 8m^2 + 30m - 27?

• (8m + 30)(m - 27)

• 2(m + 15)(4m - 9)

• 2(m + 9)(4m - 3)

• 2(4m + 9)(m - 3)