Factoring Polynomials: Difference of Squares / Instruction / Summary / Assignment

Which expression represents the area of the remaining paper shape in square centimeters? (x - 7)(x - 9) (3x - 2)(3x - 8) (3x - 4)(3x + 4) (9x - 1)(x + 16)

(3x - 4)(3x + 4)

What is the factored form of 36x4 - 25? (6x2 - 5)(6x2 + 5) (6x2 - 5)(6x2 - 5) (6x2 - 25)(6x2 + 25) (6x2 - 25)(6x2 - 25)

(6x2 - 5)(6x2 + 5)

Complete the factorization of 4x2 - 9. 4x2 - 9 = ( x - )( x + )

2 / 3 / 2 / 3

Analyze Cecile's work. Is it correct? No, adding in 0x keeps an equivalent polynomial. No, she did not fill in the X correctly. She should have 16 on top and -9 on the bottom. No, 16x6 + 12x3 - 12x3 - 9 is not equivalent to 16x6 - 9. Yes, Cecile factored the polynomial correctly.

Yes, Cecile factored the polynomial correctly.

Use the formula a2 - b2 = (a + b)(a - b) to factor completely. What are the factors of 36x8 - 49? (9x4 - 1)(4x2 + 49) (36x4 - 7)(x2 + 7) (6x4 - 7)(6x4 + 7) (6x8 - 7)(6x + 7)

(6x4 - 7)(6x4 + 7)

Factor the difference of two perfect squares using the X method. What are the two binomial factors for x2 - 25? (x - 5)(x - 5) (x + 5)(x + 5) (x - 20)(x + 5) (x - 5)(x + 5)

(x - 5)(x + 5)

Consider the polynomial 9x2 - 16. What is the value of ac? What is the value of b? What two numbers multiply to get ac and add to get b? The factored form of 9x2 - 16 is

-144 / 0 / -12 and 12 / (3x - 4)(3x + 4)

Consider the polynomial 16x2 - 1. What is the value of ac? What is the value of b? What two numbers multiply to get ac and add to get b? The factored form of 16x2 - 1 is

-16 / 0 / -4 and 4 / (4x - 1)(4x + 1)

Which expressions represent a perfect square monomial and its square root? Check all that apply. 121; 11 4x2; 2x 9x2 - 1; 3x - 1 25x; 5x 49x4; 7x2

121; 11 4x2; 2x 49x4; 7x2

Represent the polynomial x2 - 16 geometrically using algebra tiles. The number of zero pairs that will be added to the board is The equivalent factored form of .

4 / (x-4)(x+4)

The polynomial is a difference of perfect squares. Use the formula a2 - b2 = (a + b)(a - b) to factor completely. 81x2 - 49 The value of a is The value of b is The product of the prime factors is

9x / 7 / (9x-7)(9x +7)

Which board geometrically represents 4x2 - 1 using algebra tiles?

B

Use a geometric model to factor x^2 - 9 by following these steps:

Step 1: Place a big square tile in the upper left corner. Place small blue square tiles in a 3x3 square (6 small blue tiles in all), in the lower left corner. Step 2: delete all the small blue square tiles. Place three blue long tiles to the right of the big square tile. Place three red long tiles underneath the big square tile. Place a 3x3(6 tiles in all) of small blue tiles to complete the square shape. Step 3: Place a long red tile above the big square tile. Place a long red tile to the left of the big square tile. Place three small blue tiles to the right of the top long tile. Place three small red tiles under the furthest long tile to the left Step 4: C