Algebra 1: Factoring Polynomials; Difference of Squares

Which term is a perfect square of the root 3x4?

9x8

Which expression is equivalent to 100 n2 − 1?

(10n)2 − (1)2

What is the factorization of 121b4 − 49?

(11b2 + 7)(11b2 − 7)

Analyze Cecile's work. Is it correct?

Yes, Cecile factored the polynomial correctly.

Which expressions represent a perfect square monomial and its square root? Check all that apply.

a. 121;11 b. 4x2;2x e. 49x4;7x2

What is the square root of r64?

r8

What are the factors of x2 - 144?

(x-12)(x+12)

The area of a square can be represented by the expression x10. Which monomial represents a side of the square?

x5

What is the factored form of 36x4 - 25?

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

Use the formula a2 - b2 = (a + b)(a - b) to factor completely. What are the factors of 36x8 - 49?

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

What is the factorization of 49b2 − 81?

(7b - 9)(7b + 9)

Factor the difference of two perfect squares using the X method. What are the two binomial factors for x2 - 25?

(x - 5)(x + 5)

Which expressions are equivalent to 25x4 −64? Select three options.

- 25x4 + 40x − 40x − 64 - 25x4 + 13x − 13x − 64 - (5x2 + 8)(5x2 − 8)

Which monomials are perfect squares? Check all that apply.

1, 49x2,81x6

Consider the polynomial 9x2 - 16. 1.What is the value of ac? 2.What is the value of b? 3.What two numbers multiply to get ac and add to get b? 4.The factored form of 9x2 - 16 is

1. -144 2. 0 3. -12 and 12 4. (3x-4)(3x+4)

Consider the polynomial 16x2 - 1. 1. What is the value of ac? 2. What is the value of b? 3. What two numbers multiply to get ac and add to get b? 4. The factored form of 16x2 - 1 is

1. -16 2. 0 3. -4 and 4 4. (4x-1)(4x+1)

Complete the factorization of 4x2 - 9.

4x-9= (2x-3)(2x+3)

A square corner of 16 square centimeters is removed from a square paper with an area of 9x2 square centimeters. Which expression represents the area of the remaining paper shape in square centimeters?

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

Which expression is equivalent to 36x2 − 25?

(6x)2 − (5)2

What are the factors of x2 - 100?

(x - 10)(x + 10)

What are the two binomial factors for x2 - 25?

(x - 5)(x + 5)

The polynomial is a difference of perfect squares. Use the formula a2 - b2 = (a + b)(a - b) to factor completely. 81x2 - 49 1. The value of a is . 2. The value of b is . 3.The product of the prime factors is .

1. 9x 2. 7 3. (9x-7) (9x+7)

Which polynomial can be simplified to a difference of squares?

16a2 - 4a + 4a - 1