Factoring Polynomials: Difference of Squares

Question 1

Which expressions represent a perfect square monomial and its square root? Check all that apply.121; 114x2; 2x9x2 – 1; 3x - 125x; 5x49x4; 7x2

Revolt · Accepted Answer

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

Question 2

What are the factors of x2 – 144?

Revolt · Accepted Answer

✔ (x – 12); and: (x – 12); and: (x + 12)

Question 3

Consider the polynomial 16x2 – 1.

Revolt · Accepted Answer

✔ –16; What is the value of ac?: –16; What is the value of b?: 0; What two numbers multiply to get ac and add to get b?: –4 and 4; The factored form of 16x2 – 1 is .: (4x– 1)(4x+ 1)

Question 4

Complete the factorization of 4x2 – 9.

Revolt · Accepted Answer

✔ 2; 4x2 – 9 = ( x – )( x + ): 2; 4x2 – 9 = ( x – )( x + ): 3

Question 5

Represent the polynomial x2 – 16 geometrically using algebra tiles.

Revolt · Accepted Answer

✔ 4; The equivalent factored form of x2 – 16 is .: (x – 4)(x + 4)

Question 6

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

Revolt · Accepted Answer

(6x4 – 7)(6x4 + 7)

Question 7

Which expression represents the area of the remaining paper shape in square centimeters?

Revolt · Accepted Answer

(3x – 4)(3x + 4)

Question 8

Analyze Cecile’s work. Is it correct?

Revolt · Accepted Answer

Yes, Cecile factored the polynomial correctly.

Factoring Polynomials: Difference of Squares Answers

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