F3 Maths factorization

1. 80y^4 - 405
2. x^4 - 21x^2 - 100
3. 1 - 729x^6

4. Factorize x^8 - 1 and hence factorize x^1024 - 1
( Hint : Express x^1024 - 1 as (x^512)^2 -1 first )

5a Factorize x^3 - 64
5b Hence factorize x^3 - 64/x^3

6. Which of the following is NOT a factor of the expression (2x - 2)(x + 3)

A. 2 - 2x
B. 2x - 2
C. x - 1
D. x - 2

7. x^3 + 2x^2 + x^2 + 2x - x - 1 =

A. (x + 1)(x^2 + 2x -1)
B. (x + 1)(x - 1)(x + 2)
C. (x + 1)^2(x - 1)
D. (x - 1)^2(x + 1)

8. Which of the following has a common factor with the expression
x^2 + 3xy + 2y^2 ?

A. x^2 + 2xy + y^2
B. x^2 - 2xy + y^2
C. x^2 + 2xy - y^2
D. x^2 - 2xy -y^2

9. Factorize x^2 - 10x + 25 - 9y^2

A. (x + 3y + 5)(x- 3y + 5)
B. (x + 3y - 5)(x - 3y - 5)
C. (x + 3y - 5)^2
D (x + 3y - 5)(x - 3y + 5)

10. Write down 4 different polynomials that have the factors x + 3 and x - 2.
For Example : x^2 + x -6

11. Find the value of the expression (52^2 + 152^2) - (48^2 + 148^2) by using
factorization?

12. Show that x is a factor of (x^3 - 1)(x^3 + 1)(x^6 + 1)(x^12 + 1)(x^24 +1) + 1.

Determine whether each of the following statements is correct or not.

1. All polynomials can be factorized.
2. Factorization is the reverse process of expansion of an expression.
3. 2a^3 + 8b^3 = 2(a + 2b)(a^2 + 2b^2)
4. All factors of a polynomial are of degree 1.
5. a^2 - a + 1/4 = (a - 1/2)^2