Factorization problems

Posted by admin at August 5, 2021

What is Factorization in Mathematics?

Factorization of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.

To the factor, a number means to break it up into numbers that can be multiplied to get the original number. For example,


1. Factorise: 54×2 + 42×3 – 30×4
2. Factorise: 2x2yz + 2xy2z + 4xyz
3. Factorise: 30xy – 12x + 10y– 4
4. Regroup the terms and factorise: z – 19 + 19xy – xyz
5. Factorise: 100×2 – 80xy + 16y2
6. Factorise: 16×4 – y4
7. Factorise: x2 + 6x + 8
8. Factorise: 49y2 – 1
9. Divide 10(x3y2x2 + x2y3z2 + x2y2z3) by 5x2y2z2.
10. Simplify: 12(y2 + 7y + 10) ÷ 6(y + 5)

1. The factors of 6x2 + 5x – 6 are:
(a) (2x – 3)(3x – 2)
(b) (2x – 3)(3x + 2)
(c) (2x + 3)(3x – 2)
(d) (2x + 3)(3x + 2)

2. The factors of 12x2 – 7x + 1 are:
(a) (4x – 1)(3x – 1)
(b) (4x – 3)(3x + 1)
(c) (4x + 1)(3x – 1)
(d) (4x + 1)(3x + 1)

3. On dividing x3 + 3x2 + 3x + 1 by x we get remainder:
(a) 1
(b) 0
(c) -1
(d) 2

4. Find the correct identity:
(a) (a + b)2 = a2 + 2ab + b2
(b) (a + b)2 = a2 – 2ab + b2
(c) (a – b)2 = a2 + 2ab + b22
(d) (a2 – b2) = a2 + 2ab + b2

5. Find the incorrect mathematical statement.
(a) 4(x – 5) = 4x – 20
(b) 3x + 2x = 5x2
(c) x(3x + 2) = 3x2 + 2x
(d) 2x + 3x = 5x

6. Factors of a2 + 8a + 16 are:
(a) (a + 4)(a – 4)
(b) (a + 4)(a + 4)
(c) (a + 4)(4 – a)
(d) (a – 4)(a – 4)

7. Factors of 12a2b + 15ab2 is
(a) 3ab(4a + 5b)
(b) 3ab(4a + 15b)
(c) ab( 12a + 15b)
(d) None of these

8. Factors of 14pq + 35pqr is
(a) pq(14 + 35r)
(b) 7pq(2 + 5 r)
(c) 7pq(14 + 5r)
(d) None of these

9. Factors of 2xy + 2y + 3x + 3 is
(a) (x + 1)(2y + 1)
(b) (x + 1)(2y + 3)
(c) (x + 3)(2y + 1)
(d) None of these

10. Factors of 6xy – 4y + 6 – 9x is
(a) (3x – 2)(2y + 3)
(b) (3x – 1)(2y – 3)
(c) (3x + 2)(2y – 3)
(d) None of these

11. Factors of 5x2y – 15xy2 is
(a) xy(5x – 15y)
(b) 5xy(x – 3y)
(c) 5xy(x – 5y)
(d) None of these

12. Factors of 15pq + 15 + 9q + 25p is
(a) (5p + 3)(3q + 5)
(b) (5p + 3)(q + 5)
(c) (p + 3)(3q + 5)
(d) None of these

13. Factors of z – 7 + 7xy – xyz is
(a) (z – 7)( 1 – xy)
(b) (z – 7)(xy – 1)
(c) (7 – z)(1 – xy)
(d) None of these

14. Factors of x2 + 8x + 16 is
(a) (x + 8)(x + 2)
(b) (x + 4)(x + 2)
(c) (x + 4)(x + 4)
(d) None of these

15. Factors of 4y2 – 12y + 9 is
(a) (2y – 3)(2y – 6)
(b) (2y – 3)(2y – 3)
(c) (4y – 3)(y – 3)
(d) None of these

16. Factors of 49p2 – 36 is
(a) (7p – 9)(7p + 4)
(b) (4p + 4)(7p – 9)
(c) (7p – 6)(7p + 6)
(d) None of these

17. Factors of a2 – 2ab + b2 – c2 is
(a) (a – b – c)(a – b + c)
(b) (a + b – c)(a + b + c)
(c) (a – b + c)(a – b + c)
(d) None of these

18. Factors of x2 + 5x + 6 is
(a) (x + 3)(x + 2)
(b) (x + 4)(x + 2)
(c) (x + 6)(x + 1)
(d) None of these

19. Factors of 36 – 9x2 will be
(a) (6 + 3x)(6 – 3x)
(b) (3x – 6)(6 – 3x)
(c) (3x + 6)(3x -6)
(d) (12x – 3x)(3 + 3x)

20. Square of  will be:
(a) x2 – 2 – latex - Factorization problems
(b) x2 – 2 + latex - Factorization problems
(c) x2 – 4 – latex - Factorization problems
(d) x2 – 2 + latex - Factorization problems


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