FACTOR IN ONE VARIABLE WORKSHEET

Factorize the following algebraic expressions

Problem 1 :

-3x + 21

Solution

Problem 2 :

6x² + 3x

Solution

Problem 3 :

18x² + 12xy

Solution

Problem 4 :

6tm - 24m²

Solution

Problem 5 :

8x + 12y + 10x + 15y

Solution

Problem 6 :

x² - 7x + 3x - 21

Solution

Problem 7 :

7x + 4

Solution

Problem 8 :

20x - 10

Solution

Problem 9 :

18xy - 3yz

Solution

Problem 10 :

12mn + 18mp

Solution

Problem 11 :

16m² - 4m

Solution

Problem 12 :

3x² + 6x - 18

Solution

Problem 13 :

-6x - 24

Solution

Problem 14 :

-2xy - 8x

Solution

Problem 15 :

24mn - 16m²n

Solution

Problem 16 :

 -x²y - y²x

Solution

Problem 17 :

12m²n + 24m²n²

Solution

Problem 18 :

72y²p - 18y³p²

Solution

Problem 19 :

4(x + 3) + m(x + 3)

Solution

Problem 20 :

 x(x - 1) + 5(x - 1)

Solution

Problem 21 :

y(y + 4) - 6(y + 4)

Solution

Problem 22 :

  x² (x + 7) + x (x + 7)

Solution

Problem 23 :

3x(x - 4) - 7(x - 4)

Solution

Problem 24 :

The length of a rectangular game reserve is 1 mile longer than twice the width. The area of the reserve is 55 square miles. What is the width of the reserve?

Solution

Problem 25 :

The area (in square feet) of the school sign can be represented by

15x² − x − 2.

a. Write an expression that represents the length of the sign.

b. Describe two ways to find the area of the sign when x = 3.

Solution

Problem 26 :

The height h (in feet) above the water of a cliff diver is modeled by

h = −16t² + 8t + 80

where t is the time (in seconds). How long is the diver in the air?

Solution

Factories :

Problem 1 :

3^2x + 3^x

Solution

Problem 2 :

2^{n + 2} + 2ⁿ

Solution

Problem 3 :

4ⁿ + 4³ⁿ

Solution

Problem 4 :

6^{n + 1} - 6

Solution

Problem 5 :

7^{n + 2} - 7

Solution

Problem 6 :

3^{n + 2} - 9

Solution

Problem 7 :

5(2ⁿ) + 2^{n + 2}

Solution

Problem 8 :

3^{n + 2} + 3ⁿ⁺¹ + 3ⁿ

Solution

Problem 9 :

2ⁿ⁺¹ + 3(2ⁿ) + 2^{n - 1}

Solution

Problem 10 :

4^x + 11(2^x) + 18

Solution

Problem 11 :

4^x – 2^x - 20

Solution

Problem 12 :

9^x + 9(3^x) + 14

Solution

Problem 13 :

9^x + 4(3^x) - 5

Solution

Problem 14 :

25^x + 5^x - 2

Solution

Problem 15 :

49^x – 7^{x + 1} + 12

Solution

Problem 16 :

Simplify the expression 3^{2x + 1}/ 9^{x - 1}

Solution

Problem 17 :

Simplify the expression (8^{b - 2})(2^{b + 1}) / 4^{(2b - 3)} 

Solution

Problem 18 :

Simplify the expression 5^{2x - 3} ⋅ 25^{1 - x}

Solution

Problem 19 :

Simplify the expression (1/5)^{2x - 3} ⋅ 25^{x - 1}

Solution

Problem 20 :

Simplify the expression 5^{2x - 3} ⋅ 25^{1 - x}

Solution

Factorise the following :

Problem 1 :

3^2x + 3^x

Solution

Problem 2 :

2ⁿ⁺² + 2ⁿ

Solution

Problem 3 :

4ⁿ + 4³ⁿ

Solution

Problem 4 :

6ⁿ⁺¹ - 6

Solution

Problem 5 :

7ⁿ⁺² - 7

Solution

Problem 6 :

3ⁿ⁺² - 9

Solution

Problem 7 :

5(2ⁿ) + 2ⁿ⁺²

Solution

Problem 8 :

3ⁿ⁺² + 3ⁿ⁺¹ + 3ⁿ

Solution

Problem 9 :

2ⁿ⁺¹ + 3 (2ⁿ) + 2^n-1

Solution

Problem 10 :

Solve 16^2x = 8^3x

Solution

Problem 11 :

Solve 4^x = 8^{x + 1}

Solution

Problem 12 :

Solve 25^{2 - x} = 125^{2x - 4}

Solution

Problem 13 :

Solve 2^{x + 2} - 2^x  = 48

Solution

Problem 14 :

Solve 4^{x + 3} + 4^x  = 260

Solution

Problem 15 :

Solve 2^{x + 5} + 2^x  = 1056

Solution

Problem 16 :

1/256 = 2^{2 - 5x}

Solution

Problem 17 :

Solve 27^x/9^{2x - 1} = 3^{x + 4}

Solution

Problem 18 :

Solve 2^2x+1/2^{x - 3} = 4

Solution