PRACTICE QUESTIONS ON FACTORING POLYNOMIALS

Factoring the following monomials

Questions :

1)  25n^{2   Solution}

2)  18xy        Solution

3)  12y         Solution

4)  21y^{2      Solution}

5)  81a             Solution

6)  92q      Solution

7)  36x^{3        Solution}

8)  24h         Solution

9)  48x^{2       Solution}

10)  x²y^{3          Solution}

11)  9a² - 18a           Solution

12)  x³ - 5x^{2        Solution}

13)  9x² - 36        Solution

14)  8x² + 72x       Solution

15)  8x² - 80x       Solution

16)  16a⁵b³ + 32a^{4        Solution}

17)  11m² - 99m       Solution

18)  x² + x³ + x^{4        Solution}

19)  36x³ / 42 x^{2       Solution}

20)  16p² / 28 p       Solution

21)  32n² / 24n        Solution

22)  70n² / 28n         Solution

23) (2r - 4) / (r - 2)         Solution

24)  45/(10a - 25)         Solution

25)  (15 a - 3)/24       Solution

26)  (x - 4)/(3x² - 12x)        Solution

27)  27/(27x + 18)         Solution

28)  (4x - 4) / (6x - 20)          Solution

Factoring the following binomials

Factor each of the following. 

1)  4x + 24y       Solution

2)  2x² – 8x     Solution

3)  x² – 3x     Solution

4)  3a + 6ab + 9a^{2   Solution}

5)  ab + bc - 2b     Solution

6)  3(x – 6) + d(x – 6)        Solution

7)  2x(x + 4) + 3x + 12       Solution

8)  4x²y³ + 6x³y^{2     Solution}

9)  x² + 5x + 6        Solution

10)  x² - 15x + 56         Solution

11)  x² + 2x - 15           Solution

12)  x² - x - 20       Solution

13)  2x² + 9x + 9           Solution

14)  3x² + x - 4       Solution

15) x² + 8x + 16          Solution

16)  x² + 6xy + 9y^{2        Solution}

17)  4a² - 20ab + 25b^{2         Solution}

18)  9m² - 16n^{2         Solution}

19)  a²b² - c²d^{2        Solution}

20)  x⁴ - y^{4            Solution}

21)  x³ + 3x² + 6x + 18          Solution

22)  x³ + 2x² - 9x - 18          Solution

Factoring the following expressions with four terms 

1)  x² + 4x – 5x - 20       Solution

2)  x² - 7x + 3x - 21      Solution

3)  x² - 3x + 2x - 6           Solution

4)  x² - 6x - 3x + 18     Solution

5)  x² + 7x - 9x - 63   Solution

6)  2x² + x - 6x - 3       Solution

7)  3x² + 2x - 12x - 8         Solution

8)  4x² - 3x - 8x + 6      Solution

9)  9x² + 4x - 9x - 4       Solution

10)  5x³ + 25x² + 2x + 10      Solution

11)  x³ + 2x² + 3x + 6      Solution

12)  x³ - 6x² + 4x - 24      Solution

13)  x³ - 4x² - 5x + 20    Solution

14)  x³ - 5x² - 2x + 10         Solution

15)  x³ + 4x² + 5x + 20     Solution

16)  x³ + 2x² - 3x - 6    Solution

17)  x³- 2x² - 5x + 10         Solution

Question 1 :

Solve the following quadratic equations by factorization method :

√2x² + 7x + 5√2 = 0

Solution

Question 2 :

Solve the following quadratic equations by factorization method :

10x² - x - (1/5)  =  0

Solution

Question 3 :

The number of volleyball games that must be scheduled in a league with n teams is given by G (n) = (n² - n)/2 where each team plays with every other team exactly once. A league schedules 15 games. How many teams are in the league?

Solution

Question 4 :

Victor is y years old. His brother Fred is four years old than Victor. The product of their ages is 780.

(a) Set up an equation to represent this information.

(b) Solve your equation from (a) to find Victor’s age.

Solution

Question 5 :

A rectangular field is 30m longer than wide. The area of the field is 8800 m² Work out the perimeter of the field.

Solution

Question 6 :

Shown is a right angled triangle. Show that

11x² − 62x − 105 = 0

and solve for x.

Solution

Question 7 :

Shown is a right angled triangle with sides are measured in centimeters.

(a) Show that x² − 5x − 14 = 0

(b) Solve for x.

Solution

Question 8 :

The surface area of the cuboid is 270 cm².

(a) Show x² + 4x − 45 = 0

(b) Solve for x

Solution

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