FACTORING QUADRATIC TRINOMIALS

Key Concept - 1

Factoring Quadratic Trinomials in the form ax² + bx + c, where a = 1.

Key Concept - 2

Factoring Quadratic Trinomials in the form ax² + bx + c, where a ≠ 1.

Solved Problems

Factor each quadratic trinomial completely.

Problem 1 :

x² + 7x + 12

Solution :

= x² + 7x + 12

= x² + 3x + 4x + 12

= x(x + 3) + 4(x + 3)

= (x + 3)(x + 4)

Problem 2 :

x² + 5x - 14

Solution :

= x² + 5x - 14

= x² + 7x - 2x - 14

= x(x + 7) - 2(x + 7)

= (x + 7)(x - 2)

Problem 3 :

x² - 11x + 30

Solution :

= x² - 11x + 30

= x² - 6x - 5x + 30

= x(x - 6) - 5(x - 6)

= (x - 6)(x - 5)

Problem 4 :

x² - 5x - 24

Solution :

= x² - 5x - 24

= x² - 8x + 3x - 24

= x(x - 8) + 3(x - 8)

= (x - 8)(x + 3)

Problem 5 :

x² - 7x - 18

Solution :

= x² - 7x - 18

= x² - 9x + 2x - 18

= x(x - 9) + 2(x - 9)

= (x - 9)(x + 2)

Problem 6 :

x² + x - 20

Solution :

= x² + x - 20

= x² + 5x - 4x - 20

= x(x + 5) - 4(x + 5)

= (x + 5)(x - 4)

Problem 7 :

x² - 3x - 40

Solution :

= x² - 3x - 40

= x² - 8x + 5x - 40

= x(x - 8) + 5(x - 8)

= (x - 8)(x + 5)

Problem 8 :

x² + 3x - 28

Solution :

= x² + 3x - 28

= x² + 7x - 4x - 28

= x(x + 7) - 4(x + 7)

= (x + 7)(x - 4)

Problem 9 :

3x² + 15x - 150

Solution :

= 3x² + 15x - 150

= 3(x² + 5x - 50)

= 3(x² + 10x - 5x - 50)

= 3[x(x + 10) - 5(x + 10)]

= 3(x + 10)(x - 5)

Problem 10 :

2x² + x - 3

Solution :

= 2x² + x - 3

= 2x² + 3x - 2x - 3

= x(2x + 3) - 1(2x + 3)

= (2x + 3)(x - 1)

Problem 11 :

6x² + 17x + 5

Solution :

= 6x² + 17x + 5

= 6x² + 15x + 2x + 5

= 3x(2x + 5) + 1(2x + 5)

= (2x + 5)(3x + 1)

Problem 12 :

2x² + 7x + 3

Solution :

= 2x² + 7x + 3

= 2x² + 6x + 1x + 3

= 2x(x + 3) + 1(x + 3)

= (x + 3)(2x + 1)

Problem 13 :

9x² - 15x + 4

Solution :

= 9x² - 15x + 4

= 9x² - 12x - 3x + 4

= 3x(3x - 4) - 1(3x - 4)

= (3x - 4)(3x - 1)

Problem 14 :

10x² + 21x + 9

Solution :

= 10x² + 21x + 9

= 10x² - 15x - 6x + 9

= 5x(2x - 3) - 3(2x - 3)

= (2x - 3)(5x - 3)

Problem 15 :

12x² - 38x + 20

Solution :

= 12x² - 38x + 20

= 2(6x² - 19x + 10)

= 2(6x² - 15x - 4x + 10)

= 2[3x(2x - 5) - 2(2x - 5)]

= 2(2x - 5)(3x - 2)

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.