We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Quadratic factorization using splitting of middle term : In this method splitting of middle term in to two factors.In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.

To Factor the form :ax^{2} + bx + c |
Factor : 6x^{2} + 19x + 10 |

1) Find the product of 1st and last term( a x c). |
6 x 10 = 60 |

2) Find the factors of 60 in such way that addition or subtraction of that factors is the middle term (19x)(Splitting of middle term) |
15 x 4 = 60 and 15 + 4 = 19 |

3) Write the center term using the sum of the two new factors, including the proper signs. |
6x^{2} + 15x + 4x + 10 |

4) Group the terms to form pairs - the first
twoterms and the last two terms. Factor each pair by finding common factors. |
3x ( 2x + 5)+ 2(2x + 5) |

5) Factor out the shared (common)
binomial parenthesis. |
(3x + 2) ( 2x + 5) |

Example: Find the factors of 6x^{2} - 13x + 66x ^{2} - 13 x + 6 ----->(1) a.c = Product of 6 and 6 = 36 Factors of 36 = 2,18 = 3,12 = 4,9 Only the factors 4 and 9 gives 13-->(4 + 9) For -13 , both the factors have negative sign. – 4 – 9 = - 13 Equation (1) ⇒ 6x ^{2} - 4x – 9x + 6 ⇒2x ( 3x – 2 ) – 3 ( 3x – 2 ) ⇒ (3x – 2 ) ( 2x – 3) are the factors. |

Roots of the equation are

3x – 2 = 0 ⇒ 3x = 2 so x = 2/3

2x – 3 = 0 ⇒ 2x = 3 so x = 3/2

1) 12x

12x

12x

12x

12x

4x(3x + 5) - 3(3x + 5) = 0

(3x + 5)(4x - 3) = 0

3x + 5 = 0 or 4x - 3 = 0

3x = - 5 or 4x = 3

x = -5/3 or x = 3/4

Solution is (-5/3,3/4)

_________________________________________________________________

2) Find the factors of 3x

3x

⇒ 3x

⇒ 3x(x - 1) + (x - 1) = 0

⇒ (x - 1)(3x + 1) = 0

⇒ x = 1 and x = -1/3

________________________________________________________________

3) Product of two consecutive positive integers is 240. Find the integers.

Let x and x + 1 are consecutive positive integers.

x(x + 1) = 240

x

x

x

x(x + 16) - 15(x -16)= 0

(x + 16)(x -15) = 0

x = -16 and x = 15

So the positive integers are 15 and 16.

• Quadratic Factorization using Splitting of Middle Term

• By completing the square

• Factorization using Quadratic Formula

• Solved Problems on Quadratic Equation

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers