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Factorization by Middle Term Splitting

Quadratic Equations I - Concepts

Identifying Quadratic Equations

Factors of Quadratic Equation

Factorization by Grouping of Terms

Factorization by Middle Term Splitting

Factorization by Completing the Square

Statement Sums involving Linear Equations

Statement sum Involing Quadratic Equations

Solving Statements Involving Age

Statement sums involving Coins

Solving Statements For A Two Digit Number

Equations Reducible to Quadratic Form

Class - 10th IMO Subjects

Concept Explanation

Factorization by Middle Term Splitting

Factorization of quadratic polynomials in one Variables:

Let us now consider the polynomial $y^{2}-7y+12$ .

Comparing this with polynomial $y^{2}+(a+b)y+ab$ , we get a + b = -7 and ab = 12.

Now, we have to find factors of 12 whose sum is -7.

Since a + b is negative ab is positive. Therefore, a and b both must negative

Clearly, such factors are -3 and -4.

Hence, the factors of $y^{2}-7y+12$ are (y - 3) and ( y - 4 ).

$therefore ;;y^{2}-7y+12=(y-3)(y-4).$

Algorithm:

Step I Obtain the quadratic polynomial $x^{2}+px+q$ .

Step II Obtain p = coefficient of x and, q = constant term.

Step III Find two numbers a and b such that a + b = p and ab = q.

Step IV Split up the middle term as the sum of two terms ax and bx.

Step V Factorize the expression obtained in step IV by grouping the terms.

Illustration: Factorize the following expression:

$;;x^{2}+6x+8$

Solution: In order to factorize $x^{2}+6x+8$ , we find two numbers p and q such that

p + q + 6 and pq = 8

Clearly, 2 + 4 = 6 and 2 $times$ 4 = 8.

We now split the middle term 6x in the given quadratic as 2x + 4x.

$therefore ;;;x^{2}+6x+8=x^{2}+2x+4x+8$

$=(x^{2}+2x)+4(4x+8)$

$=x(x+2)+4(x+2)$

$=(x+2)(x+4)$

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Sample Questions

(More Questions for each concept available in Login)

Question : 1

Factorise the following expression: $(l + m)^2 - 4lm$
A. l - m, l - m	B. l + m, l + m	C. l + 2m, l - m	D. l + 2m, l + m
Right Option : A
View Explanation

Question : 2

Factorise : $large 36 +11(z-frac{y}{3}+x)-12(z-frac{y}{3}+x)^2+(4z-frac{4}{3}y+4x-9)(5+3z -y +2x)$
A. $large (4z-frac{4y}{3}+4x-9)left ( 1+x right )$	B. (1+x) $large (4z-frac{4y}{3}+4x-9)$	C. (1-x) $large (4z+frac{4y}{3}+4x-9)$	D. (1+x) $large (4z+frac{4y}{3}+4x+9)$
Right Option : A
View Explanation

Question : 3

Which of the following values is a zero of the polynomial $large x^2-3x+2$ ?
A. -1	B. 2	C. -2	D. 0
Right Option : B
View Explanation

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Language - English

Chapters

Real Numbers I

Real Numbers II

Pair of Linear Equations I

Pair of Linear Equations II

Polynomial I

Polynomials II

Quadratic Equations I

Quadratic Equations II

Introduction to Trigonometry I

Introduction to Trigonometry II

Arithmetic Progression I

Arithmetic Progression II

Triangles I

Triangles II

Some Applications of Trigonometry

Coordinate Geometry I

Coordinate Geometry II

Introduction to Trigonometry

Direct and Inverse Variation

Surface Area and Volume I

Surface Area and Volume II

Areas Related to Circles

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Attention !!!!!

Factorization by Middle Term Splitting

Factorization by Middle Term Splitting

Factorization of quadratic polynomials in one Variables:

Algorithm:

Students / Parents Reviews [10]

Yatharthi Sharma

Barkha Arora

Om Umang

Eshan Arora

Hiya Gupta

Archit Segal

Aman Kumar Shrivastava

Shivam Rana

Prisha Gupta

Cheshta