Subscribe to our YouTube channel for the latest videos, updates, and tips.


Factorization of Quadratic Trinomials

In factorization of quadratic trinomials there are two forms: 

(i) First form: x2 + px + q

(ii) Second form: ax2 + bx + c

(i) Factorization of trinomial of the form x^2 + px + q:

Suppose we are given a quadratic trinomial x2 + px + q.

Then, we use the identity:

x2 + (a + b) × + ab = (x + a)(x + b).


Solved examples on factorization of quadratic trinomials of the form x^2 + px + q:



1. Factorize the algebraic expression of the form x2 + px + q:

(i) x2 - 7x + 12

Solution:

The given expression is x2 - 7x + 12

Find two numbers whose sum = -7 and product = 12

Clearly, such numbers are (-4) and (-3).

Therefore, x2 - 7x + 12 = x2 - 4x - 3x + 12

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

                                = (x - 4)(x - 3).


(ii) x2 + 2x - 15

Solution:

The given expression is x2 + 2x - 15

To factorize the given quadratic trinomial, we have to find two numbers a and b, such that a + b = 2 and ab = -15

Clearly, 5 + (-3) = 2 and 5 × (-3) = -15

Therefore such numbers are 5 and -3

Now, splitting the middle term 2x of the given quadratic trinomial x2 + 2x -15, we get,

x2 + 5x - 3x -15

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

= (x + 5) (x - 3)

 

(ii) Factorization of trinomial of the form ax^2 + bx + c:

In order to factorize the expression ax2 + bx + c we have to find the two numbers p and q, such that

p + q = b and p × q = ac


Solved examples on factorization of quadratic trinomials of the form ax^2 + bx + c:

2. Factorize the algebraic expression of the form ax2 + bx + c:

(i) 15x2 - 26x + 8

Solution:

The given expression is 15x2 - 26x + 8.

Find two numbers whose sum = -26 and product = (15 × 8) = 120.

Clearly, such numbers are -20 and -6.

Therefore, 15x2 - 26x + 8 = 15x2 - 20x - 6x + 8

                                   = 5x(3x - 4) - 2(3x - 4) 

                                   = (3x - 4)(5x - 2).


(ii) 3q2 – q – 4

Solution:

Here, two numbers m and n are such that their sum m + n = -1 and their product m × n = 3 × (-4) i.e. m × n = - 12

Clearly, such numbers are -4 and 3

Now, splitting the middle term –q of the given quadratic trinomial 3q2 – q – 4 we get,

3q2 - 4q + 3q – 4

= q(3q – 4) + 1(3q – 4)

= (3q – 4)(q + 1)





8th Grade Math Practice

From Factorization of Quadratic Trinomials to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 10, 25 11:41 AM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More