Lesson Progress
0% Complete

Topic Content:

  • Factorization of Quadratic Expressions II
    • Quadratic Expression of the form ax2 + bx + c

Quadratic Expression of the form ax2 + bx + c

Factorization of Quadratic Equation by Splitting the Middle Term:

In order to factorise a quadratic expression of the form ax2 + bx + c, where \( \scriptsize a \neq 1 \)  

Consider the quadratic equation ax2 + bx + c = 0

Step 1: Multiply the coefficient of x2 and the constant term c i.e. a × c = ac

Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b.

Product: (number 1)(number 2) = ac
Sum: (number 1) + (number 2) = b

Step 3 (Fcatorise): Now, split the middle term using these two numbers,

x2 + (number 1)x + (number 2)x + c = 0

Step 4 (Simplify): Take the common factors out and simplify.

Example 6.4.2:

Factorise the following expressions:

(a) \( \scriptsize 5x^2 \: – \: 7x \: + \: 2\)
(b) \( \scriptsize 35x^2 \: + \: 31x\: + \: 6\)
(c) \( \scriptsize 20x^2\: – \: 40xy \:+ \:15y^2\)
(d) \( \scriptsize 8x^3 \:- \:44x^2 \:+ \:20x\)

Solution

(a) \( \scriptsize 5x^2\: – 7x \:+\: 2\)

Step 1: Multiply the coefficient of x2 and the constant term c i.e. a × c = ac

a = 5, c = 2

∴ 5 × 2 = 10

Step 2: Find two numbers such that their product is equal to ac and sum equals to b.

Product = \( \scriptsize -5x \: \times \: -2x = \: -10x^2 \)

Sum = \( \scriptsize -5x \: + \: -2x = \: -7x\)

 

You are viewing an excerpt of this Topic. Subscribe Now to get Full Access to ALL this Subject's Topics and Quizzes for this Term!

Click on the button "Subscribe Now" below for Full Access!

Subscribe Now

Note: If you have Already Subscribed and you are seeing this message, it means you are logged out. Please Log In using the Login Button Below to Carry on Studying!

avatar

Responses

Your email address will not be published. Required fields are marked *