Factorization of Quadratic polynomials of the form x2 + bx + c.
(i) In order to factorize x2 + bx + c we have to find numbers m and n such that m + n = b and mn = c.
(ii) After finding m and n, we split the middle term in the quadratic as mx + nx and get desired factors by grouping the terms.
Let us understand by an example:
Example: Factorize the following quadratic polynomials: x2 + 6x + 8
Solution: In order to factorize x2 + 6x + 8,
we have to find two numbers such that their sum is 6 and the product 8.
Clearly, 6 = 4 + 2 and 4 × 2 = 8
x2 + 6x + 8 = x2 + 4 x + 2x + 8
= (x2 + 4 x) + (2x + 8)
= x(x + 4) + 2 (x + 4) = (x + 2) (x + 4)
To master this middle term splitting requires enough practice. Download the below PDF that contains enough problems for practice.
Find the zeroes of the following polynomial By splitting of middle term:
Here we are providing 150 questions based on middle term splitting for practice. After solving all these problems students will be able to split the middle term faster.
This practice sheet is provided in pdf format. So students can download this practice sheet and solve at any time according to the convenience.
Hope this helps!