Factorize the Trinomial ax Square Plus bx Plus c
Factorize the trinomial ax square plus bx plus c means ax
^{2} + bx + c.
In order to factorize the expression ax
^{2} + bx + c, we have to find two numbers m and n, such that m + n = b and m × n = ac.
That is we split b into
two parts m and n whereas sum m and n = b and product m and n = ac.
Solved examples to factorize the
trinomial ax square plus bx
plus c (ax^2 + bx + c):
1. Resolve into factors:
(i) 2x
^{2} + 9x + 10
Solution:
The given expression is 2x
^{2} + 9x + 10.
Find two numbers whose sum = 9 and product = (2 × 10) = 20.
Clearly, such numbers are 5 and 4.
Therefore, 2x
^{2} + 9x + 10 = 2x
^{2} + 5x + 4x + 10
= x(2x + 5) + 2(2x + 5)
= (2x
+ 5)(x + 2).
(ii) 6x
^{2} + 7x - 3
Solution:
The given expression is 6x
^{2} + 7x - 3.
Find two numbers whose sum = 7 and product = 6 × (-3) = -18.
Clearly, such numbers are 9 and -2.
Therefore, 6x
^{2} + 7x - 3 = 6x
^{2} + 9x - 2x - 3
= 3x (2x + 3) -1 (2x + 3)
= (2x + 3)(3x - 1).
2. Factorize the trinomial:
(i) 2m
^{2} +7m + 3
Solution:
The given expression is 2m
^{2} +7m + 3.
Here, the two numbers a and b are such that their sum x + y =7 and their product x × y = 3 × 2 i.e., x × y = 6
Such numbers are 1 to 6
Now, splitting the middle term 7m of the given expression 2m
^{2} + 7m + 3 we get,
= 2m
^{2} + 1m + 6m + 3
= m(2m + 1) + 3(2m +
1)
= (2m +1)(m + 3)
(ii) 3x
^{2} - 4x - 4
Solution:
The given expression is 3x
^{2} - 4x - 4.
Find two numbers whose sum = -4 and product = 3 × (-4) = -12.
Clearly, such numbers are -6 and 2.
Therefore, 3x
^{2} - 4x - 4 = 3x
^{2} - 6x + 2x - 4
= 3x(x - 2) +2(x - 2)
= (x - 2)(3x + 2).
8th Grade Math Practice
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