Factorize the Trinomial x Square Plus px Plus q
In order to factorize the expression x2 + px + q, we find two numbers a and b such that (a + b) = p and ab = q.
Then, x2 + px + q = x2 + (a + b)x + ab
= x2 + ax + bx + ab
= x(x + a) + b(x + a)
= (x + a)(x + b) which are the required factors.
Solved examples to factorize the trinomial x square plus px plus q (x^2 + px + q):
1. Resolve into factors:
Solution:
The given expression is x2 + 3x - 28.
Find two numbers whose sum = 3 and product = - 28.
Clearly, the numbers are 7 and -4.
Therefore, x2 + 3x - 28 = x2 + 7x - 4x - 28
= x(x
+ 7) - 4(x + 7).
= (x +
7)(x - 4).
Solution:
The given expression is x2 + 8x + 15.
Find two numbers whose sum = 8 and product = 15.
Clearly, the numbers are 5 and 3.
Therefore, x2 + 8x + 15 = x2 + 5x + 3x + 15
= x(x
+ 5) + 3(x + 5).
= (x +
5)(x + 3).
2. Factorize the trinomial:
(i) x2 + 15x + 56Solution:
The given expression is x2 + 15x + 56.
Find two numbers whose sum = 15 and product = 56.
Clearly, such numbers are 8 and 7.
Therefore, x2 + 15x + 56 = x2 + 8x + 7x + 56
= x(x
+ 8) + 7(x + 8)
= (x +
8)(x + 7).
Solution:
The given expression is x2 + x - 56.
Find two numbers whose sum = 1 and product = - 56.
Clearly, such numbers are 8 and - 7.
Therefore, x2 + x - 56 = x2 + 8x - 7x - 56
= x(x
+ 8) - 7(x + 8)
= (x +
8)(x - 7).
8th Grade Math Practice
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