Question:
Give any two quadratic polynomials and factorize them by using algebric identities and by splitting the middle terms
Answer:
Let two polynomials are:
x2 - 7x + 12
Now split the middle term in such a way that its sum is 7 and multiplication is 12
So, x2 - 7x + 12 = x2 - (3 + 4)x + 12
= x2 - 3x - 4x + 12
= x(x - 3) - 4(x - 3)
= (x - 3)*(x - 4)
Let us take another example: x2 - 5x + 6
Now split the middle term in such a way that its sum is 7 and multiplication is 6
So, x2 - 7x + 6 = x2 - (6 + 1)x + 6
= x2 - 6x - x + 6
= x(x - 6) - 1(x - 6)
= (x - 6)*(x - 1)
In this way, we do it.
Hope you got the point.
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