how to solve splitting the middle term
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Type I: Factorization of Quadratic polynomials of the form x2 + bx + c. (i) In order to factorize x2 + bx + c we have to find numbers p and q such that p + q = b and pq = c. (ii) After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.
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Example- x² + 6x + 8
Step-by-step explanation:
We have to split the middle term that is-
we find two numbers p and q such that p + q = 6 and pq = 8. Clearly, 2 + 4 = 6 and 2 × 4 = 8.
= Therefore, we can say that 6x=4x + 2x
= (x² + 2x) + (4x + 8)
=x( x + 2) +4( x + 2)
We can again take (x+2) as common and write it is -
(x + 2)( x + 6)
So the final ans is (x+2)(x+6)
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