Question

Easy way to solve the Fractorisation sums

Answer 1

Answer:

Let's take a general quadratic equation to factorize,

ax2+bx+c=(a1x+p)(a2x+q)=0.

We have assumed p and q to be the second terms of two factors, and a1 and a2 the coefficients of x in the two factors.

Expanding the RHS and equating the coefficients of like terms and the numeric term we get the all too important relations,

a1a2=a, the 1st term coefficient,

pq=c, the numeric term, and

a1q+a2p=b, the middle term coefficient.

Whatever be the method you use for factorization of a quadratic equation, if these three relations are satisfied, then only you know that your factorization is correct.

In the comprehensive method, we will mainly analyze how the two factors of the coefficient of the 1st term involving x2, if it is not 1, are multiplied into two products with the two factors of the numeric term to form the middle term coefficient to satisfy,

a1q+a2p=b.

We'll form feasible factor pairs for each considering the value of the middle term, to quickly form the right combination.

Step-by-step explanation:

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