Answer :

An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

And, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.


Let’s factorize the given algebraic expression.


We have x2 + x – 6.


First: Multiply the coefficient of x2 and the constant.


Coefficient of x2 = 1


Constant = -6


1 × -6 = -6 …(a)


Now, Observe the coefficient of x = 1


We need to split the value obtained at (a), such that the sum/difference of the split numbers comes out to be 1.


To split: We need to find the factors of -6.


Factors of -6 = 2, 3, -1


Add 3 and (2 × -1 =) -2 = 3 + (-2) = 1


Multiply 3 and -2 = 3 × -2 = -6


Since, the sum of -2 and 3 is 1 and multiplication is -6. So, we can write


x2 + x – 6 = x2 + (3x – 2x) – 6


x2 + x – 6 = x2 + 3x – 2x – 6


x2 + x – 6 = (x2 + 3x) + (-2x – 6)


Now, take out common number or variable in first two pairs and the last two pairs subsequently.


x2 + x – 6 = x(x + 3) – 2(x + 3)


Now, take out the common number or variable again from the two pairs.


x2 + x – 6 = (x + 3)(x – 2)


Thus, the factorization of x2 + x – 6 = (x + 3)(x – 2).


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