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 a2 + a – 132.


First: Multiply the coefficient of a2 and the constant.


Coefficient of a2 = 1


Constant = -132


1 × -132 = -132 …(a)


Now, Observe the coefficient of a = 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 -132.


Factors of -132 = 2, 2, 3, 11, -1


Add (2 × 2 × 3 =) 12 and (11 × -1 =) -11 = 12 + (-11) = 1


Multiply 12 and -11 = 12 × -11 = -132


Since, the sum of 12 and -11 is 1 and multiplication is -132. So, we can write


a2 + a – 132 = a2 + (12a – 11a) – 132


a2 + a – 132 = a2 + 12a – 11a – 132


a2 + a – 132 = (a2 + 12a) + (-11a – 132)


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


a2 + a – 132 = a(a + 12) – 11(a + 12)


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


a2 + a – 132 = (a + 12)(a – 11)


Thus, the factorization of a2 + a – 132 = (a + 12)(a – 11).


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