Q. 1 E
I/we factorise th
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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West Bengal - MathematicsLet’s resolve int
West Bengal - Mathematics