I/we factorise the following algebraic expressions:

y² + 23y + 102

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 y² + 23y + 102.

First: Multiply the coefficient of y² and the constant.

Coefficient of y² = 1

Constant = 102

⇒ 1 × 102 = 102 …(a)

Now, Observe the coefficient of y = 23

We need to split the value obtained at (a), such that the sum/difference of the split numbers comes out to be 23.

To split: We need to find the factors of 102.

Factors of 102 = 2 × 3 × 17

Add 17 and (2 × 3 =) 6 = 17 + 6 = 23

Multiply 17 and 6 = 17 × 6 = 102

Since, the sum of 17 and 6 is 23 and multiplication is 102. So, we can write

y² + 23y + 102 = y² + (17y + 6y) + 102

⇒ y² + 23y + 102 = y² + 17y + 6y + 102

⇒ y² + 23y + 102 = (y² + 17y) + (6y + 102)

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

⇒ y² + 23y + 102 = y(y + 17) + 6(y + 17)

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

⇒ y² + 23y + 102 = (y + 17)(y + 6)

Thus, the factorization of y² + 23y + 102 = (y + 17)(y + 6).