Which expression is equivalent to n² + 26n + 88 for all values of n?

Solution:

It is given that

n² + 26n + 88 for all values of n

The given equation is of the form ax² + bx + c = 0

a = 1, b = 26 and c = 88

Two number which multiply to give ac = 88 (22 or 4)

Two numbers which add up to give 22 + 4 i.e. b = 26

So the middle term 26n can be written as 22n and 4n

n² + 22n + 4n + 88 = 0

Taking out the common terms

n(n + 22) + 4(n + 22) = 0

(n + 22)(n + 4) = 0

Therefore, the expression (n + 22)(n + 4) is equivalent to n² + 26n + 88.

Which expression is equivalent to n² + 26n + 88 for all values of n?

Summary:

The expression which is equivalent to n² + 26n + 88 for all values of n is (n + 22) (n + 4).