2. list the emperors in order of the lengths of their reigns, with the shortest reign
First ?

Explanation:

Find out the lengths of their reigns by subtraction.

Babar = 1530 - 1526

= 4 years

Humayan = 1556 - 1530

= 26 years

Akbar = 1605 - 1556

= 49 years

Jahangir = 1627 - 1605

= 22 years

Shah Jahan = 1658 - 1627

= 31 years

Aurangzeb = 1707 - 1658

= 49 years

Order them from shortest reigns to largest.

Barber ⇒ Jahangir ⇒ Humayan ⇒ Shah Jahan ⇒ Aurangzeb ⇒ Akbar

The last two reigned for the same amount of time so any order is fine.

answer

explanation

the given equation is

we can rewrite this as:

let

then the equation becomes:

the factors of 8 that sum up to -9 are {-1,-8}

we split the middle term with these factors to obtain,

we factor by grouping to obtain:

apply the zero product property to get:

but