In 3 years, dianna will be 4 times as old as she
was 33 years ago. how old is dianna now?
translate the phrase "in 3 years" into algebraic
terms.

Present age of Dianna is 45 years old

Solution:

Let "x" be the present age of Dianna

Given that, In 3 years, Dianna will be 4 times as old as she  was 33 years ago

Then: In three years time Diana’s age would be x + 3

And: thirty three years ago it would have been x - 33

From given question,

x + 3 = 4 times as old as she  was 33 years ago

x + 3 = 4(x - 33)

x + 3 = 4x - 132

x - 4x = -132 - 3

-3x = -135

x = 45

Thus present age of Dianna is 45 years old

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8