Question

What must be added to 2x^3-4x+9 to get 5x^3-13?

Answer 1

let the no. be n
acc. to the ques.
(2x³ - 4x + 9) + n = (5x³-13)  ...................1
n = (5x³-13) - (2x³ - 4x + 9) 
n =  5x³-13 - 2x³ + 4x - 9
n =  3x³ + 4x - 22

So, u need to add (3x³ + 4x - 22) to (2x³- 4x + 9) to get (5x³ - 13)

In case to make urself sure u can just put (3x³ + 4x - 22) to n in equation 1
i.e.
→ (2x³ - 4x + 9) + n = (5x³-13)
∴ L.H.S. = (2x³ - 4x + 9) + (3x³ + 4x - 22) 
→ (2x³ - 4x + 9 + 3x³ + 4x - 22)
→ (2x³ + 3x³ -4x +4x - 22 + 9)
→ (5x³ - 13)
∵ R.H.S. = (5x³ - 13)
⇒ LHS = RHS
 So, one indeed need to add (3x³ + 4x - 22) to (2x³- 4x + 9) to get (5x³ - 13)
Hope it helped

Answer 2

to find the number, let me consider the number =a so,
(5x^3-13) -(2x^3-4x+9)=5x^3-2x^3-(-4x)-13-9
=3x^3+4x-22