# How do you find the polynomial function whose graph passes through (2,4), (3,6), (5,10)?

##### 1 Answer

May 19, 2018

Simplest solution:

#f(x) = 2x#

General solution:

#f(x) = P(x)(x^3-10x^2+31x-30)+2x#

#### Explanation:

Given:

#(2, 4)# ,#(3, 6)# ,#(5, 10)#

Note that each

So a suitable polynomial function is:

#f(x) = 2x#

Note however that this is not the only polynomial function passing through these three points.

We can add any multiple (scalar or polynomial) of a cubic whose zeros lie at those three points, namely:

#(x-2)(x-3)(x-5) = x^3-10x^2+31x-30#

Hence the most general solution is:

#f(x) = P(x)(x^3-10x^2+31x-30)+2x#

for any polynomial