Write hx as a linear combination of fx and gx hx 6x210x5 fx

Write h(x) as a linear combination of f(x) and g(x).

h(x)= 6x²-10x+5

f(x)= x+1

g(x)= 2x²-2x+3

Solution

Given that

h(x)= 6x²-10x+5

f(x)= x+1

g(x)= 2x²-2x+3

Then consider 3g(x) - 4f(x) = 3( 2x² - 2x + 3 ) - 4( x + 1 )

= 6x² - 6x + 9 - 4x - 4

= 6x² - 10x + 5

= h(x)

Thus h(x) can be written as a linear combination of f(x) and g(x ) as

h(x) = 3g(x) - 4f(x)