Write an equation that defines m(x) as a trinomial where m(x)=(3x-1)(3-x)+4x^2+18

m(x) = x² + 10x + 15

Step-by-step explanation:

Rewrite m(x) = (3x-1)(3-x) + 4x² + 18 as a trinomial (three-term equation) by simplifying the equation. Expand the brackets by multiplying the binomials and collect like terms.

m(x) = (3x-1)(3-x) + 4x² + 18    Multiply brackets with terms FOIL (first, outside, inside, last)

m(x) = (9x - 3x² - 3 + x) + 4x² + 18   The brackets can be removed

m(x) = 9x - 3x² - 3 + x + 4x² + 18   See what terms have the same variables

m(x) = -3x² + 4x² + 9x + x  + 18 - 3  Like terms are rearranged together

m(x) = x² + 10x + 15    Collected like terms

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2