F(x) = 1/4 * x ^ 4 - 9/4 * x ^ 2 - x + 3 Rewrite f(x) as the product of a rational number and a polynomial with integer coefficients.

F(x) = 1/4 × (x⁴ - 9x² - 4x + 12)

Step-by-step explanation:

Since F(x) = x⁴/4 - 9x²/4 - x + 3

The L.C.M of the right hand side is 4.

So, we have

F(x) = (4 × x⁴/4 - 4× 9x²/4 - 4 × x + 4 × 3)/4

F(x) = (x⁴ - 9x² - 4x + 12)/4

F(x) = 1/4 × (x⁴ - 9x² - 4x + 12)

50*10 is greater

step-by-step explanation:

if you add the zero from 10 to 50, it will give you a bigger number.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!