Answer: Multiplication sign
f(x) times g(x) = 8x^2+8x-6
(2x-1) times (4x+6) = 8x^2+8x-6
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Step-by-step explanation:
The functions f(x) and g(x) are linear functions. The result of f(x) ___ g(x) is some quadratic function.
It's very likely that the answer is a multiplication sign because of the general template of
(linear)*(linear) = (quadratic)
For example, x*3x = 3x^2.
Let's see if the two functions multiply out to 8x^2+8x-6 or not.
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f(x) * g(x) = ( f(x) ) * ( g(x) )
f(x) * g(x) = ( 2x-1 ) * ( 4x+6 )
f(x) * g(x) = y * ( 4x+6 ) ......... let y = 2x-1
f(x) * g(x) = 4xy + 6y ......... distribute
f(x) * g(x) = 4x( y ) + 6( y )
f(x) * g(x) = 4x( 2x-1 ) + 6( 2x-1 ) .... replace y with 2x-1
f(x) * g(x) = 8x^2-4x + 12x-6 .... distribute twice more
f(x) * g(x) = 8x^2+8x-6
We end up getting the correct result. So this confirms that a multiplication sign is needed to fill in the blank.