How can i do this using f(x) = x^2 + 8x + 16 and x - 4 polynomial division and the remainder theorem create a quadratic polynomial function f(x) and a linear binomial in the form (x − a). part 1. show all work using long division to divide your polynomial by the binomial. x^2 + 8x + 16/x - 4 part 2. show all work to evaluate f(a) using the function you created. part 3. use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

See below.

Step-by-step explanation:

Part 1.

            x  +  12                   < Quotient.

x - 4  ( x^2 + 8x + 16

          x^2-  4x

                   12x + 16

                   12x - 48

                           64  < Remainder.

Part 2

f(4) =  (4)^2 +8(4) + 16 =  16 + 32 + 16

= 64  Which is the remainder we found in the long division.

Part 3.

As you see in Parts 1 and 2, the Remainder Theorem tells you what the remainder is without doing the long division. If the remainder is 0  this means that the binomial you is a factor of the polynomial.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.