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.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

i don't even know man. edge inuity be messing with us. i had to ask a question too.