Question

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! I CANNOT RETAKE THIS!!

Answer 1

Answer: B

Step-by-step explanation:

Use synthetic division to factor out the given zero: (x = 5)⇒(x - 5) = 0

5 | 1    -4    -21    100    -100

   | ↓   5       5    -80      100  

     1    1      -16    20         0   ⇒  this is the decomposed polynomial

(x - 5)(x³ + x² - 16x + 20)

Use synthetic division to find another factor: Let's try x = 2 ⇒ x - 2 = 0

2 | 1     1      -16     20        

   | ↓   2       6     -20    

     1    3      -10      0     ⇒  this is the decomposed polynomial

(x - 5)(x - 2)(x² + 3x - 10)  

(x - 5)(x - 2)(x + 5)(x - 2)

=  (x - 5)(x + 5)(x - 2)²

Answer 2

Answer:

Short Answer: B

Step-by-step explanation:

Using synthetic division to break this down a little, we get from your hint, the following

-5 || 1    - 4    -21     100    - 100

            -5      45    -120     100          

      ======================

      1     -9      24    -20       0   = x^3 - 9x^2 + 24x - 20

We can do this again, this time using 5

5 ||   1      - 9      24       - 20

                5      -20         20

===========================

       1       -4        4           0      = x^2 - 4x + 4

h(x) = x^2 - 4x + 4 factors into

h(x) = (x - 2)(x - 2)

The final result is f(x) = (x + 5)(x - 5)(x - 2) (x - 2)

which is B