Question

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

One of the zeros of the polynomial function is 5.

What is the factored form of the function?

Answer 1

Answer: B

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

Short Answer: B

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