Question

One of the zeros of the polynomial function is 5.

Answer 1

The last term  is -100 so  its either a or d.
Try a:-

(x^2 - 25)(x-2)(x - 2)

= x^2 - 25 (x^2 - 4x + 4)

= x^2 + 4x^3 + 4x^2 - 25x^2 + 100x - 100
= x^4 + 4x^3 - 21x^2 + 100x - 100   

Its a.

Answer 2

Answer:

The factored form of the function is:

A. $f(x) = (x-5)(x+5)(x-2)^{2}$

Step-by-step explanation:

To factor the expression you can use synthetic division.

f(x)=x4−4x3−21x2+100x−100

1. Take the constant and find it's factors. So the factors of 100 are:     ±1, ±2, ±4, ±5,±10,±20,±25, ±50,±100

• In this case -5 works (synthetic division is shown in the picture attached)

       Hint: you know a number divides the polynomial expression      

       when the remainder is zero

2. Therefore: $f(x) = (x+5)(x^{3}-9x^{2}+24x-20)$

   Using synthetic division once more. The factors of twenty are:

   ±1, ±2, ±4, ±5,±10,±20.

   In this case 2 works (synthetic division is shown in the picture          

   attached)

3. Therefore: $f(x)= (x+5)(x-2)(x^{2} -7x+10)$

4. Factor the last expression: $(x^{2} -7x+10)$

• _ + _ = -7 and _ x _= 10
• -5 and -2

5. So $(x^{2} -7x+10)$ $= (x-5)(x-2)$

6. Therefore: $f(x) = (x+5)(x-2)(x-5)(x-2) = (x-5)(x+5)(x-2)^{2}$