127k views
1 vote
Please Help!!!

Answer choices listed below...

What is a polynomial function in standard form with zeroes 1, 2, -3, and -1 ?

Please Help!!! Answer choices listed below... What is a polynomial function in standard-example-1

1 Answer

6 votes

Option A:


g(x) =x^4+x^3-7x^2-x+6

Solution:

Given data: Zeroes are 1, 2, –3, and –1.

To find the polynomial of the function for the given zeroes.

If 1 is a root of the polynomial then the factor is (x – 1).

If 2 is a root of the polynomial then the factor is (x – 2).

If –3 is a root of the polynomial then the factor is (x – (–3)) = (x + 3).

If –1 is a root of the polynomial then the factor is (x – (–1)) = (x + 1).

On multiplying the factors, we get the polynomial of the function.


\Rightarrow\ g(x)=(x-1)(x-2)(x+3)(x+1)


\Rightarrow\ \ \ \ \ \ \ \ =(x^2-2x-x+2)(x^2+x+3x+3)


\Rightarrow\ \ \ \ \ \ \ \ =(x^2-3x+2)(x^2+4x+3)

Now multiplying each term of the first factor by each term of the second.


\Rightarrow\ \ \ \ \ \ \ \ =x^2(x^2+4x+3)-3x(x^2+4x+3)+2(x^2+4x+3)


\Rightarrow\ \ \ \ \ \ \ \ =(x^4+4x^3+3x^2)+(-3x^3-12x^2-9x)+(2x^2+8x+6)

Removing brackets in each term.


\Rightarrow\ \ \ \ \ \ \ \ =x^4+4x^3+3x^2-3x^3-12x^2-9x+2x^2+8x+6

Combine the like terms and simplifying.


\Rightarrow\ \ \ \ \ \ \ \ =x^4+4x^3-3x^3+3x^2-12x^2+2x^2-9x+8x+6


\Rightarrow\ \ \ \ \ \ \ \ =x^4+x^3-7x^2-x+6


\Rightarrow \ g(x) =x^4+x^3-7x^2-x+6

Option A is the correct answer.

Hence
g(x) =x^4+x^3-7x^2-x+6.

User Eightball
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories