91.9k views
2 votes
Write a polynomial function in standard form with the given zeros. 1, 1, 2

A) (x−1)(x−1)(x−2)
B) (x+1)(x−1)(x−2)
C) (x−1)(x+1)(x−2)
D) (x−1)(x−1)(x+2)

1 Answer

7 votes

Final answer:

To write a polynomial function with given zeros, one must create factors from each zero and multiply them. The zeros 1, 1, and 2 translate into the factors (x - 1), (x - 1), and (x - 2). The correct polynomial function in standard form is Option A: (x - 1)(x - 1)(x - 2).

Step-by-step explanation:

Writing a Polynomial Function with Given Zeros

To write a polynomial function with given zeros, we use the fact that if a number is a zero of a polynomial, the factor corresponding to that zero is (x - zero). The given zeros are 1, 1, and 2; therefore, we have (x - 1), (x - 1), and (x - 2) as the factors of the polynomial.

The question provides multiple choices and asks us to select the polynomial in standard form. Multiplying the factors will give us the polynomial:

  • (x - 1) times itself since the zero of 1 is repeated.
  • (x - 2) for the zero of 2.

Now we multiply these factors:

(x - 1)(x - 1) = x² - 2x + 1

Then, we multiply this result by (x - 2) to get the final polynomial:

(x² - 2x + 1)(x - 2) = x³ - 2x² + x - 2x² + 4x - 2

Combine like terms to get:

x³ - 4x² + 5x - 2

This is the polynomial in standard form. Looking at the choices provided, the correct answer is (x - 1)(x - 1)(x - 2), which corresponds to Option A.

User Kuf
by
9.1k points
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