Writing Polynomials Given Roots

Front

What must you do if you are missing an exponent in your polynomial?

Back

You must put a zero as a coefficient placeholder for that exponent.

Front

What is a polynomial function of least degree with integral coefficients that has the given zeros: 1, 2, 3?

Back

(x - 1)(x - 2)(x - 3)

Front

What is the result of (3x^3 + 5x - 1) ÷ (x + 1)?

Back

3x^2 - 3x + 8 - 9/(x+1)

Front

Write a polynomial in factored form with the following roots: 3, -8, and 2.

Back

(x - 3)(x + 8)(x - 2)

Front

How should you write the answer for the polynomial problem: 2x^3 - x^2 - 25x - 12?

Back

2x^3 - x^2 - 25x - 12 is the proper way.

Front

What is the degree of the polynomial 2x^3 - x^2 - 25x - 12?

Back

The degree is 3.

Front

What does it mean for a polynomial to have integral coefficients?

Back

It means all coefficients of the polynomial are whole numbers.

Front

How do you find a polynomial given its roots?

Back

Use the factored form: (x - root1)(x - root2)...(x - rootn).

Front

What is the leading coefficient of the polynomial 2x^3 - x^2 - 25x - 12?

Back

The leading coefficient is 2.

Front

What is the standard form of a polynomial?

Back

The standard form is written in descending order of exponents.