Zeros of Polynomial Functions

Front

What are the zeros of the polynomial function P(x) = (x+2)(x+6)(x-4)?

Back

x = -2, x = -6, x = 4

Front

Find the zeros of the polynomial function P(x) = x^3 - 3x^2 - 5x + 15.

Back

x = 3, x = √5, x = -√5

Front

What is the degree of the polynomial function P(x) = 3x^4 - 7x^2 - 2x^7 - x + 4?

Back

7

Front

How many real zeros does the polynomial function P(x) = x^3 + 2x^2 + 9x + 18 have?

Back

1

Front

Factor the polynomial x^3 - 12x^2 + 47x - 60 given that 5 is a root.

Back

(x-3)(x-4)(x-5) = 0

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Front

What is a real zero of a polynomial function?

Back

A real zero of a polynomial function is a value of x for which P(x) = 0.

Front

How can you determine the number of real zeros of a polynomial function?

Back

You can use the Descartes' Rule of Signs or analyze the graph of the polynomial function.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.