Polynomial Functions Assessment

Front

What are the roots of the polynomial function y = (x + 2)(x - 7)^3?

Back

The roots are -2 and 7 with a multiplicity of 3.

Front

Which of the following is the correct factored form with roots 2, 5i, and 6?

Back

(x-6)(x-2)(x+5i)(x-5i) (Remember that complex roots come in pairs).

Front

How many linear factors does the function f(x) = 3x - 4x^3 + 2 have according to its graph?

Back

The function has 3 linear factors.

Front

What is the equation in factored form of the graph represented by the options?

Back

f(x) = (x+4)(x+1)^2(x-2)(x-4)

Front

Find the zeros of the polynomial f(x) = (x-5)(2x+3)(7x-4)(x+6).

Back

The zeros are x = 5, -3/2, 4/7, and -6.

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

Define the term 'degree' in relation to polynomial functions.

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

Explain the concept of multiplicity in polynomial roots.

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity touches the x-axis, while an odd multiplicity crosses it.

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.