Nov 26 2024 Unit 5 TEST Makeup

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) equals zero. It is also known as a root of the function.

Front

How do you determine if k = 9 is a zero of the function f(x) = 4x^2 - 33x - 27?

Back

To determine if k = 9 is a zero, substitute x = 9 into the function and check if f(9) = 0. If true, then k = 9 is a zero.

Front

What is the factored form of the polynomial 27x³ - 64?

Back

The factored form is (3x - 4)(9x² + 12x + 16).

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero appears as a root of a polynomial. For example, a zero with a multiplicity of 3 means it is a root three times.

Front

How do you write a polynomial given its zeros?

Back

To write a polynomial from its zeros, use the form (x - zero1)(x - zero2)... for each zero, raising to the power of its multiplicity.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when it is expressed in descending order of the degree of its terms, such as ax^n + bx^(n-1) + ... + c.

Front

Back

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged from the highest degree to the lowest degree.

Front

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

Back

The leading coefficient is the coefficient of the term with the highest degree. It determines the end behavior of the polynomial function.

Front

How can you verify if a polynomial is written in standard form?

Back

Check if the polynomial is arranged in descending order of the degree of each term, with no like terms combined.