Unit 3 TEST review

Front

What is the general form of a polynomial function of degree 4?

Back

A polynomial function of degree 4 can be expressed in the form: f(x) = ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are constants and a ≠ 0.

Front

How do you determine the leading coefficient of a polynomial?

Back

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in the polynomial y = x^4 - x^3 + 3x^2 + 2, the leading coefficient is 1.

Front

What is synthetic division and when is it used?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c). It is used when you want to find the quotient and remainder of the division.

Front

What mistake did Cam make when performing synthetic division?

Back

Cam did not use a zero placeholder for the x^3 term, which is necessary when the term is missing in the polynomial being divided.

Front

What does it mean for a polynomial function to approach infinity as x approaches infinity?

Back

If a polynomial function f(x) approaches infinity as x approaches infinity, it means that the values of f(x) increase without bound as x becomes very large.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for x. The solutions are the x-values where the graph intersects the x-axis.

Front

What is the factored form of a polynomial with given zeros?

Back

The factored form of a polynomial with zeros at x = a, x = b, and x = c is given by (x - a)(x - b)(x - c). For example, if the zeros are 2, 3, and -1, the factored form is (x - 2)(x - 3)(x + 1).

Front

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

Back

The leading term of a polynomial determines the end behavior of the graph. It influences whether the graph rises or falls as x approaches positive or negative infinity.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n real zeros, according to the Fundamental Theorem of Algebra.

Front

How can you identify the end behavior of a polynomial function?

Back

The end behavior of a polynomial function can be identified by examining the leading term. If the leading coefficient is positive and the degree is even, the ends of the graph will rise. If the leading coefficient is negative and the degree is even, the ends will fall.