Nov 26 2024 Unit 5 TEST Block 3

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor of the form (x - c). It is faster and requires less writing than traditional long division.

Front

How do you evaluate a polynomial function at a given value?

Back

To evaluate a polynomial function f(x) at a specific value x = a, substitute 'a' into the polynomial and simplify the expression.

Front

What is the factorization of the sum of cubes, a^3 + b^3?

Back

The factorization is (a + b)(a^2 - ab + b^2).

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How do you find the remainder when dividing polynomials?

Back

You can find the remainder by using synthetic division or polynomial long division.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial and determines the polynomial's end behavior and the number of possible roots.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.

Front

What is the process of factoring a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors, which can include numbers, variables, or other polynomials.