Polynomial Operations Review Day 2

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 1 is a polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is faster and requires less writing than long division.

Front

How do you find the rational zeros of a polynomial?

Back

To find the rational zeros of a polynomial, use the Rational Root Theorem, which states that any rational solution, expressed as a fraction p/q, has p as a factor of the constant term and q as a factor of the leading coefficient.

Front

What is the result of (5x + 2)(x^2 - 3x + 6)?

Back

5x^3 - 13x^2 + 24x + 12.

Front

What is the result of (x^3 - x^2 + 4) - (3x^3 - 2x^2 + 3)?

Back

-2x^3 + x^2 + 1.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials helps to simplify expressions, solve polynomial equations, and find the roots of the polynomial.

Front

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

Back

A polynomial is an expression made up of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 3x^4 + 2x^3 - x + 5 is in standard form.

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. For example, in 4x^3 + 2x^2 - x + 7, the leading coefficient is 4.