Polynomial Operations

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 are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3x^2 + 2x) + (4x^2 - x) = (3x^2 + 4x^2) + (2x - x) = 7x^2 + x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = (5x^2 - 2x^2) + (3 - 1) = 3x^2 + 2.

Front

What is the product of two polynomials?

Back

The product of two polynomials is found by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the difference between a monomial and a polynomial?

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A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

Front

How do you factor a polynomial?

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Factoring a polynomial involves expressing it as a product of its factors. For example, x^2 - 9 can be factored as (x - 3)(x + 3).

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What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What is the Factor Theorem?

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The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.