Polynomials REVIEW add, subtr, mult & divide

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

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What does it mean to simplify a polynomial?

Back

Simplifying a polynomial involves combining like terms and reducing the expression to its simplest form.

Front

What is the degree of a polynomial?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

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) = 3x^2 + 2.

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What is the product of two binomials?

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The product of two binomials can be found using the distributive property or the FOIL method. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is the result of multiplying a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term in the polynomial. For example, 2x(3x^2 + 4x) = 6x^3 + 8x^2.

Front

How do you divide a polynomial by a monomial?

Back

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. For example, (4x^3 + 8x^2) ÷ 4x = x^2 + 2x.

Front

What is the sum of two polynomials?

Back

The sum of two polynomials is found by adding their corresponding coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

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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.