CHS9 Combining Polynomials

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, along with coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to combine polynomials?

Back

Combining polynomials involves adding or subtracting them to simplify the expression. This is done by combining like terms.

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2+4)x^2 + (3+5)x = 6x^2 + 8x.

Front

How do you subtract polynomials?

Back

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

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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 the polynomial 4x^3 + 2x^2 - x, the degree is 3.

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What is the perimeter of a rectangle in terms of its length and width?

Back

The perimeter P of a rectangle is given by the formula P = 2(length + width).

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

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What is the result of multiplying (a + b)(c + d)?

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The result is ac + ad + bc + bd, which is obtained by distributing each term.

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What is a binomial?

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A binomial is a polynomial with exactly two terms, such as 3x + 4 or x^2 - 5.