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**Polynomial Functions and Adding and Subtracting Polynomials**

§ 5.2 Polynomial Functions and Adding and Subtracting Polynomials

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**Polynomial Vocabulary**

Term – a number or a product of a number and variables raised to powers Coefficient – numerical factor of a term Constant – term which is only a number Polynomial is a sum of terms involving variables raised to a whole number exponent, with no variables appearing in any denominator.

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**Polynomial Vocabulary**

In the polynomial 7x5 + x2y2 – 4xy + 7, there are 4 terms: 7x5, x2y2, – 4xy and 7. The coefficient of term 7x5 is 7, of term x2y2 is 1, of term – 4xy is – 4 and of term 7 is 7. 7 is a constant term.

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**Types of Polynomials Monomial is a polynomial with one term.**

Binomial is a polynomial with two terms. Trinomial is a polynomial with three terms.

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**Degrees Degree of a term Degree of a polynomial**

To find the degree, take the sum of the exponents on the variables contained in the term. Degree of a constant is 0. Degree of the term 5a4b3c is 8 (remember that c can be written as c1). Degree of a polynomial To find the degree, take the largest degree of any term of the polynomial. Degree of 9x3 – 4x2 + 7 is 3.

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**Combining Like Terms Example:**

Like terms are terms that contain exactly the same variables raised to exactly the same powers. Warning! Only like terms can be combined through addition and subtraction. Example: Combine like terms to simplify. x2y + xy – y + 10x2y – 2y + xy = x2y + 10x2y + xy + xy – y – 2y (Like terms are grouped together) = (1 + 10)x2y + (1 + 1)xy + (– 1 – 2)y = 11x2y + 2xy – 3y

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**Adding Polynomials Adding Polynomials**

To add polynomials, combine all the like terms. Example: Add. (3x – 8) + (4x2 – 3x +3) = 3x – 8 + 4x2 – 3x + 3 = 4x2 + 3x – 3x – 8 + 3 = 4x2 – 5

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**Subtracting Polynomials**

To subtract two polynomials, change the signs of the terms of the polynomial being subtracted and then add. Example: Subtract. 4 – (– y – 4) = 4 + y + 4 = y = y + 8 (– a2 + 1) – (a2 – 3) + (5a2 – 6a + 7) = – a2 + 1 – a a2 – 6a + 7 = – a2 – a2 + 5a2 – 6a = 3a2 – 6a + 11

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