exponents and polynomials chapter ten adding and subtracting polynomials section 10.1

Exponents and PolynomialsExponents and Polynomials

Chapter TenChapter Ten

Adding and Subtracting Adding and Subtracting PolynomialsPolynomials

Section 10.1

axn

x x x x4 3 23 5 6 For exampleFor example,,

This polynomial is written in This polynomial is written in descending powersdescending powers of of xx because the powers of because the powers of xx decrease from left to decrease from left to right.right.

6 0x

x x 3 2 2

6 0x

3

Types of PolynomialsTypes of Polynomials

A A monomialmonomial is a polynomial with is a polynomial with exactly one term.exactly one term.

A A binomialbinomial is a polynomial with is a polynomial with exactly two terms.exactly two terms.

AA trinomialtrinomial is a polynomial with is a polynomial with exactly three terms.exactly three terms.

4Martin-Gay, Prealgebra, 5ed

Adding PolynomialsAdding Polynomials

To To addadd polynomials, use the polynomials, use the commutative and associative commutative and associative properties and then combine like properties and then combine like terms.terms.

Add:Add: 5 4 2 3 12 2x x x x e j e jRemove parentheses.

5 3 4 2 12 2x x x xe j a f a fCombine like terms.

5 4 2 3 12 2x x x x

Simplify. 2 3 12x x5

to to subtractsubtract a polynomial, add its opposite. a polynomial, add its opposite.a - b = a + (-b)

Recalling the definition of subtraction,

Subtracting PolynomialsSubtracting Polynomials

To To subtractsubtract two polynomials, change two polynomials, change the signs of the terms of the polynomial the signs of the terms of the polynomial being subtracted, and then add.being subtracted, and then add.

6Martin-Gay, Prealgebra, 5ed

Subtracting Polynomials. . .Subtracting Polynomials. . .

Subtract:Subtract: 5 4 2 3 12 2x x x x e j e j

Remove parentheses.

5 3 4 2 12 2x x x xe j a f a fCombine like terms.

5 4 2 3 12 2x x x x

Simplify. 8 5 32x x

Add the opposite. 5 4 2 3 12 2x x x xe j e jAdd

Change the signs.

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Helpful Hint

Don’t forget to change the sign of each term in the polynomial being subtracted.

8Martin-Gay, Prealgebra, 5ed