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Big Ideas Math Algebra 1 A Bridge to Success

BI

Big Ideas Math Algebra 1 A Bridge to Success View details

Chapter Test

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Exercise 1 Page 413

Remember, only like terms can be combined.

Difference: - p^2 + 4p - 4
Degree: 2
Classification: trinomial

We want to find a difference, identify the degree of this difference and classify it by the number of terms.

Finding a Difference

The first step in finding a difference is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable and the same exponent — can be combined. ( - 2p + 4) - ( p^2 - 6p + 8)In this case, we have one p^2-term, two p-terms, and two constants. Only the p-terms and constants can be combined, so to simplify the expression we will use the Distributive Property and rearrange it according to the Commutative Property of Addition and then combine like terms.

(- 2p + 4) - (p^2 - 6p + 8)

Distribute - 1

(- 2p + 4) - p^2 + 6p - 8

Remove parentheses

- 2p + 4 - p^2 + 6p - 8

CommutativePropAdd

Commutative Property of Addition

- p^2 - 2p + 6p + 4 - 8

Add and subtract terms

- p^2 + 4p - 4

Identifying the Degree

The degree of a polynomial is the highest exponent of a variable. - p^2+4p-4 The highest exponent of the polynomial, and therefore its degree, is 2.

Classifying

We want to classify this polynomial by the number of terms. - p^2 + 4p - 4 This polynomial consists of three terms, so it is a trinomial.

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