Download 17-Distribution Combine Like terms

CC Algebra I
Ms. Socci 17-Polynomials Combining Like Terms
Name_________________________
Date_________
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Aim: What are Polynomials and how do we get them in standard form?
What is the classification of the following polynomial by its degree? by its number of terms? What is its end
behavior? 5x4 − 3x + 4x6 + 9x3 − 12 − x6 + 3x4
Step 1
Write the polynomial in standard form. First, combine any like terms. Then, place the terms of the
polynomial in descending order from greatest exponent value to least exponent value.
5x4 − 3x + 4x6 + 9x3 − 12 − x6 + 3x4
8x4 − 3x + 3x6 + 9x3 − 12
3x6 + 8x4 + 9x3 − 3x – 12
Combine like terms.
Place terms in descending order.
Step 2
The degree of the polynomial is equal to the value of the greatest exponent. This will be the exponent of
the first term when the polynomial is written in standard form.
3x6 + 8x4 + 9x3 – 3x – 12
3x6
The leading term is 3x6. There are five terms
The leading term is 3x6 the exponent of the first term is 6.
The leading coefficient is 6. This is a sixth-degree polynomial.
*Combine Like Terms
 Terms must have the exact same __________________and __________________
 Add or Subtract the coefficients of like terms
*Distributive Property
 Multiply the term being distributed to all terms inside of ____________________
 Always stop arrows when the parentheses end
 Be careful of negative signs for multiplication
2( x  4 x  3)  3( x  4 x )
2
2
Example Problems: Simplify each expression
Reminder: DISTRIBUTE BEFORE COMBINING LIKE TERMS & STANDARD FORM
1) x + 3 – 5x + 7 + 4x2
6) 5 (2r + 6) – 12r
2) – 4 (3a – 7) + 4a2
7) -7 (3m – 4) + 2
3) 9ab + 3b2 – 7b2 + 8ab – 12
8) x (2x + 7) + x (9 + 5x3)
4) 9 (x2 – 3) - 5x
9) 3t + 6 + 2t(3t - 6)
5) 2x + 7x2 – 9x + 21x3 + 5x
10) 8(2z + 4) – 3z(3z – 6)
Vocabulary with Polynomials
1. Rewrite the following polynomial in standard form:
5x  4  3x 4  2x 2

2. What is the constant term in the previous polynomial?
3. What is the leading coefficient of each of the following polynomials?
a.
2x 4  7x 2 18
b.

x 3  2x 2  5x  13

4. What is the degree of the following polynomial:
8x  3x 5  10  6x 4

5. Classify the polynomial by number of terms (give the word):
a.
2x 4  7x 2 18

b.
5x  13
b.
5x 3  1

6. Classify the polynomial by degree (give the word):
a.

2x 2  3x  8

a. A polynomial with only one term.
7. _____ binomial
8. _____ standard form
b. The number that does not multiply any power of x.
9. _____ leading coefficient
c. A polynomial with two terms.
10. _____ monomial
d. Written with terms in descending order, from largest
degree to smallest degree.
11. _____ degree
e. A polynomial with four terms.
12. _____ constant term
f. The value of the exponent in a polynomial.
13. _____ trinomial
g. The number in front of the first term of a polynomial.
h. A polynomial with three terms.
i. The first term of a polynomial.