Algebra I Chapter 8



Common Core Math I Standards Name: ________________________________

UNIT 6 REVIEW POLYNOMIALS

POLYNOMIAL IDENTIFICATION:

State whether each expression is a MONOMIAL, BINOMIAL, TRINOMIAL, or NONE.

MONOMIAL = ____________ BINOMIAL = ____________ TRINOMIAL = ___________

NONE = ______________________________________________________________________

1. [pic] 2. [pic] 3. [pic] 4. [pic]

5. [pic] 6. 9 + 3y2 – 2 7. [pic] 8. [pic]

9. [pic] 10. 36x8y2 11. 12x2 – 3x 12. 3m5 – 2m3 + 4m

Degree of Polynomials and Monomials:

• MONOMIALS: ADD the exponent of all variables.

• POLYNOMIALS: PICK the largest individual degree of all the terms.

• Hint: Invisible Exponents = 1

1. r7

2. 7p5q

3. -3x3y9

4. 12p5qr2

5. 78z

6. x + 5x7 – 8x9 + 10x3

7. 5y3 + 7y3 – 3y8 + 10y

8. 3x3 + 2x3z + 6z2

9. 3x2y6 – 6x7y3 + 11y4 + 4

10. 2ab4 – 7a3 + 9a3b4 + b9

11. 12x4 + 8x – 9 + 2x3

Arrange a polynomial into so powers of x DESCENDING order.

1. 5x2 + 7x6 - 3x9 + 10x4

2. 7 + 3x4y – 6x + 9x3y4

3. 7x3 – 8y9 + 4x2y + 3x7y

Addition and Subtraction of Polynomials:

• Combine Like Terms between different polynomials (parentheses) with add or subtract.

• Be careful of positive and negative signs.

1. (7 + 8x + 3x2) + (6x2 + 9 – 8x)

2. (5x3 – 4x + 3x2) + (6x2 – 7 + x)

3. (12y + 5xy – 2y2) – (3y2 + 5xy – 9y)

4. (9y3 + 8y) + (3y2 – 2y) – (7y3 – y2 – 4y)

5. (5a + 2b) + (9 – 3a ) + (6b – 7)

6. (3r – 5s + 6t) – (5s – 2r) + (11t + 2r)

Multiplication with Polynomials:

Simplify using the distributive property. (Multiply BIG numbers and Add Small Numbers)

1. -6(9m2 – 7m)

2. 2d(7d5 – d3 + 4)

3. 7rs(3r2 + 8s3 – 2rs)

4. 3x5(8 – 5x2)

5. 8x4(6x – 8x3 + 7)

6. -4s3t2 (3s2 – 2s4t + 6t5s)

Simplify using the FOIL BOX method. (Multiply to fill in boxes, combine terms to finish)

7. (y – 4) (y + 4)

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8. (3x + 4)(x – 5)

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9. (r + 3)(2r2 – 4r + 5)

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10. (b – 7)(b + 2)

11. (n + 4)(5n – 2)

12. (7z – 6)(7z – 6)

13. (4x + 5y) (3x + 2y)

14. (2n – 7) (3n – 1)

15. (2x + 6) (x + 9)

16. (x + 4) (6x2 + 2x – 8)

17. (3y2 – 2y) (7y2 – 3y + 5)

18. (2n – 5) (n2 – 3n – 10)

Word Problems: Use a separate sheet of paper.

1. Find the perimeter of the triangle pictured.

2. A triangle has sides of length 3x + 4y,

5y + 6 – 2x, and 7 + 8x. What is the perimeter of the triangle?

3. Find the missing side for the triangle below with a known perimeter of 12a + 7b + 5c.

[pic]

4. A triangle has a perimeter 10x2 – 3xy + 6y2. If two sides are known to be 2x2 + 2xy and 7x2 + 3y2, then what is the length of the third unknown side?

5. Find the perimeter of the trapezoid pictured.

6. Find the perimeter of the rectangle pictured.

[pic]

7. Michelle borrowed 3r3 + 5r2 + 18r + 20 dollars from her brother. If she paid back 3r3 + 2r2 – 2r + 11 dollars, then how much more money does she still owe her brother?

8. Jordan has (4c2 + 6c – 2) baseball cards and Sam has (3c2 – 4c + 8) cards. How many cards do the friends have altogether?

9. Find the area of the rectangles pictured:

[pic] [pic]

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6x2 – 7

12x + 6

8x2 + 7x + 5

7a + 3c

8b – 2a

?

5x2 + 7x + 3

7 – 2x

7 – 2x

3x2 – 4x

3x2 – 4x

3xy – 7x + 6y

5y + 4x

4x2 + 5x - 2

6x 2

3t + 4

5t - 7

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