Download 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.
3x  5 y
2. 4 x
5. 2b2  11a  2b
9.
6
y2
2
3.  4 g  7 g
2
2
6x  2 x
6. 9 + 3y2 – 2
7.
10. 36x8y2
11.
4.
7 x2  2 x  1
8. 4a 5  3a  2  4a
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
6. x + 5x7 – 8x9 + 10x3
9. 3x2y6 – 6x7y3 + 11y4 + 4
2. 7p5q
7. 5y3 + 7y3 – 3y8 + 10y
10.2ab4 – 7a3 + 9a3b4 + b9
8. 3x3 + 2x3z + 6z2
11.12x4 + 8x – 9 + 2x3
3. -3x3y9
4. 12p5qr2
5. 78z
Arrange a polynomial into so powers of x DESCENDING order.
2
6
1. 5x + 7x - 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)
4. (9y3 + 8y) + (3y2 – 2y) – (7y3 – y2 – 4y)
2. (5x3 – 4x + 3x2) + (6x2 – 7 + x)
5. (5a + 2b) + (9 – 3a ) + (6b – 7)
3. (12y + 5xy – 2y2) – (3y2 + 5xy – 9y)
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)
8.
(3x + 4)(x – 5)
9.
(r + 3)(2r2 – 4r + 5)
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.
6x2 – 7
2. A triangle has sides of length 3x + 4y,
5y + 6 – 2x, and 7 + 8x. What is the
perimeter of the triangle?
8x2 + 7x + 5
12x + 6
3.
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?
Find the missing side for the triangle below
with a known perimeter of 12a + 7b + 5c.
8b – 2a
7a + 3c
?
5. Find the perimeter of the trapezoid pictured.
3x2 – 4x
6.
Find the perimeter of the rectangle pictured.
3xy – 7x + 6y
3x2 – 4x
5y + 4x
7 – 2x
7 – 2x
5x2 + 7x + 3
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:
6x 2
4x2 + 5x - 2
5t - 7
3t + 4