Unit 5 Review -- Polynomials
NAME:
1. Give an example of each of the following. If one cannot be made, write “CANNOT BE MADE”:
Monomial
Binomial
Trinomial
Polynomial of ________ Terms
Constant
Linear
Quadratic
Cubic
Quartic
Quintic
Nth Degree
2. Rewrite each into Standard Form. Then, name the resulting polynomial.
a) 6x2 + 5 – 8x – 2x3
Name:
b) 7x2 –11x4 + 8 – 2x5
Name:
d) 3a3x2 – a4 + 4ax5 + 9a2x
Name:
c) 25x6 –3x2 + 7x5 + 15x8
Name:
e) 15x5 – 2x2 y2 – 7yx4 + x3y
Name:
3. ADDING AND SUBTRACTING POLYNOMIALS:
•
•
When adding and subtracting polynomials, you COMBINE LIKE TERMS.
Be careful of parentheses and positive or negative signs with the operations.
a) (3x2 – 4x + 8) + (2x – 7x2 – 5)
b) (3n2 + 13n3 + 5n) – (7n + 4n3)
c) (2b2 + 8ab3 + 4b) – (9b – 5ab3)
d) (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2)
e) (7y2 + 2y – 3) + (2 – 4y + 5y2)
f) (3x2 + 5x + 2) – (4 – 2x) + (5x2 + 7)
4. Find the PERIMETER of the shape.
4x -­‐ 8 b)
9x – 3y + 2 11 + y c)
d)
6 + 2a 5x – 2 3 – 2x 2y – 3x -­‐ 3 12 + 5x + 7y 3b – 4a + 5 5. Find the missing side.
a)
2x2 – 5
6 + 2a 2
a)
3b – 4a + 5 7 + 3x 5x2 – 3x + 2
?
b)
9ab + 8a2
c)
?
2
3x2 + 9x
Perimeter
5x2 + 7x + 12
4a – 4ab
?
7b2 – 2ab
Perimeter
14x2 + 4x – 8
Perimeter
9b2 – 2ab + 12a2
6. MULTIPLYING A POLYNOMIAL BY A MONOMIAL:
USE THE DISTRIBUTIVE PROPERTY with VARIABLE TERMS
Keep track of Coefficients and Exponents of Variables
Simplify each of the following:
a) -3x3y (5yx + 6y2)
b) 3a3 (2a2 – 5a + 8)
c) 3(x3+ 4x2) + 2x(x – 7)
d) 4 (3d2 + 5d) – d (d2 – 7d + 12)
7. Find the area of the shaded region.
a)
b)
11y 6y 3 -­‐ t 8 -­‐2t 6y+2 t 11y 3t c) You are putting a picture of you and your best friend in a frame. The picture is 2 inches longer than it is wide.
The frame is 4 inches wider and 3 inches longer than the picture.
i.
Draw a diagram of the picture and frame including the dimensions.
ii.
Find the area of the picture frame only!
8. Multiply the following binomials.
a) (x – 3)(x – 2)
b) 3(2x + 1)(x + 1)
c) (2x – 6)2
d) (2a – 3)(a – 2)
9. Multiply each of the following polynomials.
a) (3b2 – 4b) (2b2 – b + 7)
b) (x - 6) (x2 – 7x - 8 )
c) (y - 5) (4y2 – 3y + 2)
10. Factor Completely. Don’t forget to look for a GCF or lead negative first. Check for Standard Form too.
a) 25𝑥 ! + 15𝑥 !
b) 7𝑟 ! + 14𝑟 + 28
c) 8 + 6𝑥 + 𝑥 !
d) 15𝑛! − 21𝑛 + 35𝑛 − 49
g) 𝑔! – 2𝑔 – 63
e) 2𝑟 ! − 162
h) 4𝑥 ! − 36
j) 3𝑎 ! + 30𝑎 + 63
f) 24𝑥 + 48𝑦
i) 3𝑥 ! + 2𝑥 – 8
k) 12𝑥𝑞 ! + 34𝑥𝑞 – 28𝑥
11. The area of a rectangle is given by 2𝑎 ! + 5𝑎 + 3. What could the dimensions be?
12. Word Problems:
a) Bob mowed (2x2 + 5x – 3) yards on Monday, (4x – 7) yards on Tuesday, and (3x2 + 10) yards on Wednesday.
How many yards did he mow in the three days?
If Bob mowed 14x2 + 12x – 3 yards total for the entire week, how many yards did he mow during
the rest of the week?
b) Molly has (4x + 10) dollars and Ron has (-5x + 20) dollars.
How much money do they have altogether?
How much more money does Molly have than Ron?
c) Ross has (8x – 5) tickets for Chuck E Cheese. He is going to play today and wants to buy a prize that is
(15x + 1) tickets. How many tickets must he win to have enough tickets to buy the prize?