Name: __________________________________________
Int Math 2 Handout (Sec.11-1 thru 11-4)
What is the degree of each monomial? (Hint: Add exponents together on the variables.)
1
5x6 y3
a
b
c
d
2
2x6
3
–9
3
5
6
9
What is the sum or difference? (Hint: Do not add exponents of the variables, just carry the
variabls and the exponents to the answer; only add or subtract the coefficients.)
4
5
6x7 + 8x7
a
b
c
d
2x7 – 8x7
–2x7
48x7
14x1 4
14x7
Write the polynomial in standard form. Then name the polynomial based on its degree and
number of terms. (Hint: The degree of the polynomial is the largest exponent.)
6
7
2 – 11x2 – 8x + 6x2
a
b
c
d
6x2 – 8x + 2; cubic trinomial
–5x2 – 8x; quadratic binomial
–5x2 – 8x + 2; quadratic trinomial
–6x2 – 8x – 2; cubic polynomial
4g – 5g 3 + 9g 2 – 6
a
b
c
d
1
5g 3 – 9g 2 + 4g – 6; cubic trinomial
–5g 3 + 9g 2 + 4g – 6; cubic polynomial
–6 + 4g + 9g 2 – 5g 3 ; cubic binomial
9g 3 – 5g 2 + 4g – 6; quadratic binomial
Name: ______________________
8
ID: A
A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over
a 5-year period. The biologist modeled the populations, in thousands, with the following
polynomials where x is time, in years.
2
White-sided jackrabbits: 9.7x − 0.8x + 2.3
2
Black-tailed jackrabbits: −1.1x + 7.7x + 5.4
What polynomial models the total number of white-sided and black-tailed jackrabbits?
2
a
−8.6x + 6.9x − 7.7
b
8.6x + 6.9x + 7.7
2
2
c
8.6x − 6.9x − 7.7
d
8.6x − 6.9x + 7.7
c
0u 3 + 6u 2 – 7u + 9
0u 3 – 7u 2 + 6u – 9
2
Simplify the sum.
9
(2u 3 + 6u 2 + 3) + (2u 3 – 7u + 6)
a
b
9 – 7u + 6u 2 + 4 u 3
4u 3 + 6u 2 – 7u + 9
d
Simplify the difference.
10 (4w2 – 7w – 6) – (8w2 + 2w – 3)
Simplify the product. (Hint: Distribute the outside term to each inside term. Multiply
coefficients and add exponents on the variables.)
11 2n(n 2 + 3n + 4)
a
b
c
d
12 5a 2 (3a 4 + 3b + 2)
2n 3 + 6n 2 + 8n
2n 3 + 3n + 4
n 2 + 5n + 4
2n 3 + 6n + 8
2
Name: ______________________
ID: A
Find the GCF of the terms of the polynomial. (Hint: Break down each term and pull out the
everything that all terms have in common.)
13 Example.
14 48x6 + 6x2 – 26x3
26x2 + 34x4
2⋅3⋅x ⋅x +2⋅7⋅x ⋅x ⋅x ⋅x
2
Each term has a 2 ⋅ x ⋅ x so 2x so this is
GCF. Answer is C.
a
26x2
b
x2
2x2
2x4
c
d
15 25x3 + 20x5
a
b
c
d
20x
5x5
x3
5x3
Factor the polynomial.
18 54c3 d 4 + 9c4 d 2
16 Example.
3
2
2x + 4x + 8x
a
2⋅x ⋅x ⋅x +4⋅x ⋅x +8⋅x
b
2
Each term has a 2 ⋅ x so 2x(x + 2x + 4) is
the factored polynomial. Answer is B.
a
b
c
d
c
d
2x3 + 4x2 + 8x
2x(x2 + 2x + 4)
2x(x + 2)(x + 4)
2x(x2 + 2x + 8)
17 25w6 + 35w3
3
9c4 d 2 (6d 2 + 1)
9c4 d 2 (d 2 + 6)
9c3 d 2 (6d 2 + c)
9c3 d 2 (d 2 + 6c)
Name: ______________________
ID: A
19 A family is having a pool built in their
backyard. If their yard is rectangular and
measures 10x by 10x and the pool is
circular with a radius of 2x how much of
the yard will be left over after the pool is
built? Write your answer in factored
form.
a 100x 2 + 4πx 2
b
( 100 − 4π) x
2
c
100x − 4πx
2
2
d
( 100 + 4π) x
2
20 A sports team is building a new stadium
on a rectangular lot of land. If the lot
measures 7x by 7x and the sports field will
be 5x by 5x, how much of the lot will be
left over to build bleachers on?
Simplify the product using the distributive property. (Hint: Multiply first term of first
parentheses by both terms of second parentheses and then multiply second term of first
parentheses by both terms of second parentheses. Make sure to simplify when finished
multiplying.)
21 (3h − 7)(3h − 6)
22 (−4h + 2)(3h + 7)
3h(3h − 6) − 7(3h − 6)
2
9h − 18h − 21h + 42
2
a
9h − 3h − 42
b
9h − 39h + 42
c
9h + 3h − 42
d
9h + 39h + 42
2
2
2
Simplify the product using a table. (Hint: Fill in table and simplify for the answer.)
23 (2h − 5)(4h − 3)
24 (−5h + 4)(5h − 5)
4h
2h
–5
2
8h
−20h
5h
–3
−6h
−5h
15
4
4
–5
Name: ______________________
ID: A
What is a simpler form of the expression? (Hint: May use a table or the distributive
property. Your choice.)
25 (2n 2 + 5n + 3)(4n – 5)
2n
2
5n
3
4n
−5
26 (4k + 5)(3k2 – 4k – 4)
What is a simpler form of each product? (Hint: A binomial squared means to write the
2
binomial twice: (3m − 1) = (3m − 1)(3m − 1).)
27 (2x – 6)2
28 (4x – 6y3) 2
5
Name: ______________________
29 (7m + 5)
ID: A
2
What is a simpler form of the following expressions?
30 (j + 7)(j – 7)
a
b
j 2 – 49
j 2 + 14j – 49
j 2 – 14j – 49
j 2 + 14j – 49
c
d
31 (2n + 2)(2n – 2)
32 (4p – 8)(4p + 8)
33 (7m2 – 5)(7m2 + 5)
6