Academic Year: 2021/2022
Semester: 2
Subject: Math
Book Title: Algebra
Grade: 9
Date:……./2/2022
Student’s Name: …………………………………………………………………………..
Class: …………….
WORKSHEET NO. ( 4 )
In this worksheet, you will be able to:
1.
2.
3.
4.
Determine the type of the function
Add and subtract polynomial
Multiply polynomials
Use the Binomial Theorem to expand binomial
Identify whether the function graphed has an odd or even degree and a positive or
negative leading coefficient.
1.
2.
3.
1. Even;
negative
2. Even;
positive
3. Odd;
positive
_______________________
_______________________
________________________
Graph the function. State the end behavior, x-intercepts, and intervals where the
function is above or below the x-axis.
4.
f x x 12 x 3
End behavior:
________________________
5.
f x x 2x 3x 1
End behavior:
1
________________________
x-intercepts:
________________________
x-intercepts:
________________________
Above x-axis:
________________________
Above x-axis:
________________________
Below x axis:
________________________
Below x-axis:
________________________
5.
4.
End behavior As
End behavior As
As
x-intercepts
Above
and
(3, 0); Above
and
;
; Below
As
x-intercepts (2, 0), (1, 0) and
and
Below
Identify the degree of each monomial.
1. 6x2
2. 3p3m4
______________
3. 2x8y3
______________
______________1.2
Rewrite each polynomial in standard form. Then identify the leading
coefficient, degree, and number of terms.
2. 7
3. 11
4. 4x3  x2  7x  6;
4; 3; 4
4. 6  7x  4x3  x2
________________________________________________________________________________________
5. 2x5 
7x4  x2  12x
 3; 2; 5; 5
5. x2  3  2x5  7x4  12x
6. 11x3  x2  3x  4
3
________________________________________________________________________________________
7. 3x  8x2  6x  4
Add or subtract. Write your answer in standard form.
6.
(2x2 2x 6) (11x3 x2 25x)
7.
_______________________________________
8.
(5x4  x2) (79x2 2x4  x3)
(x2 8) (3x3 6x 49x2)
8. 3x4  x3  10x2  7
9. x7  21x2  9x  6
________________________________________
9.
(12x2  x) (69x2  x7 8x)
2.
9x(x2 2x 4)
Find each product.
1.
4x2(3x2 1)
_______________________________________
________________________________________
2
3.
6x2(x3 7x2 4x 3)
4.
5m3(7n4 2mn3 6)
________________________________________
6.
(pq)(4p2 p8q2 q)
(x 2)(y2 2y 12)
8.
_______________________________________
(2x2  xy y)(y2 3x)
9.
(3x1)
3(a4b)2
30m
10.
6. xy2  2xy  12x  2y2 
4y  24
8. 2x 2y 2  6x 3  xy 3  3x
2
y  y 3  3xy
4
(x4)
9. 27x3  27x2  9x  1
________________________________________
12.
10. x4  16x3  96x2  256x
 256
5(x2 2y)3
11. 3a2  24ab  48b2
________________________________________
12. 5x6  30x4y
_______________________________________
 60x 2y 2 
40y 3
Use the Binomial Theorem to expand each binomial.
1. (x  y)3
________________________________________________________________________________________
2. (2x  y)
1. x3  3x2y  3xy2  y3
4
2. 16x4  32x3y  24x2y2  8xy3  y4
________________________________________________________________________________________
3. m3  9m2n  27mn2  27n3
4. p5  5p4q  10p3q2  10p2q3  5pq4  q5
3. (m  3n)3
________________________________________________________________________________________
4. (p  q)5
________________________________________________________________________________________
Simplify each polynomial, if possible. Then factor it.
1.
3n2 48
2.
3x3 75x
4.
16r4 9
________________________________
3.
9m4 16
________________________________
5.
3n6 12

3
7. 4p  p  4p2q  2pq 
8pq2  q2  8q3
_______________________________________
11.
4. 4x6  10x5  7x4  2x3
________________________________________
3
2
Expand each expression.
3
3. 6x5  42x4  24x3 
18x2
________________________________________
5. 35m3n4  10m4n3
_______________________________________
7.
1. 12x4  4x2
2. 9x3  18x2  36x
_______________________________________
5.
x3(4x3 10x2 7x 2)
1.
2.
________________________________
3.
4.
________________________________
5.
6.
x6 9
3
6.
________________________________
7.
3b7 12b4 12b
________________________________
8.
________________________________
9.
x 64
3
10.
x6 64
7.
________________________________
________________________________
11.
50v6 60v3 18
x 125
8.
3
9.
________________________________
10.
12.
________________________________
x6 1
11.
________________________________
12.
Factor each polynomial by grouping.
13.
8n3 7n2 56n49
14.
________________________________
15.
9r3 3r2 21r 7
________________________________
16.
________________________________
17.
120b3 105b2 200b175
5x3 6x2 15x 18
25v3 25v2 15v 15
________________________________
18.
120x3 80x2 168x 112
13.
14.
15.
16.
17.
18.
Mr. Ahmed Fayez
4