Uploaded by Dr.Weam Ghazi S Alharbi

# WORKSHEET (4)grade 9 Alg solved

```Academic Year: 2021/2022
Semester: 2
Subject: Math
Book Title: Algebra
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
Multiply polynomials
Use the Binomial Theorem to expand binomial
Identify whether the function graphed has an odd or even degree and a positive or
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
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
```