The document provides information and examples about factors, primes, and multiples in mathematics. It defines factors as numbers that divide evenly into another number without leaving a remainder. Prime numbers are defined as numbers with exactly two factors. Multiples are numbers that appear in the multiplication table of a given number. The document includes examples of finding factors, identifying prime numbers, and determining multiples. It also covers highest common factors and factor spiders.
o level mathematics complete revision guide for quick and deep revision to solve questions with meticulous techniques and tricks with question to solve for clearance of concepts
Module 4 Homework Assignment 1
Module 4 Homework Assignment 1
MAT 110: Beginning Algebra
Daniel S. Bernardez
Ms. Carrie Dugan
August 16, 2013
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.
1.
Find the greatest common factor. 4, 6, 12.
2.
Factor. 24x3 + 30x2
3.
Factor out the GCF with a negative coefficient. –24m2n6 – 8mn5 – 32n4
4.
Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y
5.
The GCF of 15y + 20 is 5. The GCF of 15y + 21 is 3. Find the GCF of the product (15y + 20)(15y + 21).
6.
The area of a rectangle of length x is given by 15x – x2. Find the width of the rectangle in terms of x.
7.
Factor the trinomial completely. x2 + 8x – 9
8.
Factor the trinomial completely. 2x2 + 16x + 32
9.
Complete the following statement. 6a2 – 5a + 1 = (3a – 1)(__?__)
10.
State whether the following is true or false. x2 – 7x – 30 = (x + 3)(x – 10)
11.
Factor completely. x2 + 11x + 28
12.
Factor completely. 15x2 + 23x + 4
13.
Factor completely. 6z3 – 27z2 + 12z
14.
The number of hot dogs sold at the concession stand during each hour iih after opening at a soccer tournament is given by the polynomial 2h2 – 19h + 24. Write this polynomial in factored form.
15.
Find a positive value for k for which the polynomial can be factored.
x2 – kx + 29
16.
Factor completely.
9x2 + 4
17.
Determine whether the following trinomial is a perfect square. If it is, factor the binomial.x2 – 12x + 36
18.
Factor completely. 25x2 + 40xy + 16y2
19.
Factor.
s2(t – u) – 9t2(t – u)
20.
State which method should be applied as the first step for factoring the polynomial. 6x3 + 9x
21.
State which method should be applied as the first step for factoring the polynomial. 2a2 + 9a + 10
22.
Solve the quadratic equation. 5x2 + 17x = –6
23.
Solve the quadratic equation.
3x(2x – 15) = –84
24.
The sum of an integer and its square is 30. Find the integer.
25.
If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?
26.
Write in simplest form.
8
14
9
27
x
x
27.
Write in simplest form.
2
2
– 6+ 8
16
xx
x
-
28.
Write the expression in simplest form.
4 – 8 + 32
4 – 2 + 8
zyzy
yzzy
-
-
29.
The area of the rectangle is represented by 5x2 + 19x + 12. What is the length?
5x + 4
30.
Multiply.
3
8
98
2
x
x
×
31.
Multiply.
2
3127
– 54
xx
xxx
-
×
-
32.
Divide.
26515
2112
xx
--
¸
33.
Divide.
(
)
22
2
2
4
+ 2
6– 12
xy
xxy
xxy
-
¸
34.
Perform the indicated operations.
22
22
– 9368
4 – 244 – 36 + 5 – 6
xxxx
xxxxx
-
××
35.
Find the area of the rectangle shown.
36.
Subtract. Express your ...
Biological screening of herbal drugs: Introduction and Need for
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o level mathematics complete revision guide for quick and deep revision to solve questions with meticulous techniques and tricks with question to solve for clearance of concepts
Module 4 Homework Assignment 1
Module 4 Homework Assignment 1
MAT 110: Beginning Algebra
Daniel S. Bernardez
Ms. Carrie Dugan
August 16, 2013
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.
1.
Find the greatest common factor. 4, 6, 12.
2.
Factor. 24x3 + 30x2
3.
Factor out the GCF with a negative coefficient. –24m2n6 – 8mn5 – 32n4
4.
Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y
5.
The GCF of 15y + 20 is 5. The GCF of 15y + 21 is 3. Find the GCF of the product (15y + 20)(15y + 21).
6.
The area of a rectangle of length x is given by 15x – x2. Find the width of the rectangle in terms of x.
7.
Factor the trinomial completely. x2 + 8x – 9
8.
Factor the trinomial completely. 2x2 + 16x + 32
9.
Complete the following statement. 6a2 – 5a + 1 = (3a – 1)(__?__)
10.
State whether the following is true or false. x2 – 7x – 30 = (x + 3)(x – 10)
11.
Factor completely. x2 + 11x + 28
12.
Factor completely. 15x2 + 23x + 4
13.
Factor completely. 6z3 – 27z2 + 12z
14.
The number of hot dogs sold at the concession stand during each hour iih after opening at a soccer tournament is given by the polynomial 2h2 – 19h + 24. Write this polynomial in factored form.
15.
Find a positive value for k for which the polynomial can be factored.
x2 – kx + 29
16.
Factor completely.
9x2 + 4
17.
Determine whether the following trinomial is a perfect square. If it is, factor the binomial.x2 – 12x + 36
18.
Factor completely. 25x2 + 40xy + 16y2
19.
Factor.
s2(t – u) – 9t2(t – u)
20.
State which method should be applied as the first step for factoring the polynomial. 6x3 + 9x
21.
State which method should be applied as the first step for factoring the polynomial. 2a2 + 9a + 10
22.
Solve the quadratic equation. 5x2 + 17x = –6
23.
Solve the quadratic equation.
3x(2x – 15) = –84
24.
The sum of an integer and its square is 30. Find the integer.
25.
If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?
26.
Write in simplest form.
8
14
9
27
x
x
27.
Write in simplest form.
2
2
– 6+ 8
16
xx
x
-
28.
Write the expression in simplest form.
4 – 8 + 32
4 – 2 + 8
zyzy
yzzy
-
-
29.
The area of the rectangle is represented by 5x2 + 19x + 12. What is the length?
5x + 4
30.
Multiply.
3
8
98
2
x
x
×
31.
Multiply.
2
3127
– 54
xx
xxx
-
×
-
32.
Divide.
26515
2112
xx
--
¸
33.
Divide.
(
)
22
2
2
4
+ 2
6– 12
xy
xxy
xxy
-
¸
34.
Perform the indicated operations.
22
22
– 9368
4 – 244 – 36 + 5 – 6
xxxx
xxxxx
-
××
35.
Find the area of the rectangle shown.
36.
Subtract. Express your ...
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
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W2 - Lesson 3 Factors, Primes and Multiples .pptx
1. L.O: Define and find factors, primes and multiples
STARTER
Using the numbers from the
yellow box, find pairs that
multiply together to give the
totals below (YOU CAN ONLY USE
EACH NUMBER ONCE!):
a) 24 b) 36 c) 8 d) 30
SKILLS REQUIRED TODAY
Multiplication
5 September,
2022
8
3
6
6
4
2
5 6
3. Factor: A number which goes
into another number without
leaving a remainder
How can we make 12?
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
So, the factors of 12 are…
2 3
1 6 12
4
Your turn…
What are the factors of…
18?
24?
100?
13?
30?
27?
53?
41?
8?
4. Monday, 5 September 2022
Factors
Write down all the factors of…
20
1
2
20
4 5
10
5. Monday, 5 September 2022
Factors
Write down all the factors of…
28
1
2
28
4 7
14
6. Monday, 5 September 2022
Factors
Write down all the factors of…
48
1
2
48
3 16
24
4 12
10. Monday, 5 September 2022
Highest Common Factor (HCF)
What is the Highest Common Factor (HCF) of 12 and 18?
12
1
2
12
3
4
6
18
1
2
18
3
6
9
The Highest Common Factor (HCF) of 12 and 18 is 6
11. Monday, 5 September 2022
Highest Common Factor (HCF)
What is the Highest Common Factor (HCF) of 21 and 28?
21
1
3
21
7 28
1
2
28
4
7
14
The Highest Common Factor (HCF) of 21 and 28 is 7
17. Some of those numbers only had two factors.
A Prime Numberis a
number that has exactly two
factors
13, 41 and 53 are three prime numbers.
Which of these numbers are prime numbers?
12 27
3 36 18
7 19 9
11
19. 10 12 14 15 20 30
28 25 48 56 60 72
Bronze Task
Find the prim numbers of the following:
20. 10 = 2x 5 12 = 2 x 2 x 3
14 = 2 x 7 15 = 3 x 5
20 = 2 x 2 x 5 30 = 2 x 3 x 5
28 = 2 x 2 x 7 25 = 5 x 5
48 = 2 x 2 x 2 x 2 x 3 56 = 2 x 2 x 2 x 7
60 = 2 x 2 x 3 x 5 72 = 2 x 2 x 2 x
2 x 3 x 3
Answers
21. Multiples
Multiples are nice and easy. They are numbers that
appear in the Multiplication Tables of any given number.
For example:
12 27
3 36 18
40 16 9
21
Which of these numbers above are multiples of 4?
Which numbers are multiples of 9?
Which numbers are multiples of 3?
22. Multiple: A number which
appears in the given number’s
MULTIPLication table
3 8
1 16 20
12 15 2
13
24 19
17 36 18
6 4 30
7
• 6 Prime Numbers
• 6 Multiples of 6
• 6 Factors of 24
From these numbers, find me…
23. Factors of
60
Factors of
126
Numbers
less than 13
Numbers
more than
12
Multiples of
5
Prime
Numbers
Odd
Numbers
Square
Numbers
Multiples of
3
Even
Numbers
2
5
1
16 17
6
9 10
18
4
7
3
13 14
8
11 12
15 20 21 45
25 60
30
64
24. I can identify and find Factors,
Multiples and Prime Numbers
I can describe F, M and PN, but
struggle to find them
1
2
I get Factors and Multiples, but
struggle with Prime Numbers
I get confused between Factors
and Multiples
1
2
I got some questions right, but I
don’t really understand how
I don’t understand anything
we’ve covered in this topic
1
2
Choose a
statement that
matches your
ability on this
topic so far