Factorize
What is the Prime Factorization of 226
113 & 2
Find the GCF of 36 and 63
The GCF is 9
Multiply (x - 1)(x - 2)
x² - 3x + 2
Write a polynomial that represents the area of the circular puzzle.
Remember that the formula for area of a circle is:
A = 𝛑r², where r is the radius of the circle.
Leave the symbol r in your answer
Expression: r = x + 4
A = 𝛑(x + 4)²
Samantha has 12 pencils and 18 pens. She wants to pack them in boxes with an equal number of pencils and pens in each box. What is the greatest number of boxes she can pack?
Samantha can pack 6 boxes with an equal number of pencils and pens in each box. She will have 2 pencils and 3 pens in each box.
Factorize by Grouping
CHECK YOUR ANSWER
20 - 15x - 6x² + 8x.
Answer: (3x - 4)(-5 - 2x)
Check:
1: (3x - 4)(-5 - 2x) = -15x + 20 + 6x² - 8x
Simplifying this expression gives us:
6x² - 17x + 20
What is the greatest common factor of 84 and 126?
The GCF of 84 and 126 is 42.
Multiply (2x + 3)(4x - 1)
8x² + 10x - 3
A circular swimming pool has a radius of 10 meters. Write a polynomial that represents the area of the pool.
A = 𝛑(10)²
The length of a rectangle is 4 meters shorter than its width.
a. Write a polynomial that represents the area of the rectangle.
b. Find the area of the rectangle when the width is 6 meters.
a. A = x² - 4x
b. A = 6² - 4(6) = 12 square meters.
Factorize by Grouping
3x² - 15x² + 10 - 2x
(5 - x)(-12x - 2)
Find the GCF of 90 and 120
The GCF of 90 and 120 is 30
Multiply (3x² - 2xy + 4y²)(2x² + 3xy + y²)
6x⁴ + 5x2y² + 17xy³ + 8y⁴
Factorize the following polynomial: 3𝛑x² - 12𝛑xy + 9𝛑y²
Answer: 3𝛑(x - y)²
A principal wants to divide her grades of 450, 675, and 900 students into equal groups for a project. Each group should have the same number of students. What is the greatest number of students she can have in each group?
225 students!
Factorize 5x² + 25x + 30
5(x + 3)(x + 2)
Determine the greatest common factor of 180 and 225
The GCF of 180 and 225 is 45
Multiply (a³ - 2ab² + b³)(a³ + 2ab² + b³)
a⁶ + 4a³b² + b⁶
Find the greatest common factor of 16𝛑x² and 28𝛑x³
Answer: 4𝛑x²
A garden is in the shape of a rectangle with dimensions 12𝑟 by 15𝑟. If a square plot of side length 3𝑟 is removed from each corner, what is the area of the remaining garden in terms of 𝑟?
The remaining garden would have dimensions of (12r - 6r) by (15r - 6r), which simplifies to 6r by 9r. Therefore, the area of the remaining garden would be (6r)(9r) = 54𝑟².
A model rocket is fired vertically into the air at 320 It/s. The expression 16t² + 320t gives the rocket's height after t seconds.
Factor this expression.
We can factor out 16t from the expression:
16t² + 320t = 16t(t + 20)
Therefore, the expression can be written as:
h(t) = 16t(t + 20)
where h(t) is the height of the rocket in feet after t seconds.
What is the greatest common factor of 168 and 252?
The GCF of 168 and 252 is 84
Multiply (3x² - 2xy + 4y³ - 5z² + 2)(2x² + 3xy + y³ + 4z² - 3)
6x⁴ + 13x³y - 8x²y³ - 23x²z² - 4xy³ - 26y³z² + 15x² + 6xy - 12y³ - 20z² + 6
The diameter of a circular pizza is 20 inches. What is the area of the pizza to the nearest square inch?
A = 𝛑(10)² ≈ 314 square inches
The office supply room has 180 pens, 216 pencils, and 252 highlighters. The manager wants to divide them equally among different departments.
a: What is the greatest number of departments that can be created so that each department has the same number of each type of supply?
b: What is the maximum number of supplies each department will have?
c: What is the greatest number of departments that can be created if the manager wants to ensure that each department receives at least 10 pens, 15 pencils, and 20 highlighters?
a: The greatest number of departments that can be created so that each department has the same number of each type of supply is 36.
b: Each department will have a maximum of 5 pens, 6 pencils, and 7 highlighters.
c: The greatest number of departments that can be created if the manager wants to ensure that each department receives at least 10 pens, 15 pencils, and 20 highlighters is 6.