Factoring
Factor:
y2 + 6y + 9
(y + 3)2
Solve:
x(x-2) = 0
{0, 2}
Solve:
(x - 6)(x - 3) = 0
{-6, 3}
If a number is added to its square, the result is 56. Find the number(s)
7 and -8
Find two consecutive negative integers whose product is 90
-10, -9
Factor:
2x2 + 7x - 9
(x - 1)(2x+9)
Solve:
4(x - 3)(x + 2) = 0
{-2, 3}
Solve:
6x(3x - 1)(x + 4) = 0
{-4, 0, 1/3}
The product of two consecutive negative ODD integers is 255. Find the integers
-17 and -15
The length of a rectangle is 5 cm greater than its width. Find the dimensions of the rectangle is its area is 105 square meters? SETUP ONLY! Do not solve!
x(x + 5) = 105
Factor:
9x2 + 51x + 70
(3x + 7)(3x + 10)
Solve:
x2 + 4x + 4 = 0
{-2}
Solve:
x2 = 25
{-5, 5}
The length of a rectangle is 3 more than the width. The area of the rectangle is 40 square meters. Find the dimensions of the rectangle.
5m x 8m
You have a 4 x 6 in picture. You want to add a frame of universal width around the picture in order for the framed picture to have an area double that of the original picture. Find the dimensions of the framed picture. SETUP ONLY! DO NOT SOLVE
(2x + 4)(2x + 6) = 48
Factor:
2x3 - 6x2 - 5x + 15
(x - 3)(2x2 - 5)
Solve:
x2 + 10 = 15x - 34
{4, 11}
Solve:
5x2 - 5x = 30
{-2, 3}
I have three consecutive positive integers. The sum of the squares of the first and third terms is 34. Find the integers.
3, 4, 5
A positive number is 30 less than its square. Find the number
6
Factor:
a2 - x2 - 2x - 1
(a + x + 1)(a - x - 1)
Solve:
(x - 3)(x + 5) = 20
{-7, 5}
Solve:
x3 + x2 = 4x + 4
{-2, -1, 1, 2}
A rectangular picture measures 24 in by 30 in. You want to add a frame of uniform width. If the entire picture and frame has an area of 1080 square inches, what is the width of the frame?
3 inches
A farmer plants a rectangular pumpkin patch in the northeast corner of a square plot of land. The area of the pumpkin patch is 600 square meters. What is the area of the square plot of land? SETUP THE PROBLEM! DO NOT SOLVE
(Find picture on handout to give to students!)
(x - 30)(x - 40) = 600