Factoring
Factor.
28 v3 w2 y4 + 24 v7 w9
4v3 w2 (7y4 + 6v4 w7)
Solve the following system of equations.
3x + 4y = 8
5x − 3y = 23
x = 4
y = −1
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2075. What was the rate charged per hour by each mechanic if the sum of the two rates was $120 per hour?
First mechanic: $55 per hour
Second mechanic: $65 per hour
Solve for y.
y2 + 2y − 8= 0
y=-4, 2
Factor.
y2-11y+18
(y-2)(y-9)
Factor.
2u2 + 22u + 48
2(u+3)(u+8)
Use substitution to solve the system.
5x + 3y = 10
y = 2x + 7
x = −1
y = 5
The length of a rectangle is 3 m less than twice the width, and the area of the rectangle is 44 m2. Find the dimensions of the rectangle.
Length: 8 m
Width: 5.5 m
Solve for v.
v2 + 2v − 3 = 0
v = −3, 1
Factor.
x2-9xy+20y2
(x-4y)(x-5y)
Factor.
x2 + 16x + 64
(x+8)2
Solve the following system of equations.
(3/4)x +(1/2)y =−10
(-1/3)x + (1/6)y = 6
x = −16
y = 4
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chef wants to make 300 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
First brand: 240 milliliters
Second brand: 60 milliliters
Factor.
5z2 + 7z + 2
(z+1)(5z+2)
Factor.
27+ 8v3
(3 + 2v) (9 − 6v + 4v2)
Solve the following system of equations.
(1/2x) - (1/3y) =−5
2x − (1/5y)= (2/5)
x = 2
y = 18
A motorboat travels 188 kilometers in 4 hours going upstream. It travels 284 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Rate of the boat in still water: 59 km/h
Rate of the current: 12 km/h
Factor.
25z2 − 81y2
(5z+9y)(5z-9y)
Factor.
6x2 − 5x − 4
(3x-4) (2x+1)
Last year, Linda had $10,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she invested the rest in an account that paid 9% simple interest per year. After one year, she received a total of $690 in interest. How much did she invest in each account?
First account: $7000
Second account: $3000
Factor.
63-28y2
7(3+2y) (3-2y)