1
If twice a number is subtracted from its square, the remainder is 35. Find every number that works.
Chapter 14 · Solving Equations by Factoring
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
0first-try
0of 10 done
From Problems Solved by Factoring, exercise 2
Solve each problem. When asked for every number that works, list them all.
From Problems Solved by Factoring, exercise 26
Triangles: area = \tfrac{ab}{2}, altitude a times base b, over 2.
2
A triangle's altitude is 3 feet longer than its base, and its area is 6 square yards. Find both in feet.
From Solving Equations by Factoring, exercise 14
Find the roots of each quadratic. Type them separated by commas, like 3, -2.
3
x^2 - 2ax + a^2 = 0
From Problems Solved by Factoring, exercise 6
Solve each problem. When asked for every number that works, list them all.
4
A number is subtracted from 17, and also from 23. The product of the remainders is 216. Find every number that works.
From Problems Solved by Factoring, exercise 16
Solve each problem. When asked for every number that works, list them all.
5
The sum of the squares of three consecutive positive odd numbers is 251. Find them.
From Problems Solved by Factoring, exercise 29
Triangles: area = \tfrac{ab}{2}, altitude a times base b, over 2.
6
A triangle has area 2\tfrac58 square feet, and its base is 6 inches longer than twice its altitude. Find both in inches.
From Problems Solved by Factoring, exercise 11
Solve each problem. When asked for every number that works, list them all.
7
A lot of 2500 square feet is four times as deep as its frontage. Find its dimensions in feet.
From Solving Equations by Factoring, exercise 20
Find the roots of each quadratic. Type them separated by commas, like 3, -2.
8
9x^2 = 3x + 2
From Solving Equations by Factoring, exercise 6
Find the roots of each quadratic. Type them separated by commas, like 3, -2.
9
x^2 - x = 20
From Solving Equations by Factoring, exercise 12
Find the roots of each quadratic. Type them separated by commas, like 3, -2.
10
x^2 - a^2 = 0