Back when I was still in middle school, I was sitting at my kitchen table during a family gathering, and my uncle posed the following puzzle for me to solve: A vendor is selling apples for 10 cents apiece, oranges for 5 cents apiece, and peanuts two for a penny. Someone comes along and buys exactly 100 items for exactly one dollar. How many apples, oranges and peanuts did that person buy?
I...
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Factoring can be quite difficult for those who are new to the concept. There are many ways to go about it. The guess and check way seems to be the most common, and in my mind, it is the best, especially if one wants to go further into mathematics, than Calculus 1. But for those just getting through a required algebra course, here is another way to consider, that I picked up while tutoring some...
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What are the factors of x3 - 10x2 + 17?

Whenever math gives you an easy topic, take it and run with it! I am sometimes surprised by how many students struggle (really struggle) with factoring. That said, I always struggled with quadratics when I was in high school. And forgetting to move negative signs and decimals when simplifying (whoops!). Fortunately, I've gotten past that. My point is that even tutors and teachers start somewhere,...
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I was working with a student today, and as we worked through the section in his book dealing with Trigonometric Identities and Pythagorean Identities, we stumbled across a problem that gave us a bit of trouble. The solution is not so complicated, but it sure had us stumped earlier.
The problem was presented as such:
Factor and simplify the following...
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Prime Factorization
Prime factorization is used to find prime factors of any given number. Prime numbers are numbers that only have factors of 1 and the number (like 3â€”the only factors of 3 are 1 and 3). Prime factorization allows you to easily find all the prime factors of a number, and all numbers have a prime factorization. There are several different ways to write prime factorization;...
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Introduction To Factoring
A composite number is a number that can be written as the product of two positive integers other than 1 and the number itself. For example: 14 is a composite number because it can be written as 7 times 2. In this case, 7 and 2 are called factors of 14.
A composite expression is similar in that it can be written as the product of two or more expressions. For example:...
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Factoring and solving a cubic equation

A demonstration on basic factoring.

In this video, I help the student understand prime numbers and factorization.

The video shows how to solve a quadratic equation by factoring, and this is a simple case when the coefficient of the variable with highest degree is equal to 1

Factoring a perfect square polynomial