Factor a Mononomial
Algebra Help: Section 2.25
The factors of a quantity are those quantities which, being multiplied together, will produce the given quantity.
A composite quantity is one that may be produced by the multiplication of two or more factors. A composite quantity is exactly divisible by any one of its factors.
A prime quantity is one that cannot be produced by the multiplication of two or more factors, and is divisible only by itself and one.
Several quantities are prime to each other when they have no common factor, or when no quantity except one will divide each of them.
Case 1
Learn to factor a mononomial with algebra.
The prime factors of a purely algebraic quantity, consisting of a single term, are divisible to the eye. This is one of the principle advantages of an algebraic expression. Algebraic quantities are factored by inspection or by trial, the same as numbers in arithmetic.
1. What are the prime factors of 6a3b2c?
6 = 2 * 3 a3 = a * a * a b2 = b * b c = c ___________ 2 * 3aaabbc
ANALYSIS -
The prime factors of 6 are 2 and 3.
The exponents show that a is taken 3 times
as a factor, in the given term.
The exponents show that b is taken 2 times
as a factor.
Literal c is taken once.
2 x 3aaabbc
Rule
RULE - Resolve the numeral coefficient into its prime factors, and write each letter as many times as there are units in its exponent.
NOTE - Define factors. Define a composite quantity. Define a prime quantity. Define quantities prime to each other. What is Case 1? Give analysis and provide the rule.
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Help with Algebra Homework
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New Elementary Algebra
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By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.
