How can you use a graph to check a factorization?

Answer 1

You can draw a number of items, then show how they are broken down into smaller sets (factors).

For example, to demonstrate factors of 6, you could draw

O O O

O O O = OOO + OOO (two sets of three) means 6 = 2 x 3

O O O

O O O = OO + OO + OO (three sets of two) means 6 = 3 x 2

Answer 2

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.

Answer 3

This method has limited application. It works only for polynomials and only if it can be factorised into binomial terms.

Suppose you have a polynomial in x of order n which is factorised as p(x) = (x - a1)*(x - a2)* ... *(x - an)

then the graph of a polynomial must cross the x-axis at the points a1, a2, ... an.

If the factorisation is q(x) = (x - a1)*(x^2 + bx + c) then the graph will cross the x-axis at a1. You may not be able to factorise the quadratic - either because it has two irrational roots - in which case the graph will cross the x-axis at these irrational values, or the quadratic has two complex roots - in which case the graph will not cross the x-axis again.

Answer 4

Factor trees, ladders, rainbows, fireworks... Whatever works for you.

Answer 5

What is a Prime number?

Answer 6

A factor tree is one such.

Answer 7

A factor tree is one such.

Answer 8

2 x 2 x 3 x 3 = 36