Structre in Expressions
Table of Contents
1. Structure in Expressions
1.1. Trinomial
Assuming standard expression form (ie. \(-2x^2+10x-8\))
- Factor the constant expression (reduce to simpler terms)
- The resulting value can be assumed as \(c(x+a)(x+b)\)
- MUST ALSO INCLUDE NEGATIVES TOO!
- Find variables \(a\) and \(b\)
- \(a + b\) must equal coefficient \(x\)
- \(a(b)\) must equal the constant term
- Rewrite into \(c(x+a)(x+b)\)
1.1.1. Example
- Find equivalent expression to \(-2x^2+10x-8\)
- Factor out constant term \(-2\)
- \(-2(x^2-5x+4)\)
- fit \(x^2-5x+4\) into \((x+a)(x+b)\)
- \((-5+a)(4+b)\)
- Find variables \(a\) and \(b\)
- if \(a=-1\) and \(b=-4\)
- \(-1+-4 = -5\)
- \(-1(-4) = 4\)
- MATCHES
- if \(a=-1\) and \(b=-4\)
- Rewrite into \(-2(x-1)(x-4)\)
1.2. Binomial
Assuming standard binomial form (ie. \(x^2-36\))
- ENSURE BINOMIAL IS A PERFECT SQUARE!
- Use Difference of Squares special factoring relationship
- \(a^2-b^2=(a-b)(a+b)\)
- Find variables \(a\) and \(b\)
- \(a\) can be the coefficient of \(x\)
- \(b\) is the constant term
- Rewrite into \((a-b)(a+b)\)