Structre in Expressions

Table of Contents

1. Structure in Expressions

1.1. Trinomial

Assuming standard expression form (ie. \(-2x^2+10x-8\))

  1. 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!
  2. Find variables \(a\) and \(b\)
    1. \(a + b\) must equal coefficient \(x\)
    2. \(a(b)\) must equal the constant term
  3. Rewrite into \(c(x+a)(x+b)\)

1.1.1. Example

  1. Find equivalent expression to \(-2x^2+10x-8\)
  2. Factor out constant term \(-2\)
    • \(-2(x^2-5x+4)\)
  3. fit \(x^2-5x+4\) into \((x+a)(x+b)\)
    • \((-5+a)(4+b)\)
  4. Find variables \(a\) and \(b\)
    1. if \(a=-1\) and \(b=-4\)
      • \(-1+-4 = -5\)
      • \(-1(-4) = 4\)
      • MATCHES
  5. Rewrite into \(-2(x-1)(x-4)\)

1.2. Binomial

Assuming standard binomial form (ie. \(x^2-36\))

  1. ENSURE BINOMIAL IS A PERFECT SQUARE!
  2. Use Difference of Squares special factoring relationship
    1. \(a^2-b^2=(a-b)(a+b)\)
  3. Find variables \(a\) and \(b\)
    • \(a\) can be the coefficient of \(x\)
    • \(b\) is the constant term
  4. Rewrite into \((a-b)(a+b)\)

Author: Troy Dwijanto

Created: 2022-04-05 Tue 03:15

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