Lesson 7

Integers of Quadratics

  • Let’s explore operations with integers

7.1: Math Talk: Missing Values

Mentally solve each equation for \(a\).

\(7\boldcdot a = 49\)

\(7 \boldcdot a= \text{-}49\)

\(\text{-}7\boldcdot a= 49\)

\(\text{-}7\boldcdot a = \text{-}49x\)

7.2: Finding Pairs that Work

For each question, find a pair of integers with the given product and sum.

  1. product: 6, sum: 5
  2. product: 6, sum: 7
  3. product: 4, sum: -5
  4. product: -1, sum: 0
  5. product: -6, sum: 1
  6. product: -12, sum: -1
  7. product: -12, sum: 4

7.3: Factor Expansion

For each question:

  • rewrite the expression in standard form
  • compare your question and solution with your partner
  • be prepared to explain anything you notice in the comparison

Partner A:

  1. \((x-1)(x-2)\)
  2. \((x-1)(x+2)\)
  3. \((x+4)(x-4)\)
  4. \((x+3)(x-6)\)
  5. \((x-2)(x-3)\)
  6. \((x-2)(x+7)\)
  7. \((x+5)(x-2)\)
  8. \((4-x)(1-x)\)

Partner B:

  1. \((x+1)(x+2)\)
  2. \((x+1)(x-2)\)
  3. \((x-4)(x+4)\)
  4. \((x-3)(x+6)\)
  5. \((2-x)(x-3)\)
  6. \((x+7)(x-2)\)
  7. \((x-5)(x+2)\)
  8. \((x-4)(x-1)\)

Summary