Ch09 Polynomials

Edit 0 15 …

Chapter 9 Syllabus.pdf

9.1 Adding and Subtracting Polynomials

9.2 Multiplying and Factoring

9.3 Multiplying Binomials

  • Notes 9-3.pdf
  • You can use the acronym FOIL to multiply two binomials:
    • F – First/first
    • O – Outer/outer
    • I – Inner/inner
    • L – Last/last
  • Example: (x + 3 ) * (x + 4)
    • First/first: x * x = x2
    • Outer/outer: x * 4 = 4x
    • Inner/inner: 3 * x = 3x
    • Last/last: 3 * 4 = 12
    • Adding these up: (x + 3)(x+4) = x2 + 4x + 3x + 12 = x2 + 7x + 12

9.4 Multiplying Special Cases

  • (x+a)2 = (x+a)(x+a) = x2 + xa + ax + a2 = x2 + 2ax + a2
  • (x–a)2 = (x–a)(x–a) = x2 – xa – ax + a2 = x2 – 2ax + a2
  • (x+a)(x–a) = x2 + xa – ax – a2 = x2 – a2

9.5 Factoring Trinomials of the Type x2 + bx + c

  • Notes 9-5.pdf
  • Find factors of c that add up to b.
  • Example: Factor x2 + 5x + 6.
    • Factors of 6 might be (6,1), (–6, –1), (2, 3), and (–2, –3).
    • The (2, 3) combination fits the bill: 2 + 3 = 5.
    • x2 + 5x + 6 = (x + 2) (x + 3).
    • Use FOIL to check your answer.

9.6 Factoring Trinomials of the Type ax2 + bx + c

9.7 Factoring Special Cases




9.8 Factoring by Grouping