2.5 apply the remainder and factor theorem long division and synthetic division pg. 85
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2.5 2.5 Apply the Apply the RemainderRemainder and and
Factor TheoremFactor Theorem
Long DivisionLong Division and and Synthetic DivisionSynthetic Division
Pg. 85Pg. 85
Remainder TheoremRemainder Theorem
If a polynomial P is divided by x-k, then the If a polynomial P is divided by x-k, then the remainder is P(k)remainder is P(k)
(x – k) is a factor of a polynomial P iff P(k) = (x – k) is a factor of a polynomial P iff P(k) = 0.0.
What is the remainder when P(x) = x3 + 2 is divided by x + 1
Is x + 1 a factor of P(x) = x3 + 2 ?
Factor TheoremFactor Theorem
Dividing PolynomialsDividing Polynomials
Dividing Polynomials to get the Dividing Polynomials to get the factors can be done in one of two factors can be done in one of two waysways
Long Division or Synthetic DivisionLong Division or Synthetic Division
Lets start with Long DivisionLets start with Long Division
4274 3 3 24 5 2 2x x x x
3 23 4 12 2x x x x Long DivisionLong Division
3 2 24 2x x x x Long DivisionLong Division
3 48 3x x Long DivisionLong Division
3 24 5 2 2x x x x 3 24 5 2 2x x x x
Long DivisionLong Division Synthetic DivisionSynthetic Division
3 23 4 12 2x x x x Synthetic DivisionSynthetic Division
3 2 24 2x x x x Synthetic DivisionSynthetic Division
Can’t be done!!!Can’t be done!!!
3 48 3x x Synthetic DivisionSynthetic Division
HomeworkHomeworkPg.Pg. 87,87, 1 – 121 – 12
Pg. 88,Pg. 88, 1 – 81 – 8
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