lesson 11-2 remainder & factor theorems
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Lesson 11-2 Remainder & Factor Theorems. Objectives Students will: Use synthetic division and the remainder theorem to find P(r) Determine whether a given number is a root of P(x) Determine whether x – r is a factor of P(x) and solve P(x) = 0. P(x) = 5x 4 + 4x 3 + 3x 2 + 2x + 1 - PowerPoint PPT PresentationTRANSCRIPT
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Lesson 11-2Remainder & Factor Theorems
ObjectivesStudents will:Use synthetic division and the remainder theorem to find P(r)Determine whether a given number is a root of P(x)Determine whether x – r is a factor of P(x) and solve P(x) = 0
![Page 2: Lesson 11-2 Remainder & Factor Theorems](https://reader036.vdocuments.us/reader036/viewer/2022080905/56812c81550346895d913278/html5/thumbnails/2.jpg)
P(x) = 5x4 + 4x3 + 3x2 + 2x + 1
What is the remainder when P(x) divided by x – 3?
Find P(3)
Let P(x) = x3 + x – 10
What is the remainder when P(x) is divided by x + 2?
Find P(-2)
![Page 3: Lesson 11-2 Remainder & Factor Theorems](https://reader036.vdocuments.us/reader036/viewer/2022080905/56812c81550346895d913278/html5/thumbnails/3.jpg)
Remainder Theorem
The function value P(r) = remainder,
when P(x) is divided by x - r
Factor Theorem
If P(r) = 0, then x – r is a factor of P(x), also
If x – r is a factor, then P(r) = 0
Using the Theorems
If the roots are integers, then they will be factors of a0
“Factors of the constant (last) term”
If we know x – r is a factor, then dividing P(x) by x – r gives other factors
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Example 1 P(x) = x3 – 10x – 75
Is 5 a root? Find P(-2)
Example 2 Factor P(x) = x3 + 3x2 – 9x + 5
HW 106