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  5. Lesson 15 The Remainder Theorem
Lesson 15 The Remainder Theorem

Lesson 15 The Remainder Theorem

Assessment

Presentation

Mathematics

8th - 12th Grade

Practice Problem

Medium

CCSS
HSA.APR.B.2, HSA.APR.B.3

Standards-aligned

Created by

Andrew Witczak

Used 19+ times

FREE Resource

11 Slides • 8 Questions

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Lesson 15 The Remainder Theorem

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Multiple Choice

For the polynomial function

 f(x)=x32x25x+6f\left(x\right)=x^3-2x^2-5x+6  , we have f(0)=6, f(2)=-4, f(-2)=0, f(-1)=8, f(1)=0.  Rewrite f(x) as a product of linear factors.

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 f(x)=(x1)(x3)(x+2)f\left(x\right)=\left(x-1\right)\left(x-3\right)\left(x+2\right)  

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 f(x)=(x+1)(x+3)(x2)f\left(x\right)=\left(x+1\right)\left(x+3\right)\left(x-2\right)  

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 f(x)=(x+1)(x+3)(x+2)f\left(x\right)=\left(x+1\right)\left(x+3\right)\left(x+2\right)  

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 f(x)=(x+1)(x3)(x2)f\left(x\right)=\left(x+1\right)\left(x-3\right)\left(x-2\right)  

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Multiple Select

Select all the polynomials that have (x−4) as a factor.

1

x313x12x^3-13x-12

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x3+8x2+19x+12x^3+8x^2+19x+12

3

x3x210x8x^3-x^2-10x-8

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x24x^2-4

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Open Ended

Write a polynomial function, p(x), with degree 3 that has p(7)=0.

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Fill in the Blank

Long division was used here to divide the polynomial function

 p(x)=x3+7x220x110p\left(x\right)=x^3+7x^2-20x-110  by (x-5) and to divide is by (x+5).  What is p(-5)?

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Fill in the Blank

Long division was used here to divide the polynomial function

 p(x)=x3+7x220x110p\left(x\right)=x^3+7x^2-20x-110  by (x-5) and to divide is by (x+5).  What is p(5)?

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Multiple Choice

Which polynomial function has zeros when

 x=5, 23, 7x=5,\ \frac{2}{3},\ -7  ?

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 f(x)=(x+5)(2x+3)(x7)f(x)=(x+5)(2x+3)(x−7)  

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 f(x)=(x+5)(3x+2)(x7)f(x)=(x+5)(3x+2)(x−7)  

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 f(x)=(x5)(2x3)(x+7)f(x)=(x−5)(2x−3)(x+7)  

4

 f(x)=(x5)(3x2)(x+7)f(x)=(x−5)(3x−2)(x+7)  

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Multiple Choice

The polynomial function

 q(x)=3x4+8x313x222x+24q\left(x\right)=3x^4+8x^3-13x^2-22x+24  has known factors (x+3) and (x+2).  Rewrite q(x) as the product of linear factors.

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 q(x)=(x+3)(x+2)(x1)(3x4)q(x)=(x+3)\left(x+2\right)(x-1)\left(3x-4\right)  

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 q(x)=(x+3)(x+2)(x1)(3x+4)q(x)=(x+3)\left(x+2\right)(x-1)\left(3x+4\right)  

3

 q(x)=(x3)(x2)(x+1)(3x+4)q(x)=(x-3)\left(x-2\right)(x+1)\left(3x+4\right)  

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Open Ended

We know these things about a polynomial function f(x): it has degree 3, the leading coefficient is negative, and it has zeros at x=-5,-1,3. Sketch a graph of f(x) given this information.

Lesson 15 The Remainder Theorem

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