Hotmath
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Title:
Hotmath
Author:
Hotmath
Chapter: Polynomial Functions Section: Polynomial Division, The Remainder and Factor Theorems
 

Problem: 1

Divide the expression.

 

Problem: 3

Divide the expression.

 

Problem: 5

Divide the expression.

 

Problem: 7

Divide the expression.

 

Problem: 9

Divide the expression.

 

Problem: 11

Divide the expression.

 

Problem: 13

Divide the expression.

 

Problem: 15

Simplify the expression.

 

Problem: 17

Simplify the expression.

 

Problem: 19

Simplify the expression.

 

Problem: 21

Divide using polynomial long division.

( x 2 + 7 x – 5) ( x – 12)

 

Problem: 23

Divide using polynomial long division.

(4 x 4 + 9) ( x 2 – 1)

 

Problem: 25

Divide.

 

Problem: 27

Divide.

 

Problem: 29

Divide.

 

Problem: 31

Perform he division.

 

Problem: 33

Divide.

 

Problem: 35

Divide using synthetic division:

( x 3 – 5 x – 6) ( x – 2)

 

Problem: 37

Divide using synthetic division:

(3 x 2 + 7 x – 3) ( x + 2)

 

Problem: 39

Perform synthetic division.

 

Problem: 41

Perform synthetic division.

 

Problem: 43

Perform synthetic division.

 

Problem: 45

Perform synthetic division.

 

Problem: 47

Find the remainder of the polynomial using synthetic division:

 

Problem: 49

Find the remainder of the polynomial using synthetic division:

 

Problem: 51

Evaluate the function using the remainder theorem:

f ( x ) = x 2 + 3 x + 7 at x = – 4

 

Problem: 53

Evaluate the function using the remainder theorem:

f ( x ) = 2 x 2 – 3 x + x + 2 at x = 2

 

Problem: 55

Use synthetic substitution to find f (1) and f (–2) for a function.

f ( x ) = 2 x 2 –7 x + 5

 

Problem: 57

Use synthetic substitution to find f (2) and f (–1) for a function.

f ( x ) = x 3 – 12 x 2 – 4 x + 3

 

Problem: 59

Factor the polynomial given that f ( k ) = 0.

f ( x ) = x 3 – 6 x 2 – 7 x + 60, k = – 3

 

Problem: 61

Factor the polynomial given that f ( k ) = 0.

f ( x ) = x 3 – 16 x 2 + 43 x + 60, k = 12

 

Problem: 63

Factor the polynomial given that f ( k ) = 0.

f ( x ) = x 3 – 2 x 2 – 32 x + 96, k = – 6

 

Problem: 65

One of the zeroes of the function f ( x ) = x 3 x 2 – 12 x is at x = –3. Determine the other zeroes.

 

Problem: 67

Given a polynomial and one of its factors, find the remaining factors of the polynomial.

81 x 5 – 243 x 4 – 256 x + 768, x – 3

 

Problem: 69

Given one zero of the polynomial function, determine the other zeros.

f ( x ) = 7 x 3 + 15 x 2 – 19 x – 3, –3

 

Problem: 71

Given one zero of the polynomial function, determine the other zeros.

f ( x ) = 3 x 3 + 7 x 2 – 43 x – 15, 3

 

Problem: 73

Find polynomial Q ( x) and constant R in 2 x 3 + 3 x 2 + 1 = Q ( x )( x + 2) + R .

 

Problem: 75

Find polynomial Q ( z ) and constant R in 2 z 3 – 3 z 2 + 2 z – 1 = Q ( z )( z + i ) + R .

 

Problem: 77

You are given an expression for the volume of the rectangular prism. Determine an expression for the missing dimension.

V = 4 x 3 + 5 x 2 – 32 x – 33 and the dimensions are ( x + 1) and ( x + 3).