In problems 1 through 4, write out the polynomial that has the listed factors:
Example: (x), (x-1) ANS: x2-x

1. (x-2), (x+3)

2. x, (x-2), (x-1)

3. (x-2i), (x+2i)

4. x, (x-1), (x+1), (x-2)

In problems 5 through 8, write the polynominal having the listed roots:

5. i

6. 2, 1, -1

7. 1, 3, 2, -1

8. -2, +3, i

In problems 9 through 11, use synthetic substitution to find f(-3) and f(4).

In problems 12 through 15, you are given a polynomial and one of its factors. Find the remaining factors of the polynomial. Some factors may not be binomials.

In problems 1 through 4, write out the polynomial that has the listed factors:
Example: (x),(x-1) ANS: x2-x

1. (x-2),(x+3)

Solution. We assume that the leading coefficient of the polynomial is 1. So, the polynomial is

(x-2)(x+3) = x^2 + x - 6

2. x, (x-2), (x-1)
Solution. We assume that the leading coefficient of the polynomial is 1. So, the polynomial is

x(x-2) (x-1) = x^3 - 3x^2 + 2x

3. (x-2i), (x+2i)
Solution. We assume that the leading coefficient of the polynomial is 1. So, the polynomial is

(x - 2i)(x + 2i) = x^2 + 4

4. x, (x-1), (x+1), (x-2)
Solution. We assume that the leading coefficient of the polynomial is 1. So, the polynomial is

x(x-1)(x + 1)(x - 2) = x^4 - 2x^3 - x^2 + 2x

In problems 5 through 8, write the polynominal having the listed roots:

5. i
Solution. We assume that the leading coefficient of the polynomial is 1. We know that if i is a root, then -i is another root. So, the polynomial is

(x-i)(x+1) = x^2 + 1

6. 2, 1, -1
Solution. We assume that the leading coefficient of the polynomial is 1. So, the polynomial is

(x-2)(x-1)(x+1) = x^3 - 2x^2 - x + 2

7. 1, 3, 2, -1
Solution. We assume that the ...

Solution Summary

The solution examines algebraic synthetic divisions.

1 and 2 can have multiple answers
1) Which of the given functions is a one-to-one function? Select all that apply
g(x)=2sqrt(x+5)
g(x)=5x^2-2
h(x)=x^4+5
f(x)=Abs(x)
f(x)=-5x+2
2) Which of the given functions is a one-to-one function? Select all that apply
g(x)=3sqrt(x)
f(x)=-2x+3
g(x)=2x^2-3x
f(x)=1/x
h(

1) Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).
P(x) = 3x^2 + 4x â?' 1, D(x) = x + 5
P(x) =(x+5)(_____)+______
2) Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and

1) Use the syntheticdivision to find: f(-2)
f(x)= 2x^2 - 3x^2 + 7x - 12
2) For the function f(x) = -x^3 + 8x^2 - 40
Show how to use syntheticdivision to find out if -1 is a zero.
3) One of the zeros of the function f(x) = x^3 - 7x^2 + 17x - 15 is 2-i. Find all the other zeros
4) Use the intermediate value theor

1. Explain what syntheticdivision is and what it is used for. (include at least 2 different uses for syntheticdivision) Give an example of syntheticdivision, show all steps. Explain what your answer means.
2. Pick a cubic function. (use something not too simple. a good example: y = 2(x+1)^3 - 5) Starting with y = x^3, use

1.) Write the following as an algebraic expression using x as the variable : the sum of a number and -8
2.) Write the following as an algebraic expression using x as the variable: Five more than the product of 7 and a number.
3.) Solve -3 ( -19+4 )/-5

Please help me with the attached problems by explaining how to solve them.
Use syntheticdivision to divide the polynomial 4x3 + 10x2 - 11 by x + 3, and state the quotient polynomial and the remainder. [Be careful - notice that there is no x term.]. Show work.
Consider the polynomial f(x) = 5x3 - 9x2 - 17x - 3.
(a) By u