Writing Polynomials Given Roots

For the following problem write a polynomial in factored form with the following root: 4 and -6i

• (x + 4) ( x - 6i) (x - 4)

• (x - 4) ( x - 6i) (x + 6i)

• (x + 4) ( x - 6i) (x - 6i)

• (x + 4) (x - 4) (x - 6i)

For the following problem write a polynomial in factored form with the following root: 5 and 4i

• (x + 5) (x - 4i) (x + 4i)

• (x -5) (x - 4i)

• (x -5) (x - 4i) (x + 4i)

• (x -5i) (x - 4i) (x + 4i)

For the following problem write a polynomial in factored form with the following roots: 3, -8, and 2

• (x - 3) (x + 8) (x -2i)

• (x - 3i) (x + 8) (x -2)

• (x + 3) (x - 8) (x +2)

• (x - 3) (x + 8) (x -2)

For the following problem write a polynomial in factored form with the following roots:

 $1\ +\sqrt{2}and\ 9$  

•  $4x^3\ +\ 11x^2\ +\ 7x\ +1$  

•  $x^3\ -\ 11x^2\ +\ 17x\ +9$  

•  $-11x^3\ -\ x^2\ +\ 9x\ +17$  

• Peanut Butter

For the following problem write a polynomial in standard form with the following roots: 2 + i and 3

• $x^3\ -x^2\ +25x\ -25$

• $x^3\ -7x^2\ +11x\ -3$

• $x^3\ -7x^2\ +17x\ -15$

• $x^3\ -12x^2\ +48x\ -64$

For the following problem write a polynomial in standard form with the following roots:

 $2\ -\sqrt{5}\ and\ 3$  

•  $x^3\ -12x^2\ +\ 48x\ -64$  

•  $x^3\ +\ \frac{8}{3}x^2\ -17x\ +6$  

•  $x^3\ +\ 7x^2\ -10x\ -16$  

•  $x^3\ -7x^2\ +11x\ +3$  

For the following problem write the simplest polynomial function with the given zeros:

 $-3,6,\ and\ \frac{1}{3}$  

•  $x^3\ +\ \frac{8}{3}x^2\ -17x\ +6$  

•  $x^3\ -12x^2\ +48x\ +\ 6$  

•  $x^3\ -7x^2\ +11x\ +3$  

•  $x^3\ -8x^2\ =17x\ -6$  

For the following problem write the simplest polynomial function with the given zeros: 2, -1, and -8

• $x^3\ +7x^2\ +10x\ +16$

• $x^3\ +7x^2\ +10x\ -16$

• $x^3\ +7x^2\ -10x\ -16$

• $x^3\ -7x^2\ -10x\ -16$

For the following problems write the simplest polynomial function with the given zeros: 7 with multiplicity of 2 and -3

• $x^3\ -11x^2\ +7x\ -49$

• $x^3\ -11x^2\ +7x\ +49$

• $x^3\ -11x^2\ +7x\ -147$

• $x^3\ -11x^2\ +7x\ \ +147$

Simplify (10 – 7i) - (6 + 5i)

• 4 -12i

• 16 -2i

• 95 - 8i

• 95 - 2i