SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. {{{ f(x) = x^4 + 6x^3 + 17x^2 + 54x + 72 }}} a. f(x) = (x - 4)(x + 2)(x

SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. {{{ f(x) = x^4 + 6x^3 + 17x^2 + 54x + 72 }}} a. f(x) = (x - 4)(x + 2)(x - 3)(x +

Question 472101: Find all zeros of the function and write the polynomial as a product of linear factors.

a. f(x) = (x - 4)(x + 2)(x - 3)(x + 3)
b. f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i)
c. f(x) = (x - 1)(x - 8)(x - 3i)(x + 3i)
d. f(x) = (x - i(sqrt8))(x + i(sqrt8))(x - 3)(x +3)

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = x^4 + 6x^3 + 17x^2 + 54x + 72
a. f(x) = (x - 4)(x + 2)(x - 3)(x + 3)
b. f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i)
c. f(x) = (x - 1)(x - 8)(x - 3i)(x + 3i)
d. f(x) = (x - i(sqrt8))(x + i(sqrt8))(x - 3)(x +3)
**
We could use the Rational Roots Theorem to solve this one, but because there would be so many possible roots it would be a long and drawn out process. Hopefully, you are allowed to get the first two roots with a graphing calculator. The graphing calculator shows that there are only two real rational roots, -2 and -4. I will show you how to find the other pair of imaginary roots.
..
Using synthetic division:
-2).....1......6.......17......54........72
................-2.......-8....-18......-72
..........1......4.......9........36.........0 (-2 is a root)
-4............-4.......0......-36
..........1.....0........9.........0 (-4 is a root)
f(x)=(x+2)(x+4)(x^2+9)
x^2+9=0
x^2=-9
x=�√-9
x=�3i
f(x)=(x+2)(x+4)(x-3i)(x+3i)
b. is the correct ans
RELATED QUESTIONS
Find all zeros of the function and write the polynomial as a product of linear factors. (answered by Edwin McCravy)

Find all zeros of the function and write the polynomial as a product of linear factors. (answered by ewatrrr)

Find all the Zeros of the function and write the polynomial as a product of linear... (answered by edjones)

Find all zeros of the function and write the polynomial as a product of linear factors. (answered by Alan3354)

Find all zeros of the function and write the polynomial as a product of linear factors. (answered by MathLover1)

Please help me solve this. Find all zeros of the function and write the polynomial as a... (answered by MathLover1)

find all zeros of the polynomial function and write the polynomial as a product of its... (answered by Fombitz)

Find all zeros of the function and write the polynomial as a product of linear factors. (answered by ikleyn)