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 +
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Polynomials-and-rational-expressions
-> 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 +
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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)
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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.
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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
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