Question

Factor the polynomial function f(x). Then solve the equation f(x)= 0. f(x) x^4 -x^3 -19x^2 +49x -30

Answer 1

http://openstudy.com/study#/updates/5356d738e4b01d52d929fb88

Answer 2

I'd say try and find 4 factors of -30

use the factor theorem and try

\[\pm 1, \pm 2, \pm 3 \pm 5\]

with 4 factors you'll need a odd number of negative factors

so start by finding

P(1), then P(2), P(3) and P(5)

if any equal to zero... then you have a zero... and can write the factor...

Answer 3

\[f(x) = x^4 - x^3 - 19x^2 + 49x - 30\]
\[=x^3(x - 1) - x(19x - 49) - 30\]
\[=x^3(x - 1) - x(x - 1 + 18x - 48) - 30\]
\[=x^3(x - 1) - x(x - 1) - 18x^2 + 48x - 30\]
\[=x^3(x - 1) - x(x - 1) - 18x^2 + 48x - 30\]
\[=(x - 1)(x^3 - x) - 18x^2 + 48x - 30\]
\[=x(x - 1)(x^2 - 1) - 6(3x^2 - 8x + 5)\]
\[=x(x - 1)(x + 1)(x - 1) - 6(x - 1)(3x - 5)\]
\[=(x - 1)(x(x + 1)(x - 1) - 6(3x - 5))\]
\[=(x - 1)(x(x + 1)(x - 1) - 6(x - 1 + 2x - 4))\]
\[=(x - 1)(x(x + 1)(x - 1) - 6(x - 1) - 12x + 24)\]
\[=(x - 1)(x(x + 1)(x - 1) - 6(x - 1) - 12(x - 2))\]
\[=(x - 1)((x - 1)(x(x + 1) - 6) - 12(x - 2))\]
\[=(x - 1)((x - 1)(x^2 + x - 6) - 12(x - 2))\]
\[=(x - 1)((x - 1)(x + 3)(x - 2) - 12(x - 2))\]
\[=(x - 1)((x - 2)(x - 1)(x + 3) - 12))\]
\[=(x - 1)(x - 2)(x^2 + 2x - 3 - 12)\]
\[=(x - 1)(x - 2)(x^2 + 2x - 15)\]
\[0=(x - 1)(x - 2)(x - 3)(x + 5)\]

x - 1 = 0
x - 2 = 0
x - 3 = 0
x + 5 = 0