factoring polynomial Consider the following x 711x2 18 a Us

factoring polynomial...

Consider the following /(x) =7-11x2 + 18 (a) Use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to three decimal places. (Enter your answers as a comma separated list.) (b) Determine the exact value of one of the zeros (use synthetic division to verify your result). x=3 (c) Factor the polynomial completely -2)2-9 f(x) =

Solution

1) f(x) = x^4 -11x^2 +18

Roots are correct

c) ay be try with f(x) = (x+ sqrt2)(x- sqrt2)(x+ 3)(x-3)

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

Roots of h(x) = -2 , 1+i*sqrt2 , 1- i*sqrt2

Product of linear factors : h(x) = (x+2)(x-1 -i*sqrt2)(x-1 +i*sqrt2)

3) polynomial with roots -4,1,4,8 can be written as

p(x) = (x+4)(x-1)(x-4)(x-8)

p(x) = (x^2+3x-4)(x^2-12x+32)

on multiplying we get

p(x) = x^4 - 9x^3 - 8x^2 + 144x - 128