Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.

Question

1. f(x)=7x^3-x^2+7x-1
2. f(x)=x^4+6x^3-11x^2-24x+28
3. f(x)=4x^4+5x^3+13x^2+15x+3

Answer 1

For problem#1 use factoring by grouping

(7x^3 -x^2) +7x -1

x^2(7x-1) +1(7x-1)

(x^2+1)(7x-1)=0

x^2+1=0. 7x=1

x^2=-1. X=(1/7)

x=(+/-)I

Problem#2 need to use synthetic division and 1 works so (x-1) is a factor

Then use 2 and this works so (x-2) is a factor which leaves us with x^2+9x+14 which factors to (x+2)(x+7)

So all our factors are (x-1)(x-2)(x+2)(x+7)