Functions and math

Question

f(x)=7x³-5x²-63x+45

1. Use synthetic division to test several possible rational zeros in order to identify one actual zero.

2. Use the zero from part 1. to find all the zeros of the polynomial function.

 

Please help, I can't figure this out.

Thanks!!

Answer 1

I tried synthetic division by 5 but that was way off.  Then I realized that f(-x) would have only one sign change so there's exactly one real negative root.  So I did synth division by -3 and that was successful (remainder zero), so we know that the depressed polynomial is 7x² -26x + 15 and setting this to zero is easy to solve by factoring.