Question

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.

k = -1; f(x) = 4x3 - 2x2 + 2x + 4; Lower bound?

Answer 1

4x^3-4x^2+6x-4+(8/k+1)

Answer 2

Agreed?

Answer 3

Atleast up to that part and how synthetic division works and how to write the polynomial after it

Answer 4

yes, but how do I know if it is upper or lower bound?

Answer 5

and thankyou !

Answer 6

well lets see
What is the pattern you see with the numbers at the bottom of the synthetic division line?

Answer 7

and no problem :)

Answer 8

I see what the numbers are but I dont see a pattern

Answer 9

well lets see
4 -4 6 -4 8
Look at the signs.

Answer 10

it's lower bound right ? it keeps going back down to -4

Answer 11

correct

Answer 12

actually its lower bound because the signs alternate

Answer 13

if all the signs are positive then it is upper bound

Answer 14

gotcha , thankyou so much for your help !

Answer 15

:)

Answer 16

Happy New Year!

Answer 17

you too !!