Question

According to the Rational Root Theorem ,Which Could be a factor of the polynomial F(x)=60x^4+86x^3-46x^2-43x+8?
A)x-6
B)5x-8
C)6x-1
D)8x+5

Answer 1

someone please help I'm so confused

Answer 2

one approach
if a factor then there is no remainder
find the value of x when potential factor = 0
use this value in f(x) if the value computed = 0 then confirmed a factor.

another approach
synthetic division

F(x)=60x^4+86x^3-46x^2-43x+8
+ + - - +
no yes no yes 2 real positive roots
+ - -++
yes no yes no 2 real negative roots

Answer 3

im still confused

Answer 4

i think it might be c but im not sure

Answer 5

if (x-6) is a factor then when x = 6 f(6) = 0
if (6x-1) is a factor then when x = 1/6 is used f(1/6) = 0 etc

Answer 6

huh sorry im not good at math at all

Answer 7

this is not using the theorem but I am checking option B
60x^4+86x^3-46x^2-43x+8?
60(8/5)^4 + 86(8/5)^3 - 46(8/5)^2-43(8/5) +8

Answer 8

I used the graph it confirmed the answer should be B

Answer 9

the instruction is to use the theorem which is not hard but need to remember how

Answer 10

the decimal values for x are -1.6, -7.07, 0.707 and 0.167 according to the graph

Answer 11

the first term is 60x^4
this means will have 4 roots and the product of the coefficients = 60
dividing by x^2 the remainder is -43x + 8 divide by x to get -43 remainder = 8
option B ends in 8

Answer 12

A statement of the RR Theorem is here;

http://www.mathwords.com/r/rational_root_theorem.htm

For what it's worth, here's a link which connects to a sample problem to which the Rational Root Theorem has been applied.

http://www.purplemath.com/modules/rtnlroot.htm

Answer 13

C) 6x -1 @17merenfrow0412

The RR theorem offers 1/6 as a possible root. Run it through the given equation by synthetic division to see if it yields 0.

As a factor, the root 1/6 would correspond to (6x - 1).

6x -1 = 0
x = 1/6