Question

Find all the rational zeros of the function.
x^3-31x-30

Answer 1

let p(x) =x^3-31x -30
find p(-1)

Answer 2

0

Answer 3

p(x)=0

Answer 4

right
(x-1) is a factor of p(x)

Answer 5

divide p(x) with (x-1)

Answer 6

how did you know to use -1?

Answer 7

sum of the coefficients odd powers x = sum of the coefficients even powers of x
then x-1 is a factor

Answer 8

is it clear

Answer 9

what happens

Answer 10

can you use the rational roots theorem?

Answer 11

is it remainder theorem

Answer 12

no I mean to find all the possible roots

Answer 13

ok ,
can u divide given expression with (x-1)

Answer 14

sorry divide with x+1

Answer 15

yes

Answer 16

write the answer

Answer 17

x^2-x-30

Answer 18

very good

Answer 19

now split middle term
x^2-6x+5x-30

Answer 20

x(x-6)+5(x-6)
=(x-6)(x+5)
these are other two factors

Answer 21

so all of the factors are -1,6,-5, 0 ?

Answer 22

p(x)= x^3-31x-30
=(x+1)(x^2-x-30)
+(x+1)(x-6)(x+5)

Answer 23

x+1,(x-6),(x+5) are factors

Answer 24

-1, 6 and -5 are roots

Answer 25

is it clear

Answer 26

Yea thank you @dayakar