Question

is x + 10 a factor of the function f (x) = x^3 - 75x + 250?

Answer 1

try algebraic long division. If you dont get a remainder then it is factor :)

Answer 2

hmm can you explain further?

Answer 3

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/dividing_polynomials/v/algebraic-long-division

Answer 4

try that. ANd i will add if you get no remainder left then it is a factor

Answer 5

i still dont get it at all

Answer 6

can you do a walkthrough with my example?

Answer 7

hint: if x-p is a factor of f(x), then f(p) = 0

this is the remainder theorem

Answer 8

can someone do a step by step walkthrough of my problem please

Answer 9

x + 10

is the same as

x - (-10)

Answer 10

match x - (-10) up with x - p and you'll see that p = -10

Answer 11

so you just need to see if f(-10) = 0 is true or not

Answer 12

not true

Answer 13

?

Answer 14

you need to show why it's not true

Answer 15

plug x = -10 into f (x) = x^3 - 75x + 250 to see what you get

Answer 16

-10 cubed is -1000 correct?

Answer 17

yes it is

Answer 18

ok then the function would equal

Answer 19

-1500?

Answer 20

is that right?

Answer 21

you made an error

Answer 22

try it again

Answer 23

-1000+750+250= 0 so 0 is the answer

Answer 24

so because f(-10) = 0, this means that x - (-10) or x + 10 is a factor

Answer 25

so it is a factor because the remainder is zero?

Answer 26

or is it a factor because the remainder is NOT zero?

Answer 27

it's a factor because the remainder is 0

Answer 28

that's exactly what the factor theorem says above

Answer 29

thank you so much man!

Answer 30

hey can you help me with a couple more?

Answer 31

they deal with remainder questions in long division

Answer 32

sure, one more