Question

Find k so that the quotient (x^4-8x^3+kx^2+15x-18)/x-6 has a zero remainder?

Answer 1

let x = 6 and find a value that makes the entire function 0

Answer 2

so by synthetic division?

Answer 3

just algebraic substitution

Answer 4

how do i do that?

Answer 5

replace "x" with 6 and set the function equal to 0

then find k

Answer 6

[just the numerator]

Answer 7

let me try it.

Answer 8

so k is equal to 10?

Answer 9

yup that's your answer

Answer 10

so that will give me a zero remainder?

Answer 11

yes

Answer 12

ok thank you again.

Answer 13

I dunno

The problem is to find k so that:

\( \dfrac{x^4-8x^3+kx^2+15x-18}{x-6} = \alpha , ~~~ \alpha \in \mathbb Z \)


Or:

\( (x^4-8x^3+kx^2+15x-18) = \alpha (x-6), ~~~ \alpha \in \mathbb Z \)

Whichever way, solving by setting x = 6 and solving the numerator for 0 amounts to dividing 0 by 0

So specify that \(x \ne 6\) but find any other value of x that sets the numerator to zero works

Yes ?!?!

Answer 14

I noticed that too, I will admit it's not the most mathematically sound method I could have used

Answer 15

😂