(Solved) Write the function in the form f(x)= (x-k)q(x) +r for the given value of k?

fodog414

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9 years ago

Write the function in the form f(x)= (x-k)q(x) +r for the given value of k?

Write the function in the form
f(x) = (x − k)q(x) + r for the given value of k.

f(x) = x^3 − x^2 − 22x + 15, k = 5

I know it stars like this
... (x-5) but there are no examples in the book and the video lecture provided doesn't cover this
I am just confused on how we get q(x)

f(x)=(x-5)( Neutral Face

?)+5

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bio_man

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Educator

9 years ago

See if this helps...

Let me know what you come up with.

Also:

Similar Question

write the function in the form f(x)=(x-k)q(x)+r(x)for the given value of k. Use a graphing utility todemonstrate the f(k)=r
f(x)=x^3-x^2-14x+11 k=4

Answer:

use the synthetic division:
divide by 4
the you will get x2+3x- 2
remainder is 3
f(x)=(x- 4)(x2+3x- 2)+3
since 3 is remainder, then f(4)=3

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metal_zelda

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9 years ago Edited: 9 years ago, metal_zelda

This type of problem is supposed to get you thinking about what division actually means and how to use it to factor polynomials. Synthetically divide your function by x-5, and whatever x-5 goes into evenly is q(x) and r is the remainder. It should be (x-5)(x^2+4x-2)+5

Edit: I should mention that you could use polynomial long division if you were so inclined. Let me know if you need to see some work-- I didn't type out the synth division because it is hard to format in latex.

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fodog414 Author

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9 years ago

Ahhh Yes! Okay I was able to work it out as well and got (x-5)(x^2+4x-2)+5

thanks bio-man for the provided image

and too you as well metal zelda for the break down Slight Smile

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