If $4x^{10}-x^9-3x^8+5x^7+kx^6+2x^5-x^3+kx^2+5x-5 $ when divided by $(x+1)$ gives a remainder of -14, then the value of k equals?

Question

I got this and similar type of question in a book and I don't really know how to exactly solve it. Any help will be appreciated.

@egreg why did you censor your comment ? was it wrong ? – Evariste Apr 29 '17 at 17:21 — Evariste, Apr 29 '17 at 17:21
@Evariste what do you mean? – Iti Shree Apr 29 '17 at 17:22 — Iti Shree, Apr 29 '17 at 17:22

score 5 · Accepted Answer · answered Apr 29 '17 at 17:27

5

Let $f(x)=4x^{10}-x^9-3x^8+5x^7+kx^6+2x^5-x^3+kx^2+5x-5 $. Then $f(-1)=-14$ since the remainder when we divide by $x+1$ is $-14$.

So, $4+1-3-5+k-2+1+k-5-5=-14$ Thus, $2k=4$and $k=2$

answered Apr 29 '17 at 17:27

daruma

So for this kind of question we just substitute -1 randomly? – Iti Shree Apr 29 '17 at 17:40
You might want to check the factor theorem. – daruma Apr 29 '17 at 17:45
Can you provide any link @daruma – Iti Shree Apr 29 '17 at 17:47
It's in almost any common textbook on high school algebra. Google "Factor theorem" . You will get a lot of results. But if you really insist on a reference, https://en.m.wikipedia.org/wiki/Factor_theorem – daruma Apr 29 '17 at 18:08

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