Remainder theorem - Need Help

Remainder theorem - Need Help

Postby Guest » Wed Jun 09, 2021 2:44 pm

Need help on the below home work problem -
When P(x) is divided by x-1, the remainder is 1.
When divided by (x-2)(x-3), the remainder is 5.
What is the remainder when P(x) is divided by (x-1)(x-2)(x-5) ?
Guest
 

Re: Remainder theorem - Need Help

Postby Baltuilhe » Thu Jun 10, 2021 10:42 am

Good morning!

[tex]P(x)=q_1(x)(x-1)+1[/tex]
[tex]P(x)=q_2(x)(x-2)(x-3)+5[/tex]

[tex]P(x)=q_3(x)(x-1)(x-2)(x-3)+R(x)[/tex]
[tex]R(x)=ax^2+bx+c[/tex]

[tex]P(1)=1\\
P(2)=5\\
P(3)=5[/tex]

[tex]\begin{cases}a+b+c=1\\4a+2b+c=5\\9a+3b+c=5\\\end{cases}[/tex]

Solution:
[tex]\begin{cases}a=-2\\b=10\\c=-7\end{cases}[/tex]

So:
[tex]R(x)=-2x^2+10x-7[/tex]

Baltuilhe
 
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