We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Suppose $f(x)$ is a polynomial of degree $4$ or greater such that $f(1)=2$, $f(2)=3$, and $f(3)=5$. Find the remainder when $f(x)$ is divide

+1
1387
2

Suppose $f(x)$ is a polynomial of degree $4$ or greater such that $f(1)=2$, $f(2)=3$, and $f(3)=5$. Find the remainder when $f(x)$ is divided by $(x-1)(x-2)(x-3)$.

Jan 23, 2018

### 2+0 Answers

#1
0

Suppose f(x)  is a polynomial of degree 4 or greater such that f(1)=2,   f(2)=3, and    f(3)=5. Find the remainder when f(x)    is divided by    (x-1)(x-2)(x-3).

I don't know the answer but I would like to see someone else discuss it :/

Jan 24, 2018
edited by Melody  Jan 24, 2018
#2
+2

I consulted with a higher power and got a great answer!  Thank you Suppose f(x)  is a polynomial of degree 4 or greater such that f(1)=2,   f(2)=3, and    f(3)=5. Find the remainder when f(x)    is divided by    (x-1)(x-2)(x-3).

\begin{align} \frac{f(x)}{(x-1)(x-2)(x-3)}&=g(x)+\frac{ax^2+bx+c}{(x-1)(x-2)(x-3)}\\ \frac{f(x) \times (x-1)(x-2)(x-3)}{(x-1)(x-2)(x-3)}&=g(x)(x-1)(x-2)(x-3)+\frac{ax^2+bx+c}{(x-1)(x-2)(x-3)}\times (x-1)(x-2)(x-3)\\ f(x)&=g(x)(x-1)(x-2)(x-3)+ax^2+bx+c\\ now\;\;substitute\\ f(1)&=a+b+c=2\\ f(2)&=4a+2b+c=3\\ f(3)&=9a+3b+c=5\\ \end{align}

So now I have 3 equations and 3 unknowns so I just have to solve them simultaneously.

I solved them using matrices.  These are the unknowns.

$$c=2, \;\; b=\frac{-1}{2} \;\;and\;\;a=\frac{1}{2}\\ \text{So when f(x) is divided by (x-1)(x-2)(x-3) the remainder is } \frac{x^2}{2}-\frac{x}{2}+2$$

.
Jan 27, 2018
edited by Melody  Jan 27, 2018