Question

If f(x)= 3x^2-9x-20, find the value of f(5) using synthetic division. this means, what is the remainder

a. 10
b. 15
c. -7
d. 0

Answer 1

10

Explanation:

Just plugging in!

So you could substitute the 5 into
`3x^2-9x-20 to` find the remainder of
`(3x^2-9x-20)/(x-5)`.

`3(5)^2-9(5)-20`

`3(25)-9(5)-20` (exponents first since there are no grouping symbols)

`75-45-20` (multiplication/division after exponents)

`30-20` (addition/subtraction after multiplication/division)

`10`

Synthetic division (the requested route):

So when we do the above division using synthetic division we should get the same thing for the remainder as the above evaluation.

5 | 3 -9 -20

| 15 30

-----------------------------

3 6 10

The remainder is 10, so f(5)=10.

Answer 2

`f(5)=10`

Explanation:

Step 1: Solve f(5)

Synthetic Division

`\begin{array}{rrrr}\multicolumn{1}r{5} & {3} & -9 & -20 \\\cline{2-4} & & 15& 30\\\cline{2-4} & 3 & 6 & \multicolum 10\end{array}`

Answer:
`f(5)=10`

Substitution Method

`f(5)=3x^2-9x-20\\f(5)=3(5)^2-9(5)-20\\f(5)=3(25)-45-20\\f(5)=75 - 45-20\\`

`f(5)=10`

Answer:
`f(5)=10`