Answer:
10
Step-by-step explanation:
Just plugging in!
So you could substitute the 5 into [tex]3x^2-9x-20 to[/tex] find the remainder of [tex]\frac{3x^2-9x-20}{x-5}[/tex].
[tex]3(5)^2-9(5)-20[/tex]
[tex]3(25)-9(5)-20[/tex] (exponents first since there are no grouping symbols)
[tex]75-45-20[/tex] (multiplication/division after exponents)
[tex]30-20[/tex] (addition/subtraction after multiplication/division)
[tex]10[/tex]
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:
[tex]f(5)=10[/tex]
Step-by-step explanation:
Step 1: Solve f(5)
Synthetic Division
[tex]\begin{array}{rrrr}\multicolumn{1}{r|}{5} & {3} & -9 & -20 \\\cline{2-4} & & 15& 30\\\cline{2-4} & 3 & 6 & \multicolum{|} 10\end{array}[/tex]
Answer: [tex]f(5)=10[/tex]
Substitution Method
[tex]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\\[/tex]
[tex]f(5)=10[/tex]
Answer: [tex]f(5)=10[/tex]
