Question

Find w(-3) using synthetic substitution
w(x)=11x^3-6x^2+2

Answer 1

Sorry it's w(-3)

Answer 2

hmmm do you know how to do synthetic division?

Answer 3

A little bit

Answer 4

ok... let us drop our 1st number and multiply by -3 \(\bf x=-3\implies x+3=0\implies (x+3)=0\\ \quad \\
11x^3-6x^2+2\implies 11x^3-6x^2+0x+2\quad \textit{arrange in descending order}\\ \quad \\
\begin{array}{rrrrrrrl}
-3&|&11&-6&+0&+2\\
&|&&-33\\
\hline\\
&&11&-39
\end{array}
\)

Answer 5

so -6-33 = -39

so now let's multiply -3 * -39 and use the product in the following term

\(\bf \begin{array}{rrrrrrrl}
-3&|&11&-6&+0&+2\\
&|&&-33&117\\
\hline\\
&&11&-39&117
\end{array}\)

Answer 6

and now -3 * 117 to be added to +2, the following term
\(\bf \begin{array}{rrrrrrrl}
-3&|&11&-6&+0&+2\\
&|&&-33&117&-351\\
\hline\\
&&11&-39&117&-349
\end{array}\)

Answer 7

so we use those coefficients, in our new expression lessened by 1 degree from the original

the original was 3rd degree, the quotient will be 2nd degree then
\(\bf \begin{array}{rrrrrrrl}
-3&|&11&-6&+0&+2\\
&|&&-33&117&-351\\
\hline\\
&&11&-39&117&-349
\end{array}\implies 11x^2-39x+117-\frac{-349}{x+3}\)

Answer 8

the last term is the remainder, so it stays in "division form", or you can just say it's the remainder

Answer 9

Is the last supposed to be - -349? So I would write that like 117- (-349/x+3)

Answer 10

well.... the "remainder" stays as a division, so it'd be written as a fraction

Answer 11

ohh.... ahemm... I see what you mean, well - * - = + .... so could be also written as \(\bf 11x^2-39x+117+\frac{349}{x+3}\) but still as fractional

Answer 12

Oh ok, but I can't type a fractional in word...

Answer 13

check in MS Word under I think is under ..... Format > insert > Equation
Word has an equation editor

Answer 14

I think the teacher will understand though, how do I do direct substitution for my next problem? Do I just plug in the number?

Answer 15

well.... you question was " Find w(-3) using synthetic substitution"


w(-3) will give you the REMAINDER

you simply were asked to get it by using synthetic division
so the answer I gather is -349

you can check by doing w(-3) on the equation and using direct substitution like \(\bf w(x)=11x^3-6x^2+2\implies w(-3)=11(-3)^3-6(-3)^2+2\)

Answer 16

that should yield you as the synthetic division did, -349

Answer 17

The direct substitution problem is: Find m(5) using direct substitution: m(x)=x^2+x-1

Answer 18

Do I just plug 5 into the equation?

Answer 19

yeap

Answer 20

So 5^2+5-1= 29. That's the answer?

Answer 21

yes, that means that 29 is the remainder were you to use synthetic diviision

Answer 22

And for the synthetic substitution problem I should write out the entire answer right? Like the whole 11x^2 to the remainder

Answer 23

I'd say yes

Answer 24

I agree. Thanks a lot man! If I have more questions, would you mind if I tag you?

Answer 25

sometimes you may just be asked to write the expression without the remainder and then write the remainder on the side

Answer 26

tis ok