I need to figure out how synthetic division works. The problem is ( 2 x 3 </msup>

Cristopher Knox 2022-07-07 Answered
I need to figure out how synthetic division works. The problem is
( 2 x 3 + 7 x 2 13 x 3 ) ÷ ( 2 x 3 )
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Answers (2)

fugprurgeil
Answered 2022-07-08 Author has 12 answers
Since you have taken 3 / 2 while doing synthetic division, we can write
2 x 3 + 7 x 2 13 x 3 = ( x 3 2 ) ( 2 x 2 + 10 x + 2 )
Now rearranging terms in RHS we get
2 x 3 + 7 x 2 13 x 3 = ( 2 x 3 ) ( x 2 + 5 x + 1 )
which is the same answer you got when you did the long division.

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antennense
Answered 2022-07-09 Author has 7 answers
Step 1: is to get the divisor in (x-a) format. There cannot be a coefficient. It is done by factoring:
( 2 x 3 ) = 2 ( x 3 2 )
The problem now looks like this
2 x 3 + 7 x 2 13 x 3 2 ( x 3 2 )
Step 2: is divide by 2
2 2 x 3 + 7 2 x 2 13 2 x 3 2 x 3 2
Step 3: Now the problem is setup for synthetic division
3 2 [ 1 10 3.5 6.5 1.5 100 1.5 100 7.5 10 1.5 _ 1 100 5 100 1 1000 0 ] = x 2 + 5 x + 1

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