Question

Using synthetic division, what is the quotient: (2x3 - 2x - 12) ÷ (x - 2)
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Answer 1

it is almost impossible to write synthetic division here but i will try
first list the coefficients
2 0 -2 -12

don't forget the \(0\) for the missing \(x^2\) term

Answer 2

then since you are dividing by \(x-2\) put a \(2\) on the side

2 0 -2 -12
2
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Answer 3

ok i won't

Answer 4

bring down the top 2
2 0 -2 -12
2
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2

Answer 5

then 2 times 2 is 4
2 0 -2 -12
2 4
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2

Answer 6

0 + 4 = 4


2 0 -2 -12
2 4
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2 4

Answer 7

ok i did that and everytime i got a number on the bottom i multiplied it by 2 and i got a remainder of 0.am i right?

Answer 8

then 2 times 4 = 8
2 0 -2 -12
2 4 8
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2 4

Answer 9

-2 + 8 = 6

2 0 -2 -12
2 4 8
____________________
2 4 6

Answer 10

yes, the remainder is 0

Answer 11

2 0 -2 -12
2 4 8 12
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2 4 6 0

Answer 12

your quotient is \(2x^2+4x+6\) and the remainder is \(0\)

Answer 13

that tells you
\[2x^3 - 2x - 12=(x-2)(2x^2+4x+6)\]

Answer 14

so the answer is\[(x-2)(x ^{2}+4x+6)\]

Answer 15

well the actual answer to the division is \(2x^2+4x+6\)

Answer 16

the quotient is only 2x^2 +4x+6

Answer 17

ok thanks