Question

Divide using polynomial synthetic division.

(6x^3-7x+2) / (x-2)

Answer 1

list the coefficients, don't forget to keep the place for the missing \(x^2\) term

Answer 2

the coefficients are
6 0 -7 2

Answer 3

then put a 2 on the side

6 0 -7 2
2_________________

Answer 4

yeah i got 6x^2+12x+17+36/2
but i didnt get a zero so im confused...

Answer 5

bring down the 6
6 0 -7 2
2_________________
6

Answer 6

oh ok
no reason to necessarily get no remainder
usually when you divide, there is a remainder, just like with numbers

Answer 7

so my answer is correct?

Answer 8

yes

Answer 9

well almost
the remainder is not \(\frac{36}{2}\) it is \(\frac{36}{x-2}\)

Answer 10

oh yes

Answer 11

could u please help me with this: Find the product: (2x+3y)^3

Answer 12

you only get zero if the polynomial factors exactly
you should not think you are wrong if you do not get a zero as a remainder

Answer 13

\[ (2x+3y)^3=(2x+3y)(2x+3y)(2x+3y)\] you can either grind it till you find it, or use
\[(a+b)^3=a^3+3a^2b+3ab^2+b^3\] with
\[a=2x,b=3y\]

Answer 14

wait so can i use foil?