Question

According to the synthetic division below, which of the following statements are true?

Check all that apply.

2(3 -11 10)
6 -10
____________
3 -5 0

A. (3x2 - 11x + 10) (x - 2) = (3x - 5)
B. (3x2 - 11x + 10) (x + 2) = (3x - 5)
C. (x - 2) is a factor of 3x2 - 11x + 10.
D. (x + 2) is a factor of 3x2 - 11x + 10.
E. The number -2 is a root of F(x) = 3x2 - 11x + 10.
F. The number 2 is a root of F(x) = 3x2 - 11x + 10.

Answer 1

\[\frac{P(x)}{x-c}=Q(x)+\frac{R}{x-c} \\ \\ \text{ where } Q(x) \text{ is quotient } \\ \text{ and } R \text{ is remainder } \\ \text{ if } R=0 \text{ then } (x-c) \text{ divides } P(x) \\ \text{ and both } (x-c) \text{ and } Q(x) \text{ are factors of } P(x) \\ \text{ and so } P(x)=Q(x)(x-c) \\ \text{ also } x=c \text{ is a root since when } x=c \text{ we have } P(c)=Q(c)(c-c)=0 \\ \]

Answer 2

would that be a?

Answer 3

your goona have to dumb that down for me

Answer 4

the remainder is the number left over in the division

Answer 5

what number is leftover in your division above

Answer 6

would'nt it be 3, -5, 0

Answer 7

no

Answer 8

the remainder is not 3 different numbers

Answer 9

the number left over is the last number in the last column

Answer 10

so 0

Answer 11

yep so we do have R=0
that is the remainder is 0
just apply the other things I mentioned above

Answer 12

can you identify what P(x) is
and what c is

Answer 13

and what Q(x) is

Answer 14

so the answers for the questions would be A, C, and F

Answer 15

A is not correct unless you made a type-o in A

Answer 16

ok not A what about the rest

Answer 17

so there isn't a type-o in A?
you wrote A exactly as it was written in your worksheet or whatever you are getting these questions from?

Answer 18

(3x^2-11x+10)/(x-2)=3x-5 would have been right
but (3x^2-11x+10)(x-2)=3x-5 is totally not true

Answer 19

\[\frac{P(x)}{x-c}=Q(x)+\frac{R}{x-c}\]

so you are right C and F are definitely true
but I'm still concerned you have mistyped A

Answer 20

so would b be right

Answer 21

no a 2nd deg polynomial times a 1st degree polynomial is a 3rd deg polynomial
not a first degree polynomial

did you read what I said?
I think there is a type-0 in A
I showed you by changing the operation from times to division would make A correct

Answer 22

for example x^2*x is x^3
this would not magically end up being x

Answer 23

unless you had x^2/x which is x

Answer 24

did you read what I typed earlier which was this:
"(3x^2-11x+10)/(x-2)=3x-5 would have been right
but (3x^2-11x+10)(x-2)=3x-5 is totally not true
"

Answer 25

i checked it there was a typo sorry
A. (3x2 - 11x + 10) / (x - 2) = (3x - 5)

Answer 26

ok

Answer 27

so you do have 3 answers then