Question

The binomial x + 4 is one factor of 3x3 + 5x2 - 26x + 8. Use complete sentences to explain how you use (either) polynomial division or synthetic division to find the remaining factors. List the remaining factors.

Please help I have no clue

Answer 1

actually you need neither method. you can see what you need by writing
\[3x^3 + 5x^2 - 26x + 8=(x+4)(ax^2+bx+c)\] and thinking about what a, b and c have to be

Answer 2

I wish I could say that but we have to use either one of those

Answer 3

we know \(a=3\) since that is the only way you are going to get \(3a^3\) and we know \(c=2\) because that is the only way you are going to get 8

Answer 4

well if your teacher does not like you to think, then we can use synthetic division, which is easy to do but hard to write here

Answer 5

list the coefficients and write
3 5 -26 8

Answer 6

then underneath put -4
3 5 -26 8
-4
______________________

Answer 7

bring down the 3

3 5 -26 8
-4
______________________
3

Answer 8

I did out and I got 0 at the end

Answer 9

then 3 times -4 is -12

3 5 -26 8
-4
-12
____________________
3

Answer 10

but it says list the remaining factors what does that mean

Answer 11

ooh so you did it? what did you get?

Answer 12

I got the remaining of zero so it would be what 3x^2-7x+2?

Answer 13

is that right

Answer 14

??

Answer 15

sorry i got logged out and couldn't get back in

Answer 16

they wanted you to finish factoring as
\[3x^2-7x+2=(3x-1)(x-2)\]