Polynomial Division

[loud sedge]

i got 3x^2+1((3x^2+5x+4)/5x^2-3x+1). But everyone in my class has gotten a different answer. can someone explain how to get the write answer or tell me where I went wrong in my work. Ill attach the question and my work

[dense abyss]

what's 3 x² (5 x² - 3 x + 1)?

and what happens when you subtract that from the numerator?

[loud sedge]

it should be 15x^4-9x^3+3x^2 and leave you with 8x^2+2x+5?

[loud sedge]

its the part after this that i'm mainly confused about because other had decimals and idk where that was coming from

[dense abyss]

there's an error here

you're subtracting 9 x³ from - 9 x³

what's the result?

[halcyon mural]

-11x² - (-3x²) is -8x² not 8x²

[loud sedge]

I’m confused it’s not positive 9x^3 it’s negative?

I redid the thing and this is what I got this time

[dense abyss]

you're subtracting 15 x⁴ - 9 x³ + 3 x², which is like adding - 15 x⁴ + 9 x³ - 3 x²

[dense abyss]

you need to subtract the whole thing

you're subtracting - 9 x³

[loud sedge]

are you not meant to just distribute the negative on to the whole thing

[dense abyss]

yes

[loud sedge]

so it would be written -(15x^4-9x^3-3x) which still means adding 9x^3 to -9x^3

My brain feels so fried right now 😔

[dense abyss]

you want to subtract 15x^4-9x^3+3x^2

so that line should read

-15 x^4 + 9 x^3 - 3x^2

all of the signs get swapped

[loud sedge]

No I understand that when I write it out I leave teh negative sign out because it’s how visualize it. I don’t distribute I just use it as a subtraction sign

It should still be the same regardless of writing format for the first line shoudnt it?

[dense abyss]

let's think about what we're doing here: we've discovered the largest multiple of 5 x³ - 3 x + 1 that goes into 15 x⁴ - 9 x³ + 11 x² + 2 x + 5 is 3 x², so we make a note of that and then subtract 3 x² · (5 x³ - 3 x + 1) from 15 x⁴ - 9 x³ + 11 x² + 2 x + 5 to get the remainder so far