When using synthetic division to divide 3x^4-2x^3-4x^2-31x-15 by 3x+1, why is it x^3-x^2-x-10-5/3x+1 rather than 3x^3-3x^2-3x-30-5/3x+1?

Question

Vocaloid · Answer

just look at the first terms

3x^4/3x = x^3 not 3x^3 so you know straight off the bat the first term in the quotient must be x^3

sunisround · Answer

wait what, can you draw it please?.

sunisround · Answer

alright.

Vocaloid · Answer

sorry I was trying to find a website that would format the synthetic division correctly

Vocaloid · Answer

anyway, you start off by factoring out the 3 and then applying synthetic division

Vocaloid · Answer

attachment

Vocaloid · Answer

sorry this is giving me a bit of a headache

Vocaloid · Answer

their result is obtained by first factoring out the 3 and then apply synthetic division, then multiplying the result again by 3

Vocaloid · Answer

I suppose you could try applying synthetic division without factoring out the 3 first and your result should still be mathematically equivalent