What is the quotient (6x^4 + 15x^3 − 2x^2 + 10x − 4) ÷ (3x^2 + 2)?
someone , i'm very confused.

So hmm notice the picture below

the dividend, has all terms, already in descending order
the divisor, is missing one, the "x", so that means is 0x, so we add it

the idea is, you want to knock down the leftmost term in the dividend

so... to do say the first term.. then, we need to find  say
some value to multiply times 3x² to mimick or resemble 6x⁴

so.. that value is 2x²....the we slap a -( ..... ) to the whole product, thus in effect hosing 6x⁴ with a 6x⁴ - 6x⁴ or 0x⁴ or 0

and so on