Final answer:
This mathematics question involves dividing the polynomial 3x³+26x²+10x-4 by 3x+2 using long division, which entails dividing coefficients, subtracting exponents, and repeatedly subtracting the product of the divisor and the current quotient term from the remaining polynomial until the remainder has a degree less than that of the divisor or is zero.
Step-by-step explanation:
The question is about dividing polynomials using long division. In the division of 3x³+26x²+10x-4 by 3x+2, we would apply the long division method to find the quotient and the remainder. We consider the leading terms, divide the coefficient of the highest degree term in the numerator (3x³) by the coefficient of the leading term in the denominator (3x), which gives us x². Multiplying x² by the entire divisor (3x+2) and subtracting that product from the original polynomial, we can find the next term of the quotient. This process is repeated until the degree of the remainder is less than the degree of the divisor or until the remainder is 0.
To perform long division, we divide the coefficients and subtract the exponents when working with variables. It's similar to division with exponential terms where you would divide the numeric part of the terms and subtract exponents of like bases to simplify the expression.