Q. Divide. If there is a remainder, include it as a simplified fraction.(3s3+26s2+48s)÷(s+6)______
Use Polynomial Long Division: To divide the polynomial 3s3+26s2+48s by the binomial s+6, we will use polynomial long division.
Find First Quotient Term: First, we divide the leading term of the polynomial, 3s3, by the leading term of the binomial, s, to get the first term of the quotient, which is 3s2.
Subtract and Find Remainder: Next, we multiply the entire binomial (s+6) by the term we just found, 3s2, to get 3s3+18s2. We then subtract this from the original polynomial to find the remainder.(3s3+26s2+48s)−(3s3+18s2)=8s2+48s.
Find Next Quotient Term: Now, we divide the leading term of the new remainder, 8s2, by the leading term of the binomial, s, to get the next term of the quotient, which is 8s.
Subtract and Check Remainder: We multiply the binomial (s+6) by 8s to get 8s2+48s and subtract this from the remainder we had.(8s2+48s)−(8s2+48s)=0.
Finalize Quotient: Since the remainder is 0, we have no remainder in our division, and the quotient is the final answer.
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