Final answer:
To divide the polynomials (x²+5x+1) by (x+3), perform polynomial long division and repeat the process until the remainder is lesser in degree than the divisor. For dividing exponentials, divide the coefficients and subtract exponents. For example,
divided by
would result in
Step-by-step explanation:
To divide the polynomials (x²+5x+1) by (x+3), we perform polynomial long division. We start by asking how many times does x go into x², which is x times. We then multiply (x+3) by x and subtract this from (x²+5x+1). The process is repeated with the resulting polynomial until the remainder is of lesser degree than the divisor or until it becomes zero.
The division of the exponentials works by subtracting the exponent of the denominator from the exponent of the numerator while dividing their coefficients. For example, given
, the division of the coefficients (2.56/5) gives us 0.512, and subtracting the exponents (-38 - (-21)) gives us
, so the result would be