The polynomial to be subtracted is derived from the multiplication of the first term of the quotient and is given as: x³ + 2x²
<h3>What are polynomials?</h3>
Polynomials are mathematical expressions consisting of variables, constants and exponents, which are combined using mathematical operations such as addition, subtraction, multiplication and division.
The long division is as follows:
(x³ + 3x² + x) ÷ x + 2
The first quotient will be x².
Multiplying (x + 2) and x² gives the polynomial to be subtracted from the dividend.
(x + 2)×(x²) = x³ + 2x²
Therefore, the polynomial to be subtracted is x³ + 2x².
Learn more about polynomials at: brainly.com/question/497625
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Answer:
![\log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}](https://tex.z-dn.net/?f=%5Clog_5%7B%5Cdfrac%7Bx%5E5%7D%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%7D)
Step-by-step explanation:
Make use of the rules of logarithms:
log(a/b) = log(a) - log(b)
log(a^b) = b·log(a)
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![5\log_5{x}-\dfrac{1}{4}\log_5{(8-x)}=\log_5{x^5}-\log_5{\sqrt[4]{8-x}}=\log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}](https://tex.z-dn.net/?f=5%5Clog_5%7Bx%7D-%5Cdfrac%7B1%7D%7B4%7D%5Clog_5%7B%288-x%29%7D%3D%5Clog_5%7Bx%5E5%7D-%5Clog_5%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%3D%5Clog_5%7B%5Cdfrac%7Bx%5E5%7D%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%7D)
