Respuesta :
It must be A cause if it was one then it would have to be 1x1 or it would have to be 3x1
Long division of a polynomial is given dividing the first term of the dividend or the numerator by the first term of the denominator or the divisor, and placing the result at the top
The term 3·x² in the quotient is the result of dividing 3·x⁴ by x², therefore, the correct option is option A.
A. x²
Reason:
The given expression in the question is presented as follows;
(3·x⁴ + 7·x³ + 2·x² + 13·x + 5) ÷ (x² + 3·x + 1)
Solution:
- When performing long division of a polynomial, the term with the highest value exponent in the divisor, is used to divide the term with the highest value exponent in the dividend, to give the first term of the quotient
- The first term of the quotient is then used to multiply the divisor which is added to the second row of the division operation
- The difference between the first and second expression under the division symbol is found, and written in the third row
- The process is repeated by dividing only the first terms of the obtained subtraction expression by the first term of the given divisor, up to the point where the power of the term in the difference expression is less than the power in the divisor
Which gives;
[tex]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \cdot x^2 - 2 \cdot x + 5\\x^2+ 3\cdot x + 1 \overline{)3\cdot x^4 +7 \cdot x^3 + 2\cdot x^2 + 13\cdot x + 5}\\{} \hspace{62} \underline{3\cdot x^4 + 9\cdot x^3 + 3\cdot x^2}\\ {} \hspace{89} {-2\cdot x^3 - x^2 + 13\cdot x}\\{} \hspace{89} \underline{{-2\cdot x^3 - 6\cdot x^2 - 2\cdot x}}\\{} \hspace{131} {5\cdot x^2 + 15\cdot x + 5}\\{} \hspace{131} \underline{5\cdot x^2 + 15\cdot x +5}\\{} \hspace{201} 0[/tex]
Therefore, the term 3·x² in the quotient is the result of dividing 3·x⁴ in the dividend by x² in the divisor. The correct option is option A.
Learn more about the long division of a polynomial here:
https://brainly.com/question/12002790
