QuestionJuly 20, 2025

(1 point)Divide x^5-3x^4-23x^3+51x^2+94x-120b x^2-4x+3 Answer: square x^3+square x^2+square x+ square

(1 point)Divide x^5-3x^4-23x^3+51x^2+94x-120b x^2-4x+3 Answer: square x^3+square x^2+square x+ square
(1 point)Divide
x^5-3x^4-23x^3+51x^2+94x-120b
x^2-4x+3
Answer: square x^3+square x^2+square x+
square

Solution
4.2(152 votes)

Answer

x^{3} + x^{2} - 19x + 25 Explanation 1. Perform Polynomial Long Division Divide the leading term of the dividend x^5 by the leading term of the divisor x^2, which gives x^3. Multiply the entire divisor x^2 - 4x + 3 by x^3 and subtract from the original polynomial. 2. Subtract and Bring Down Next Term After subtraction, bring down the next term to get a new polynomial. Repeat the division process with the new leading term. 3. Continue Division Process Continue dividing, multiplying, and subtracting for each subsequent term until all terms are processed. 4. Collect Quotient Terms The quotient is formed by collecting all the terms obtained during the division process.

Explanation

1. Perform Polynomial Long Division<br /> Divide the leading term of the dividend $x^5$ by the leading term of the divisor $x^2$, which gives $x^3$. Multiply the entire divisor $x^2 - 4x + 3$ by $x^3$ and subtract from the original polynomial.<br /><br />2. Subtract and Bring Down Next Term<br /> After subtraction, bring down the next term to get a new polynomial. Repeat the division process with the new leading term.<br /><br />3. Continue Division Process<br /> Continue dividing, multiplying, and subtracting for each subsequent term until all terms are processed.<br /><br />4. Collect Quotient Terms<br /> The quotient is formed by collecting all the terms obtained during the division process.
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