QQuestionMathematics
QuestionMathematics
"Divide 42x^3−21x^2 + 49x by 7x.
A. 6x^3−3x+ 7
B. 6x^3 + 3x−7
C. 6x^2−3x+ 7
D. 6x^2 + 3x−7"
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Answer
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Step 1:I'll solve this polynomial long division problem step by step:
Step 2:: Set up the polynomial division
We need to divide $$42x^{3} - 21x^{2} + 49x$$ by $$7x
Step 3:: First term of the quotient
- Divide the leading term $$42x^{3}$$ by $$7x
- 42x^{3} \div 7x = 6x^{2}
Step 4:: Multiply the divisor by the first term of the quotient
- $$7x \times 6x^{2} = 42x^{3}
Step 5:: Subtract this result from the original polynomial
- $$42x^{3} - 21x^{2} + 49x - (42x^{3}) = -21x^{2} + 49x
Step 6:: Repeat the division process with the new polynomial
- Divide $$-21x^{2}$$ by $$7x
- - 21x^{2} \div 7x = - 3x
Step 7:: Multiply and subtract again
- $$7x \times (-3x) = -21x^{2}
- - 21x^{2} + 49x - (- 21x^{2}) = 49x
Step 8:: Final division
- $$49x \div 7x = 7
Step 9:: Combine the terms
The quotient is $$6x^{2} - 3x + 7
Final Answer
C. 6x^{2} - 3x + 7
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