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Chapter 3: Problem 10

Divide. $$-33 h^{12} \div(-11 h)$$

Short Answer

Expert verified
Question: Divide the terms $$-33 h^{12}$$ and $$-11h$$. Answer: $$3h^{11}$$

Step by step solution

01

Divide coefficients

Divide the coefficients of both terms: $$\frac{-33}{-11}$$ This results in $$3$$.
02

Subtract exponents

Subtract the exponent of h in the second term from the exponent of h in the first term: $$(12 - 1)$$ which results in $$11$$.
03

Combine the results

Combine the results from Step 1 and Step 2 to form the final answer: $$3h^{11}$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Division of Polynomials
When dealing with the division of polynomials, you're working with expressions that include variables and coefficients. Imagine breaking apart two expressions to see how many times one fits into the other. It鈥檚 similar to dividing regular numbers, but requires a careful consideration of both coefficients (the number part) and the variables with their exponents.
  • Identify the Terms: In our exercise, the terms are \-33h^{12}\ and \-11h\.
  • Simplify the Coefficients: Divide the numerical coefficients separately 鈥� in this case, \frac{-33}{-11} = 3\.
  • Adjust the Exponents: Handle the variable part by considering the exponents 鈥� subtract the exponents for the same base (here, h).
The ultimate goal is to produce a simpler form of the expression, as seen in our solution: \(3h^{11}\). Practice makes perfect, and understanding each part of the division can greatly ease the process.
Exponents
Exponents are the little numbers placed to the upper right of base numbers or variables. They show how many times the base is multiplied by itself.In polynomials, exponents help define the degree of the terms and expression as a whole.
  • Values: Exponents can be any integer, but in polynomial division, we only subtract positive exponent values.
  • Subtracting Exponents:When dividing terms with the same base, like \(h^{12} \) and \( h \), subtract the exponents \ (12 - 1 = 11)\.
  • Simplification: Always simplify expressions by lowering the exponent value after performing operations.
Assessing and manipulating exponents is crucial for properly executing polynomial operations. Always ensure consistency in exponent use to simplify your polynomials effectively.
Coefficients
Coefficients are the numbers in front of the variables in algebraic expressions. They play a key role in scaling the variable part of polys.To divide coefficients, focus solely on the numeric part.
  • Recognize the Parts: In our exercise, the coefficients are -33 and -11. Coefficients can be positive or negative, impacting the direction of scaling.
  • Simplify: Calculate \( \frac{-33}{-11} \) to get \( 3 \). This operation deals purely with arithmetic.
  • Effect on Final Result: The simplified coefficient \( 3 \) is then used with the variable portion \( h^{11} \) for the ultimate answer \( 3h^{11} \).
By understanding coefficients, you will be able to handle the numeric aspect of polynomial expressions confidently. They determine a large part of the expression's value and behavior.

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Most popular questions from this chapter

Simplify by combining like terms. $$17 c^{4}-c^{4}$$

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Multiply. $$(a-7)(2 a-5)$$

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