Math Problem Statement
(4x^5-6x^4+5x^2-x-10)÷(2x^2+3)
Solution
To divide the polynomial by , we'll use polynomial long division. Here are the steps:
Step 1: Set up the division
We write the division as:
Step 2: Divide the first term of the dividend by the first term of the divisor
Divide by :
This will be the first term of the quotient.
Step 3: Multiply the entire divisor by this term and subtract
Multiply by the divisor :
Now subtract this from the original polynomial:
Step 4: Repeat the process
Now, divide the new leading term by :
Multiply by the divisor :
Subtract this from the current polynomial:
Step 5: Continue dividing
Next, divide by :
Multiply by the divisor :
Subtract this from the polynomial:
Step 6: Divide again
Divide by :
Multiply by the divisor :
Subtract this from the polynomial:
Final Answer:
The quotient is:
And the remainder is:
So, the complete expression is:
Would you like any additional details or explanations?
Related Questions:
- How do you perform synthetic division on polynomials?
- What are the applications of polynomial division in calculus?
- How can you determine if a polynomial is divisible by another polynomial without a remainder?
- What is the significance of the remainder in polynomial division?
- Can polynomial division be used to find roots of polynomials?
Tip:
Always double-check each step in polynomial division to avoid mistakes, especially when subtracting polynomials during the process.
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Math Problem Analysis
Mathematical Concepts
Polynomial Division
Long Division of Polynomials
Formulas
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Theorems
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Suitable Grade Level
High School
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