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What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ?
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Introduction:
In this question, we are required to find the term that must be added to the given polynomial so that it is exactly divisible by 2x³ - 3.
Method:
To solve this problem, we can use the factor theorem. According to the factor theorem, if p(x) is a polynomial and (x-a) is a factor of p(x), then p(a) = 0.
Step 1:
First, we need to find the value of a such that 2a³ - 3 = 0.
Step 2:
Solving this equation, we get a = ∛(3/2).
Step 3:
Now, we know that (2x³ - 3) is a factor of the required polynomial. Therefore, we need to divide the given polynomial by (2x³ - 3) to find the missing term.
Step 4:
Performing the division, we get:
2x³ + 9x² - 5x - 15 ÷ (2x³ - 3) = x² + 3x + 5 + (0)/(2x³ - 3)
Step 5:
Therefore, the missing term is x² + 3x + 5.
Conclusion:
Hence, the term that must be added to the given polynomial to make it exactly divisible by 2x³ - 3 is x² + 3x + 5.
In this question, we are required to find the term that must be added to the given polynomial so that it is exactly divisible by 2x³ - 3.
Method:
To solve this problem, we can use the factor theorem. According to the factor theorem, if p(x) is a polynomial and (x-a) is a factor of p(x), then p(a) = 0.
Step 1:
First, we need to find the value of a such that 2a³ - 3 = 0.
Step 2:
Solving this equation, we get a = ∛(3/2).
Step 3:
Now, we know that (2x³ - 3) is a factor of the required polynomial. Therefore, we need to divide the given polynomial by (2x³ - 3) to find the missing term.
Step 4:
Performing the division, we get:
2x³ + 9x² - 5x - 15 ÷ (2x³ - 3) = x² + 3x + 5 + (0)/(2x³ - 3)
Step 5:
Therefore, the missing term is x² + 3x + 5.
Conclusion:
Hence, the term that must be added to the given polynomial to make it exactly divisible by 2x³ - 3 is x² + 3x + 5.
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What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ?
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What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ?.
What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What must be added to polynomial 2x³ 9x² - 5x - 15 so that the resulting polynomial is exactly divisible by 2x 3 ?.
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