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What must be subtracted from a3 – 4a2 + 5a – 6 to obtain a2 – 2a + 1?
  • a)
    a3 – 5a2 + 7a – 7
  • b)
    a3 – 4a2 + 7a – 6
  • c)
    a3 – 5a3 + 5a – 7
  • d)
    None of these 
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What must be subtracted from a3 – 4a2 + 5a – 6 to obtain a...
Here, a3– 4a2 +  5a – 6 – (a2 – 2a + 1)
= a3– 4a2 + 5a – 6 – a2 + 2a – 1
= a3– 5a2 + 7a – 7
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Most Upvoted Answer
What must be subtracted from a3 – 4a2 + 5a – 6 to obtain a...
Understanding the Problem
To find what must be subtracted from the polynomial a3 – 4a2 + 5a – 6 to yield a2 – 2a + 1, we need to set up the equation:
a3 – 4a2 + 5a – 6 - X = a2 – 2a + 1
where X is the polynomial we want to determine.
Rearranging the Equation
We can rearrange this equation to isolate X:
X = a3 – 4a2 + 5a – 6 - (a2 – 2a + 1)
Combining Like Terms
Now, we will simplify the right-hand side:
1. Distributing the negative sign:
-X = a3 - 4a2 + 5a - 6 - a2 + 2a - 1
2. Combining like terms:
- a3 (remains)
- (-4a2 - a2) = -5a2
- (5a + 2a) = 7a
- (-6 - 1) = -7
So, we have:
X = a3 - 5a2 + 7a - 7
Identifying the Correct Option
Now we compare our result with the given options:
- a) a3 – 5a2 + 7a – 7 (This matches our result)
- b) a3 – 4a2 + 7a – 6
- c) a3 – 5a3 + 5a – 7
- d) None of these
Conclusion
The polynomial that must be subtracted is indeed:
a3 – 5a2 + 7a – 7
Thus, the correct answer is option 'A'.
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Question Description
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