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Question
By how much does 3x2 − 5x + 6 exceed x3 − x2 + 4x − 1?
Solution
To calculate how much does 3x2 − 5x + 6 exceed x3 − x2 + 4x − 1, we have to subtract x3 − x2 + 4x − 1 from 3x2 − 5x + 6.
Change the sign of each term of the expression that is to be subtracted and then add.
Term to be subtracted = x3 − x2 + 4x − 1
Changing the sign of each term of the expression gives -x3 + x2 - 4x + 1.
On adding:
(3x2 − 5x + 6)+(-x3 + x2 - 4x + 1 )
= 3x2 − 5x + 6-x3 + x2 - 4x + 1
= -x3 + (3+1)x2 +(-5-4)x+6 + 1
= -x3 +4 x2 - 9x + 7
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