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Question
What must be added to 5x3 − 2x2 + 6x + 7 to make the sum x3 + 3x2 − x + 1?
Options
4x3 − 5x2 + 7x + 6
−4x3 + 5x2 − 7x − 6
4x3 + 5x2 − 7x + 6
none of these
Solution
−4x3 + 5x2 − 7x − 6
In order to find what must be added, we subtract (5x3 − 2x2 + 6x + 7) from (x3 + 3x2 − x + 1).
(x3 + 3x2 − x + 1) − ( 5x3 − 2x2 + 6x + 7)
or, x3 + 3x2 − x + 1 − 5x3 + 2x2 − 6x − 7
or, x3 − 5x3+ 3x2+ 2x2− x − 6x+ 1 − 7
or, −4x3 + 5x2 − 7x − 6
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