Mathematics
What must be subtracted from 19x4 + 2x3 + 30x - 37 to get 8x4 + 22x3 - 7x - 60?
Answer
Let A be the number that should be subtracted from 19x4 + 2x3 + 30x - 37 to get 8x4 + 22x3 - 7x - 60
(19x4 + 2x3 + 30x - 37) - A = (8x4 + 22x3 - 7x - 60)
⇒ (19x4 + 2x3 + 30x - 37) - (8x4 + 22x3 - 7x - 60) = A
⇒ A = 19x4 + 2x3 + 30x - 37 - 8x4 - 22x3 + 7x + 60
⇒ A = (19x4 - 8x4) + (2x3 - 22x3) + (30x + 7x) + (- 37 + 60)
⇒ A = 11x4 - 20x3 + 37x + 23
Hence, the number is 11x4 - 20x3 + 37x + 23.
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