Mathematics
What must be added to x4 - x3 + x2 + x + 3 to obtain x4 + x2 - 1 ?
Algebraic Expressions
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Answer
Let the number Z must be added to x4 - x3 + x2 + x + 3 to obtain x4 + x2 - 1
⇒ Z + (x4 - x3 + x2 + x + 3) = (x4 + x2 - 1)
⇒ Z = (x4 + x2 - 1) - (x4 - x3 + x2 + x + 3)
⇒ Z = x4 + x2 - 1 - x4 + x3 - x2 - x - 3
Arrange the polynomial with like terms together and combine them.
⇒ Z = (x4 - x4) + x3 + (x2 - x2) - x + (- 1 - 3)
⇒ Z = 0 + x3 + 0 - x - 4
Hence, the number is x3 - x - 4.
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