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Sagot :
Solution:-
Let the number to be added be A
Now,
[tex]\begin{gathered}\implies\quad \sf −5x^3 + 4x − 3 + A = x^2 − x − 1 \\\end{gathered} [/tex]
Transposing (−5x³+ 4x − 3 ) to other side-
[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 -( −5x^3 + 4x − 3) \\\end{gathered} [/tex]
Remember if there is a -ve sign before a bracket the signs of whole of the terms changes on opening bracket
[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 + 5x^3 - 4x + 3\\\end{gathered} [/tex]
Putting like terms together -
[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 - x -4x +3 -1 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 -5x +2 \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Therefore, 5x³+x²-5x +2 should be added to −5x³+ 4x − 3 to get x²− x − 1
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