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Solnce55 [7]
3 years ago
7

Please help!what polynomial must be added to −5x^3 + 4x − 3 so that the sum is x^2 − x − 1?

Mathematics
1 answer:
lakkis [162]3 years ago
6 0
<h3><u>Solution:- </u></h3>

Let the number to be added be A

Now,

\begin{gathered}\implies\quad \sf −5x^3 + 4x − 3  + A = x^2 − x − 1 \\\end{gathered}

Transposing (−5x³+ 4x − 3 ) to other side-

\begin{gathered}\\\implies\quad \sf   A = x^2 − x − 1 -( −5x^3 + 4x − 3) \\\end{gathered}

Remember if there is a -ve sign before a bracket the signs of whole of the terms changes on opening bracket

\begin{gathered}\\\implies\quad \sf   A = x^2 − x − 1 + 5x^3 - 4x + 3\\\end{gathered}

Putting like terms together -

\begin{gathered}\\\implies\quad \sf   A = 5x^3 +x^2 - x -4x +3 -1  \\\end{gathered}

\begin{gathered}\\\implies\quad \sf   A = 5x^3 +x^2 -5x +2 \\\end{gathered}

\longrightarrowTherefore, 5x³+x²-5x +2 should be added to −5x³+ 4x − 3 to get x²− x − 1

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