Answer:
x^3-x^2+3x+3
Step-by-step explanation:
Subtract x3 + 2x − 6 from 2x3 − x2 + 5x − 3 and you will get x^3-x^2+3x+3.
The polynomial must be subtracted from 2x³ − x² + 5x − 3 so that the difference is x³ + 2x − 6 is x³ - x² + 3x + 3 .
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.
According to the question
2x³ − x² + 5x − 3
polynomial must be subtracted so that the difference is
x³ + 2x − 6
Let the value of polynomial is A .
Now,
(2x³ − x² + 5x − 3 ) - A = x³ + 2x − 6
A = 2x³ − x² + 5x − 3 - (x³ + 2x − 6 )
A = 2x³ − x² + 5x − 3 - x³ - 2x + 6
Like terms will add or subtract only
A = x³ - x² + 3x + 3
Hence, The polynomial must be subtracted from 2x³ − x² + 5x − 3 so that the difference is x³ + 2x − 6 is x³ - x² + 3x + 3 .
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