Question

The product of the polynomial (x² - x + 2) and (x - 1) is

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Answer 1

(x²-x+2) *( x-1) =x³-x²-x²+x+2x-2

=x³-x⁴+3x-2

Answer 2

Given: the polynomials are $(x^{2} - x + 2) and (x - 1)$.

To find: the product.

Solution:

Understand that to find the product of the given terms, multiply each term of the each polynomial to all the the terms of the other polynomial, then simplift the resulant.

Find the product of $(x^{2} - x + 2) and (x - 1)$.

$\[\left( {{x^2} - x + 2} \right) \times \left( {x - 1} \right) = x\left( {{x^2} - x + 2} \right) - 1\left( {{x^2} - x + 2} \right)\]$

                                  $\[\begin{array}{l} = {x^3} - {x^2} + 2x - {x^2} + x - 2\\ = {x^3} - {x^2} - {x^2} + 2x + x - 2\\ = {x^3} - 2{x^2} + 3x - 2\end{array}\]$

Hence, the product of $(x^{2} - x + 2) and (x - 1)$ is $\[{x^3} - 2{x^2} + 3x - 2\]$.