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The polynomials that are given are P(x)=
[tex] {x}^{3} - {x}^{2} - 18[/tex]
and Q(x)= P (2x-1)
Show that the result of Q is going to be Q(x)=
[tex]8 {x}^{3} - 16 {x}^{2} + 10x - 20x[/tex]
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Respuesta :

devishri1977

Answer:

Step-by-step explanation:

P(x)=  x³ - x² - 18

Q(x) = P(2x-1)

       = (2x-1)³ - (2x-1)² -18

       = (2x)³ - 3*(2x)² * 1 + 3*2x* 1² - 1³ - [ (2x)² - 2*2x*1 + 1 ] - 18

=8x³ - 12x² + 6x - 1 - [4x² - 4x +1 ] - 18

= 8x³ - 12x² + 6x - 1 - 4x² + 4x - 1  - 18

= 8x³ - 16x² + 10x - 20

Hint : (a-b)³ = a³-3a²b+3ab²-b³

(a-b)² = a² -2ab + b²

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