Question

The polynomials that are given are P(x)=


`{x}^(3) - {x}^(2) - 18`
and Q(x)= P (2x-1)
Show that the result of Q is going to be Q(x)=

`8 {x}^(3) - 16 {x}^(2) + 10x - 20x`
​

Answer 1

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