Question

on dividing x cube minus 3 X square + X + 2 by a polynomial G of X the quotient and remainder when x minus 2 minus 2 X + 4 respectively find gfx ​

Answer 1

Answer:

$g(x)={x}^{2} - x + 1$

Step-by-Step Solution:

To find g(x) on dividing

${x}^{3} - 3x + x + 2$

by a polynomial g(x) the quotient and remainder when x-2 and - 2x + 4 respectively find g(x)

According to Division algorithm

$p(x) = g(x)q(x) + r(x) \\ \\ {x}^{3} - 3 {x}^{2} + x + 2 = g(x)(x - 2) + ( - 2x + 4) \\ \\ {x}^{3} - 3 {x}^{2} + x + 2 + 2x - 4 = g(x)(x - 2) \\ \\ {x}^{3} - 3 {x}^{2} + 3x - 2 = g(x)(x - 2) \\ \\ g(x) = \frac{{x}^{3} - 3 {x}^{2} + 3x - 2}{x - 2}$

Now divide to find g(x)

$x - 2 \: ){x}^{3} - 3 {x}^{2} + 3x - 2 \: ( {x}^{2} - x + 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{3} - 2 {x}^{2} \\ \: \: \: \: \: ( - ) \: \: \: \: \: ( + ) \\ \: \: \: \: \: \: - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: - {x}^{2} + 3x - 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: - {x}^{2} + 2x \\ \: \: \: \: \: \: \: \: \: \: ( + ) \: \: \: ( - ) \\ \: \: \: \: \: \: \: \: - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x - 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x - 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: ( - ) \: \: ( + ) \\ \: \: \: \: \: \: \: \: \: \: - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0$

Hope it helps you

Answer 2

Answer:

Step-by-step explanation: