Question

pls answer correctly ​

Answer 1

p (x) =

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

the dividend

g (x) =? the divisor

quotient = (x-2)

remainder = (-2x+4)

we know that

dividend = divisor × quotient + remainder

${x}^{3} - 3 {x}^{2} + x + 2 = g (x) \times (x - 2) + ( - 2 + 4) \\ {x}^{ 3} - 3 {x}^{2} + x + 2 + 2x - 4 = g(x)(x - 2) \\ {x}^{3 } - 3 {x}^{2} + 3x - 2 = g(x)(x - 2) \\ hence \: g(x) \: is \: the \: quotient \: when \: we \: devide \: ( {x}^{3} - 3 {x}^{2} + 3x - 2) \: by \: (x - 2)$