Question

*what must be added to the polynomial X^4+2x^3-2x^2+x-1 so that the resulting polynomial is exactly divisible by x^2+2x-3?​

Answer 1

Answer:

${x}^{2} + 2x - 3) {x}^{4} + 2 {x}^{3} - 2 {x}^{2} + x - 1( {x}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{4} +2 {x}^{3} - 3 {x}^{2} \\ {x }^{2} + 2x - 3) {x}^{2} + x - 1(1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} + 2x - 3 \\ the \: remainder \: is \: - x + 2 \\ hence \: we \: have \: to \: add \: - x + 2 \: to \: the \: {x}^{4} + 2 {x}^{3} - 2 {x}^{2} + x - 1$

Step-by-step explanation:

for exactly divisible we have to add the remainder

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