Question

What must be added to x^4+2x^3-13x^2-12x+21 so that it is exactly divisible by x^3-4x+3 ....plss answer quickly its very urgent..I will mark you as the brainliest

Answer 1

Let's factorize  x⁴ + 2x³ - 13x² - 12x + 21.

$x^4+2x^3-13x^2-12x+21 \\ \\ x^4+2x^3-4x^2-9x^2+3x-8x-7x+6+15 \\ \\ x^4-4x^2+3x+2x^3-8x+6-9x^2-7x+15 \\ \\ x(x^3-4x+3)+2(x^3-4x+3)-(9x^2+7x-15) \\ \\ (x^3-4x+3)(x+2)-(9x^2+7x-15)$

Here, - (9x² + 7x - 15) is the remainder.

∴ 9x² + 7x - 15 should be added to it to be a multiple of x³ - 4x + 3.

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