Question

x4 - 6x³ + 16x² - 25x + 10 is divided by x² - 2x +k, the remainder comes out to be x+a, find k and a, pls fast

Answer 1

Answer:

k = 5

a = -5

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Step-by-step explanation:

Rather than messy division, things like this are easiest with multiplication and "equating coefficients".

The given statement means

x⁴ - 6x³ + 16x² - 25x + 10 = ( x² - 2x + k ) ( bx² + cx + d ) + ( x + a )

Coefficients of x⁴:  1 = b

Coefficients of x³:  -6 = c - 2b  => c = 2b - 6 = 2 - 6 = - 4

Coefficients of x²:  16 = d - 2c + bk => d = 16 + 2c - bk = 16 - 8 - k = 8 - k

Coefficients of x: -25 = -2d + ck + 1 => - ck = -2d + 25 + 1

=> 4k = -2d + 26 => 2k = - d + 13

=> 2k = ( k - 8 ) + 13

=> k = 13 - 8 = 5

Coefficient of 1: 10 = dk + a

=> a = 10 - dk = 10 - k ( 8 - k ) = 10 - 5 × ( 8 - 5) = 10 - 5 × 3 = 10 - 15 = -5

So a = -5