Question

IF THE POLYNOMIAL
${x}^{4} - 6 {x}^{3} + 16 {x}^{2} - 25x + 10$
IS DIVIDED BY ANOTHER POLYNOMIAL
${x}^{2} - 2x + k$
, THE REMINDERS COME OUT TO BE x+a , FIND k AND a.

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Answer 1

Step-by-step explanation:

Thus ,

Remainder = -9x + 2kx + 10 - 8k + k²

= ( 2k -9 ) x+ k² -8k + 10

According to question

Remainder = x + a

( 2k -9) x + k² - 8k + 10 = x+a

comparing

2k - 9 = 1

2k = 10

k = 5

k² - 8k + 10 = a

Putting k = 5

a= (5)² - 8(5) + 10

a = 25 - 40 + 10

a = -5

Therefore, k = 5 and a = -5

Hope it helps you