Question

If x - 6x + 16x2 - 25x + 10 is divided by another polynomial x? - 2x + k, the remainder is (x + a). Find k and a​

Answer 1

Step-by-step explanation:

We know that,

Dividend Divisor x Quotient + =

Remainder

>Dividend - Remainder = Divisor

Quotient

→ Dividend - Remainder is always divisible by the divisor.

Now, it is given that f(x) when divided by x²-2x+ k leaves (x + a) as remainder.

NOW SEE THE IMAGE

So, for f(x) to be completely divisible by x² - 2x + k, remainder must be equal to zero

(-10 + 2k)x+ (10-a-8k+k²) = 0 → -10 + 2k = 0 and 10-a 8k + k ^ 2 = 0

k = 5 and 10 - a - 8(5) + 5 ^ 2 = 0

→ k = 5 and - a - 5 = 0

→ k = 5 and a = - 5

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