# If the polynomial x^{4} - 6x^{3} + 16x^{2} - 25x + 10 is divided by another polynomial x^{2} - 2x + k, the remainder comes out to be x + a, find k and a

**Solution:**

The given polynomial is p(x) = x^{4} - 6x^{3} + 16x^{2} - 25x + 10

We can solve it by using a division algorithm: Dividend = Divisor × Quotient + Remainder

⇒ Dividend – Remainder = Divisor × Quotient

Let us divide and equate the obtained remainder with (x + a)

Now, it is given that p(x) when divided by x^{2 }– 2x + k leaves (*x *+ a) as remainder.

Let us equate the remainder with x + a (as given in the question)

(-9 + 2k)x + 10 - 8k + k^{2} = x + a

Let us compare the coefficient of both LHS and RHS.

-9 + 2k = 1

⇒ 2k = 10

⇒ k = 5 -----(1)

Also, 10 - 8k + k^{2} = a -------(2)

As we obtained the value of k, let us substitute in equation (2) to find the value of a.

a = 10 - 40 + 25

a = - 5

Therefore, the value of k is 5 and a is - 5.

**Video Solution:**

## If the polynomial x^{4} - 6x^{3} + 16x^{2} - 25x + 10 is divided by another polynomial x^{2} - 2x + k, the remainder comes out to be x + a, find k and a

### NCERT Solutions Class 10 Maths - Chapter 2 Exercise 2.4 Question 5:

If the polynomial x^{4} - 6x^{3} + 16x^{2} - 25x + 10 is divided by another polynomial x^{2} - 2x + k, the remainder comes out to be x + a, find k and a

k = 5 and a = −5 if the polynomial x^{4} - 6x^{3} + 16x^{2} - 25x + 10 is divided by another polynomial x^{2} - 2x + k, and the remainder comes out to be x + a