Question

divide x³-6x²+9x+3 by (x-1) .find the remainder. ​

Answer 1

Answer:

remainder theorem : if a polynomial f(x) is divided by (x - a) then remainder must be f(a). Therefore the remainder will be 7 after dividing (x³ - 6x² + 9x + 3) by (x - 1)

Remainder theorem says that,

f(x) is a polynomial of degree n (n ≥ 1) and ‘a’ is any real number. If f(x) is divided by (x – a), then the remainder will be f(a).

Let us solve the following questions on the basis of this remainder theorem.

Let f(x) = x3 – 6x2 + 9x – 8 …(1)

When x3 – 6x2 + 9x – 8 is divided by (x – 3).

Now, let’s find out the zero of the linear polynomial, (x – 3).

To find zero,

x – 3 = 0

⇒ x = 3

This means that by remainder theorem, when x3 – 6x2 + 9x – 8 is divided by (x – 3), the remainder comes out to be f(3).

From equation (1), remainder can be calculated as,

Remainder = f(3)

⇒ Remainder = (3)3 – 6(3)2 + 9(3) – 8

⇒ Remainder = 27 – 54 + 27 – 8

⇒ Remainder = -27 + 27 – 8

⇒ Remainder = 0 – 8

⇒ Remainder = -8

∴ the required remainder = -8

Step-by-step explanation:

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