Chapter 2: Polynomials

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Q
Polynomials CBSE NCERT Solutions

Question:

On dividing x3 - 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x).

Answer:

Solutions: Suppose p(x) = x3 - 3x2 + x + 2,

We have,

Dividend p(x) = x3 - 3x2 + x + 2

Quotient = x - 2

Remainder = –2x + 4

As we know,

Dividend = Divisor × Quotient + Remainder

x3 - 3x2 + x + 2 = g(x) × (x - 2) + (-2x + 4)

 

 

Rightarrow x3 - 3x2 + x + 2 - (-2x + 4) = g(x) × (x - 2)

Therefore, g(x)  (x - 2) = x3 - 3x2 + 3x - 2

Now, to finding g(x) we will divide x3 - 3x2 + 3x - 2 with (x - 2).

Hence, g(x) = (x2 – x + 1).

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