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Polynomials CBSE NCERT Solutions
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).
Solutions: Suppose p(x) = x3 - 3x2 + x + 2,
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)
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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