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

We have,
Dividend p(x) x³– 3x² + x + 2
Divisor g(x) = ? Quotient q(x) = x – 2 and Remainder r(x) = –2x + 4
According to division algorithm
Dividend p(x) = Divisor g(x) ^x Quotient q(x)+ Remainder r(x)

We have,Dividend p(x) x3 – 3x2 + x + 2Divisor g(x) = ? Quotient q

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Short Answer Type

347. Give examples of polynomials p(x),g(x), q(x) and r(x), which satisfy the division algorithm and
deg p(x) = deg q(x)

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348. Give examples of polynomials p(x),g(x), q(x) and r(x), which satisfy the division algorithm and
deg r(x) = 0

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349. Give examples of polynomials p(x),g(x), q(x) and r(x), which satisfy the division algorithm and
deg q(x) = deg r(x)

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Long Answer Type

350. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also, verify the relationship between the zeroes and coefficients in each case:
2x³+ x²–5x + 2; 1/2, 1,–2

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