Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial. ( 2 x 3 − 3 x 2 + x ) ÷ ( x − 1 )

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Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial.   (  2      x          3        −  3      x          2        +  x  )  ÷  (  x  −  1  )

garnboernl · Accepted Answer

Remainder Theorem:If a polynomial P(x) is devided by x-r, the remainder is a constant P(r), andP(x)=(x-r)Q(x)+P(r).Where Q(x) is a depressed polynomial with one degree less than the degree of P(x).Factor theorem:The binomial x-r is a fractor of the polynomial P(x) if and only if P(r)=0.For   (  2      x          3        −  3      x          2        +  x  )  ÷  (  x  −  1  ), we compute f(1) to determine the remainder of the division:f(1)=2-3+1=0The remainder is 0, x-1 is a factor of   2      x          3        −  3      x          2        +  x.

Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial. (2x^3 -3x^2 +x)div (x-1)

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