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Math Help - Q. on polynomials, plz help!

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    Q. on polynomials, plz help!

    p(x) is a polynomial of degree>2. When p(x) is divided by x-2, it leaves remainder 1, and when divided by x-3, leaves rem. 3. Find the remainder when p(x) is divided by (x-2)(x-3)
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    Hello,
    Quote Originally Posted by deadmandx View Post
    p(x) is a polynomial of degree>2. When p(x) is divided by x-2, it leaves remainder 1, and when divided by x-3, leaves rem. 3. Find the remainder when p(x) is divided by (x-2)(x-3)
    p(x)=(x-2)Q(x)+1
    p(x)=(x-3)R(x)+3

    thus we know that p(2)=1 and p(3)=3

    Let s(x) be the remainder of p when divided by (x-2)(x-3)
    p(x)=(x-2)(x-3)T(x)+s(x)

    Since (x-2)(x-3) is of degree 2, s(x) has to be of degree 0 or 1.

    Substituting x=2 and x=3, this gives the system :
    \left\{\begin{array}{ll} 1=p(2)=0+s(2) \\ 3=p(3)=0+s(3) \end{array} \right.

    So we're looking for s(x)=ax+b and such that s(2)=1 and s(3)=3

    Substitute :
    \left\{\begin{array}{ll} s(2)=1=2a+b \\ s(3)=3=3a+b \end{array} \right.

    You can finish it eh ?
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