



 
Hi, The key here is the Polynomial Remainder Theorem which states that if a a polynomial $f(x)$ produces a remainder of $R$ when divided by $(xk)$ then $f(k) = R.$ Suppose your quadratic polynomial is $f(x) = a x^2 + b x + c.$ Since its remainder upon dividing by $x1$ is $1$ the Remainder Theorem tells us that $f(1) = 1$ and hence \[f(1) = a \times 1^2 + b \times 1 + c = a + b + c = 1.\] In a similar fashion division by $x  2$ and $x + 2$ give us two further linear equations in $a, b$ and $c.$ Solve for $a, b$ and $c.$ Penny 



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