本题目来源于试卷: Properties of Functions，类别为 IB数学
[问答题]
It is given that $f(x)=2 x^{4}+5 x^{3}+a x^{2}+b x+4$ , for x $\in \mathbb{R}$ , where a, b $\in \mathbb{Z}^{+}$ .
1. Given that $x^{2}+x-2$ is a factor of f(x) , find the values of a and b .
2. Factorise f(x) into a product of linear factors.
3. Sketch the graph of y=f(x) , labeling the maximum and minimum points and the x and y intercepts.
4. Using your graph, state the range of values of c for which f(x)=c has exactly four distinct real roots.
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