A calculus of the absurd
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4.3.4 Comparing coefficients
Would you like to know why this section went here? (I’m sure you wouldn’t, but I shall provide some context anyway). It goes here because it is useful for solving lots of problems that will occur later.
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Example 4.3.3 Let us suppose that we have these two polynomials
\(\seteqnumber{0}{4.}{23}\)\begin{align} & f(x) = ax^3 + bx^2 + cx + d, \\ & p(x) = 4x^3 + 3x^2 + 2x + 8. \end{align}
And we know that \(f(x) = p(x)\). How would you find \(a, b, c\) and \(d\)?
This is not the hardest problem in the metaphorical book (far from it), but it’s also not a bad place to start. Intuitively we know that \(a = 4, b = 3, c = 2\) and \(d = 8\).
The general principle here is that two polynomial functions are equal if and only if their coefficients are equal. In non-mathematics speak, this means that we look at the values in front of the numbers and check if they are the same.
TODO: some examples