<p>Given that&nbsp;\( P(x) = x^4 - 4x^3 + ax^2 + bx + 12\) leaves the same remainder when divided by \(x - 1\) and \(x + 2\).<br>It is also given that&nbsp;\(x - 3\) is a factor of \(P (x) \).<br>Find the values of \(a\) and \(b\)</p>

Given that \( P(x) = x^4 - 4x^3 + ax^2 + bx + 12\) leaves the same remainder when divided by \(x - 1\) and \(x + 2\).
It is also given that \(x - 3\) is a factor of \(P (x) \).
Find the values of \(a\) and \(b\)

Polynomials, Cubic Equations and Partial Fractions

Polynomials, Cubic Equations and Partial Fractions