1. ## help polynomial

given that (x^2-2x+3)(x^2+Kx-2) = x^4-15x^3+qx^2+px-6
find the values of K, p and q

iv tried n jst keep gettin lost
thx

2. Originally Posted by kls7162
given that (x^2-2x+3)(x^2+Kx-2) = x^4-15x^3+qx^2+px-6
find the values of K, p and q

iv tried n jst keep gettin lost
thx
Hello,

1. expand the brackets at the LHS of your equation.
2. collect like terms

You'll get:

$(x^2-2x+3)(x^2+Kx-2) = x^4+x^3(k-2)+x^2(1-2k)+x(3k+4)-6$

Now compare this result with the coefficients at the RHS of the given equation:

$\begin{array}{l}k-2=-15\\1-2k=q \\ 3k+4=p\end{array}$ This is a system of 3 linear equations which could be solved for k, p, q.

(For confirmation only: I've got k = -13, q = 27, p = -35) but you'd better check my calculations!