SOLUTION: find the value of p and q when the polynomial (x*x*x)+ p(x*x)+ qx + 6 gives remainder 3 when divided by x-3 and leaves the remainder 0 when divided by x-2.

SOLUTION: find the value of p and q when the polynomial (xxx)+ p(x*x)+ qx + 6 gives remainder 3 when divided by x-3 and leaves the remainder 0 when divided by x-2.

Question 450013: find the value of p and q when the polynomial (x*x*x)+ p(x*x)+ qx + 6 gives remainder 3 when divided by x-3 and leaves the remainder 0 when divided by x-2.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the value of p and q when the polynomial (x*x*x)+ p(x*x)+ qx + 6 gives remainder 3 when divided by x-3 and leaves the remainder 0 when divided by x-2.
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Polynomial x^3 + px^2 + qx + 6
-----
Using synthetic division:
3)....1....p......q.......6
.......1....p+3..3(p+3)+q..|9(p+3)+3q +6
----
Equation:
9p + 3q + 33 = 3
3p + q = -10
========================
2)....1....p.......q........6
.......1...p+2..2(p+2)+q...|4(p+2)+2q+6
------
Equation:
4p+2q = -14
2p+q = -7
=====================
Solve the system:
3p+q = -10
2p+q = -7
Subtract to get:
p = -3
---
Solve for "q":
2p+q = -7
2*-3 + q = -7
-6 + q = -7
q = -1
====================
Cheers,
Stan H.
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