SOLUTION: Please help I really need to know the method for this one,but not using long division..Thank you so much: P(x)=9x^3+12x^2+hx+k. When you divide by 3x-1, 2=remainder. When you di

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help I really need to know the method for this one,but not using long division..Thank you so much: P(x)=9x^3+12x^2+hx+k. When you divide by 3x-1, 2=remainder. When you di      Log On


   

Question 1049759: Please help I really need to know the method for this one,but not using long division..Thank you so much:
P(x)=9x^3+12x^2+hx+k. When you divide by 3x-1, 2=remainder. When you divide by x+2, -5= remainder. Find h and k.
Please help,thank you!!
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
P(x)=9x^3+12x^2+hx+k. at x=1/3

2=9(1/3)^3+12(1/3)^2+h(1/3)+k.
2=9(1/27)+12(1/9)+h(1/3)+k.
2=(1/3)+(4/3)+(h/3)+k.
6=(1)+(4)+(h)+3k.
1=h%2B3k
at x=-2
-5=9(-2)^3+12(-2)^2+h(-2)+k.
-5=-72+12(4)-2h+k.
-5=-72+(48)-2h+k.
-5=(-24)-2h+k.
19=-2h%2Bk
solve
1=h%2B3k
19=-2h%2Bk
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Ch+%2B+3%5Ck+=+1%2C%0D%0A++++-2%5Ch+%2B+1%5Ck+=+19+%29%0D%0A++We'll use substitution. After moving 3*k to the right, we get:
1%2Ah+=+1+-+3%2Ak, or h+=+1%2F1+-+3%2Ak%2F1. Substitute that
into another equation:
-2%2A%281%2F1+-+3%2Ak%2F1%29+%2B+1%5Ck+=+19 and simplify: So, we know that k=3. Since h+=+1%2F1+-+3%2Ak%2F1, h=-8.

Answer: system%28+h=-8%2C+k=3+%29.