SOLUTION: Please help me to solve those problems. I would really appreciate any help.Thanks! 1)There is a polynomial which, when multiplied by x^2+2x+3, gives 2x^5+3x^4+8x^3+8x^2+18x+9. Wha

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: Please help me to solve those problems. I would really appreciate any help.Thanks! 1)There is a polynomial which, when multiplied by x^2+2x+3, gives 2x^5+3x^4+8x^3+8x^2+18x+9. Wha      Log On

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Question 477248: Please help me to solve those problems. I would really appreciate any help.Thanks!
1)There is a polynomial which, when multiplied by x^2+2x+3, gives 2x^5+3x^4+8x^3+8x^2+18x+9. What is that polynomial?
2)What are the coordinates of the points where the graphs of f(x) = x^3-x^2 + x + 1 and g(x) = x^3 + x^2 + x-1 intersect?
3)The polynomial f(x) has degree 2. If f(0) =-21, f(1) = -16, and f(2) = -9, then what are the x-intercepts of the graph of f?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1) Carry out long division of polynomial.

2) Let x%5E3+-+x%5E2+%2B+x+%2B+1+=+x%5E3+%2B+x%5E2+%2B+x+-+1
==> 2x%5E2+=+2 ==> x%5E2+=+1 ==> x = -1, 1
When x = -1, f(-1) = g(-1) = -2
When x = 1, f(1) = g(1) = 2
==> points of intersection are (-1,-2) and (1,2).
3) let f%28x%29+=+ax%5E2+%2B+bx+%2B+c.
f(0) = -21 ==> c = -21.
f(1) = -16 ==> a + b - 21 = -16 ==> a+b = 5
f(-1) = -9 ==> 4a + 2b - 21 = -9 ==> 4a + 2b = 12 <==> 2a + b = 6.
Subtract the top equation from the bottom equation, to get a = 1
==> b = 4.
==> f%28x%29+=+x%5E2+%2B+4x+-21+=+%28x%2B7%29%28x-3%29.
==> x-intercepts are (-7, 0) and (3,0).