SOLUTION: 1. Use synthetic division to divide p(x) = x^4 - 10x^2 - 2x + 4 by x + 3 2. Let f(x) = 3x^3 + 8x^2 + 5x - 7. Use synthetic division to find f(-2) 3. Use synthetic division to

Algebra ->  Functions -> SOLUTION: 1. Use synthetic division to divide p(x) = x^4 - 10x^2 - 2x + 4 by x + 3 2. Let f(x) = 3x^3 + 8x^2 + 5x - 7. Use synthetic division to find f(-2) 3. Use synthetic division to      Log On


   

Question 1156575: 1. Use synthetic division to divide p(x) = x^4 - 10x^2 - 2x + 4 by x + 3
2. Let f(x) = 3x^3 + 8x^2 + 5x - 7. Use synthetic division to find f(-2)
3. Use synthetic division to factor f(x) = x^3 - 5x^2 - x + 5 completely. Then sketch the graph of f. [Hint: Guess an initial zero of f(x). Then apply synthetic division.]
4. Use synthetic division to perform the division.
(a) x^3 + 3x^2 + 11x + 9 by x + 1
(b) x^4 + 4x^3 + 2x^2 + 9x + 4 by x + 4

These are homework problems I need help with.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Too many exercises; just doing some of #3.

Choices to check as roots are -1, -5, 1, 5.
-1   |    1    -5    -1    5
     |         -1    6    -5
     |------------------------------
         1     -6    5    0

-1 found to be a root.


%28x%2B1%29%28x%5E2-6x%2B5%29

That quadratic factor is factorable into %28x-1%29%28x-5%29.

f%28x%29=%28x%2B1%29%28x-1%29%28x-5%29

The roots are -1, 1, and 5.
Degree is odd (three) and lead coefficient is positive, telling you something about shape - decreases without end to the left; increases to the right without end,...

graph%28400%2C400%2C-12%2C12%2C-16%2C8%2Cx%5E3-5x%5E2-x%2B5%29