SOLUTION: I need help asap with the following much appreciated. Find all the zeros of the polynomial function by graphing on the calculator to narrow down the real solutions, then use synth

Question 1172358: I need help asap with the following much appreciated.
Find all the zeros of the polynomial function by graphing on the calculator to narrow down the real solutions, then use synthetic division until you get a quadratic to solve. Solve the quadratic equation to complete the list of zeros.
7. h(x) = x^3 − 3x^2 − x + 3
8. f(x) = x^4 − 4x^3 − 20x^2 + 48x
9. g(x) = x^3 + 5x^2 + x + 5

10. g(x) = x^4 − 9x^3 + 23x^2 − 81x + 126

Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find all the zeros of the polynomial function by graphing on the calculator to narrow down the real solutions, then use synthetic division until you get a quadratic to solve. Solve the quadratic equation to complete the list of zeros.
7. h(x) = x^3 − 3x^2 − x + 3
8. f(x) = x^4 − 4x^3 − 20x^2 + 48x
9. g(x) = x^3 + 5x^2 + x + 5

10. g(x) = x^4 − 9x^3 + 23x^2 − 81x + 126
====================================
Do you have a graphing calculator?
If so, do that.
If not, DL the FREE graphing software at
www.padowan.dk

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x^3-3x^2-x+3=h(x)
x^2(x-3)-(x-3)=h(x)
=(x^2-1)(x-3)=(x+1)(x-1)(x-3)
zeros are -1, 1, 3

-
factor out an x
x(x^3-4x^2-20x+48)
2 is a root.
1--- -2---- -24----0
(x^2-2x-24)(x-2)(x)
factors are (x-6)(x+4)(x-2)*(x)
roots are -4,0,2,6

-
factor by grouping into (x^3+5x^2)+(x+5)
(x^2+1)(x+5) with only zero at x= -5.

-
graph

roots are 2 and 7
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