SOLUTION: 1. Describe the behavior of the graph at the x-intercepts for the function f(x)=(2x-7)^7(x+3)^4. Be sure to identify each x-intercept and justify your answer. 2. Use the Remaind

Question 1058365: 1. Describe the behavior of the graph at the x-intercepts for the function f(x)=(2x-7)^7(x+3)^4. Be sure to identify each x-intercept and justify your answer.
2. Use the Remainder Theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5-7x^3-11x^2+2.
3. Find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30. If you use synthetic division, show all three lines of numbers.
Thank you so much!!
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)=(2x-7)^7(x+3)^4
When y=0, (2x-7)^7=0 and x=3.5 OR
(x+3)^4=0, and x=-3
===================================
Look at x=h or f(2)
That is 96-56-44+2 and it is not equal to 0. (x-2) is not a factor.
===================================
x^3-5x^2+6x-30
after trying 1,2, and 3, I tried 5
5/1===-5===6===-30
==1===0====6====30
(x^2-6) with no remainder
the factors are (x-5)(x^2+6)
the zeroes are 5, +/- i sqrt (6). Only one real 0.

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