7. Given f(x) = x 3 (x +
5)2( 2 x-7)
a) What is the degree of this polynomial?
b) List the real zero's of f. Give the multiplicity of each zero.
c) Does the graph off touch or cross the x-axis at each zero?
d) Determine the 'end behavior' of this function. Find the monomial power function that the graph off
resembles for very large positive or negative values of x.

a)  6.

b)  0 (multiplicity 3), -5 (multiplicity 2) and 7/2.

c) and (d) - See below.

Step-by-step explanation:

(a)  f(x) = x^3(x + 5)^2 (2x - 7)

The highest degree of x  (= x^3*x^2*x) = 3+2+1 = 6.  

(b) The zeros are 0 ( from the x^3 = 0) multiplicity 3, from  x + 5 = 0 we have -5 (multiplicity 2) and from 2x - 7 =0, 7/2.

(C)  The graph just touches the x axis at (-5, 0) and pass through at (0,0) and (7/2, 0).

(d) The graph rises to the left for very large negative values of x and falls to the right at very large values of x.

At the extreme ends this graph resembles the graph of -x^3.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?