SOLUTION: a) Find all zeros of the polynomial algebraically {{{ P(x)=18x^4-21x^3-81x^2+84x+36 }}}. b) Then write the polynomial in factored form. c) Sketch the graph of P(x) showing all re

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Question 1155519: a) Find all zeros of the polynomial algebraically .
b) Then write the polynomial in factored form.
c) Sketch the graph of P(x) showing all real zeros, y-intercept, and end behavior.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
a) Find all zeros of the polynomial algebraically

b) Then write the polynomial in factored form.














zeros:
if =>
if =>
if =>
if =>



c) Sketch the graph of P(x) showing all real zeros, y-intercept, and end behavior.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
a) Find all zeros of the polynomial algebraically .
b) Then write the polynomial in factored form.
c) Sketch the graph of P(x) showing all real zeros, y-intercept, and end behavior. 


Using the RATIONAL ROOT THEOREM, we find 2 of the zeroes of the function to be: - 2 and 2, thereby leading to factors: 

Now, using the divisor:  and LONG-DIVISION of POLYNOMIALS, we find the QUOTIENT of  to be: , which can be factored as: .

This gives us: (3x + 1)(2x - 3) = 0

3x + 1 = 0            or            2x - 3 = 0

3x = - 1              or            2x = 3



Therefore, zeroes of 

We ALSO see that the factors of:  

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