question #13

Question

Determine whether the given number is a zero of the polynomial function following it. 

-2, w(x)=3x^3+5x^2-5x-6

Is -2 a zero of the polynomial functions, w(x)=3x^3+5x^2-5x-6?

_ No

_ Yes 

 

help is greatly appreciated, thank you!

Answer 1

Hi Laura,

 

when we substitute value x= -2 in poynomial function,

 

w(-2) = 3(-2)³ + 5(-2)² -5(-2) -6

         =-24+20+10-6

         =0

 

-2 is a zero of the polynomial function w(x).

Answer 2

Divide the coefficients of w(x) by the root (synthetic division).  The remainder if the division must be zero. 

 

 

-2  |  3      5      -5      -6

 

               -6       2       6

    _____________________

        

         3    -1      -3       0

 

 

Since the last number under the line in synthetic division is zero, -2 is a root of w(x).

 

w(x) in factored form is then

 

(x + 2)(3x² - x - 3)