Find real zeros of f. Use real zeros to factor f

Question

F(x)=x^3-3x^2-x+3

Answer 1

Your leading coefficient is 1, so we can use the factors of 3 as possible roots.  Possible roots are 3, -3, 1, -1.

 

(Remember:  if x = N, then N is a root.  (x-N) is a factor.)

 

Use synthetic division to find values where the remainder is 0.

 

Let's try x = 1

 

  1 |  1  -3  -1   3

             1  -2  -3     so x = 1 is a root

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        1  -2  -3   0   <===  this quotient gives us  x^2 - 2x - 3 = 0

 

for x^2 - 2x - 3  factors into (x - 3)(x + 1) = 0   

 

So x = 3 and x = -1

 

Therefore, the roots of the equation are x = -3, -1, and 1

 

The factors would be (x+3)(x + 1)(x - 1)

 

Ms. Gayle