How to use synthetic division to find which value of k will guarantee that the given binomial is a factor of the polynomial. x^3-kx^2-6x+8;x+2?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

given `x^3-kx^2-6x+8` find `k` such that x+2 will be a factor:

We use synthetic division; if x+2 is a factor , x=-2 is a zero:

-2 | 1    -k     -6       8
     ------------------------
       1  -k-2   6k-2  -4k+12

So if -2 is a zero ( (x+2) a factor) then -4k+12=0 or k=3.

Thus the value we need is k=3

------------------------------------------------------

If k=3 we have:

`x^3-3x^2-6x+8=(x+2)(x-4)(x-1)` , verifying that x+2 is a factor.

 

 

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial