Question

Determine, if possible, if (x – 8) is a factor of (x3 – 3x2 – 31x – 72)

Answer 1

Hmmm I'd do synthetic division here.

you set it up as

n | coefficient of first, second, third,...so on|

where n is from x-n, a factor of my polynomial. I realize that's a bad explanation so I'll show it with this one

so, setting this up, I have x-8 as my potential factor, so n would equal 8.

8 |

now list the coefficients of all the terms in your polynomial.

8 | 1... -3.... -31.... -72 |

you drop down the first coefficient shown, and multiply it by n, and put that under the second coeffiecient, then add.

8 | 1 ...-3 ....-31 ....-72|
......1 ..+ 8 (1)

8 + -3 is 5, so multiply 5 by 8 and put that under the next coeffient, add, and so on.

8 | 1 ......-3..... -31..... -72|
......1 .....+ 8... +40 ...+72
...............5 ........9........ 0

if I get a remainder of 0, or a 0 after you've done everything (which we have) then whatever x-n you have IS a factor of your polynomial. so, x-8 is a fsctor. :) hope that helps!

EDIT: sorry about the periods haha. just trying to make it easier to see.