Question

Divide x^3-3x^2-10x+24 by x-2

Answer 1

Answer:

Step-by-step explanation:

K 1-3-10 24

K=2

A=1

Answer 2

You can do this using synthetic division, which is the easiest way.  If x - 2 = 0, then x = 2.  That 2 will go outside the "box" and the leading coefficients of the terms in the polynomial will go inside the "box".  2    (1   -3    -10    24).  Bring down the first number, the 1.  Multiply that 1 by the 2 to get 2.  Put that 2 up under the -3 and add to get -1.  Multiply that -1 by the 2 to get -2.  Put that =-2 up under the -10 and add to get -12.  Multiply that -12 by the 2 to get -24.  Put the -24 up under the 24 and add to get 0.  That means that x - 2 is a factor of the polynomial.  What's left, the bolded numbers, are the coefficients of a new polynomial that is one degree less than the polynomial you started with.  In other words, when we divide your polynomial by x-2, you get $x^2-x-12$.