Remainder Theorem

[jshaziza]

In an example in my book, they tell me given the polynomial 2x^3-5x^2-3x+11, find the value o the polynomial if x=-2.
Than it tells me we can find the value when x=-2 by dividing the polynomial by x-(-2)=x+2.
Now my problem is when they use synthetic division they tell me the value of x is -2. So does the x=-2 change twice first to x+2 and then when using synthetic division changing again to -2 or did they make a mistake? Thx to anyone who explains it.

 

[arthur ohlsten]

y=2x^3 - 5x^2 -3x +11
let x=-2
y=2[-8] -5[4]-3[-2]+11
y=-16-20+6+11
y=-19 answer

let x=-2 then
x+2=0

divide [2x^3-5x^2-3x+11]/[x+2]
I can't do the math here because on transmission everything gets moved to the left

.............2x^2 - 9x +15
.............__________________
......x+2.l2x^3-5x^2-3x+11
.............2x^3+4x^2
.............---------------
......................-9x^2 -3x +11
......................-9x^2-18x
......................------------------
................................15x + 11
................................15x + 30
................................-----------
.......................................-19 remainder

you can repeat the division by synthetic division

Arthur