# How do you use synthetic substitution to find x=1 for #P(x)=4x^3-5x^2+3#?

##### 1 Answer

#### Explanation:

The remainder of the synthetic substitution will be equal to

The terms in the top row of the division will be the coefficients of the terms. Don't forget the missing

#{:(ul1"|",4,-5," 0"," 3"," "),(" ",ul" ",ul(" "color(red)4),ulcolor(blue)(-1),ulcolor(green)(-1),+),(" ",color(red)4,color(blue)(-1),color(green)(-1),"|"mathbf(" 2")," "):}#

The following is an explanation of the synthetic division:

Bring the original

Since the remainder is

This also shows us that

#(4x^3-5x^2+3)/(x-1)=4x^2-x-1+2/(x-1)#