How do you use the remainder theorem to find the remainder for the division #(2x^3-3x^2-10x+3)div(x-3)#?

1 Answer
EZ as pi
Sep 2, 2016

Evaluate #f(3)# The answer is the remainder.

In this case there is no remainder which means that (x-3) is a factor.

Explanation:

#(2x^3-3x^2-10x+3)divcolor(red)((x-3))#

#rarr "make " color(red)(x-3 =0, rarr x=3)#

#"Let " f(x) =2x^3-3x^2-10x+3#

#f(color(red)(3)) # will give the remainder.

#f(3) = 2(3)^3-3(3)^2-10(3)+3#

# color(white)(xxxx)=54-27-30+3#

# color(white)(xxxx) = 0 " "larr " this is the remainder"#

There is no remainder.

This means that #(x-3) " is a factor of " 2x^3-3x^2-10x+3#

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