How do you use the factor theorem to determine whether x-2 is a factor of #P(x)=2x^3 -7x^2 + 7x - 2#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Alan P.
Dec 10, 2015

Since #P(2)=0#
#color(white)("XXX")(x-2)# is a factor of #P(x)#

Explanation:

The Factor Theorem tells us that
#color(white)("XXX")(x-a)# is a factor of #P(x)# if and only if #P(a)=0#

Given
#color(white)("XXX")P(x)=2x^3-7x^2+7x-2#

then
#color(white)("XXX")P(2)= 2(2^3)-7(2^2)+7(2)-2#

#color(white)("XXX")=2(8)-7(4)+7(2)-2#

#color(white)("XXX")=16-28+14-2#

#color(white)("XXX")=0#

So #(x-2)# is a factor of #P(x)=2x^3-7x^2+7x-2#

Related questions
See all questions in Remainder and Factor Theorems
Impact of this question
2421 views around the world
You can reuse this answer
Creative Commons License