If P(x)=2x^3-3x^2-5x+6P(x)=2x3−3x2−5x+6 is divided by x-2x−2, then (1) what is the remainder; (2) what is the quotient and (3) how we can express P(x)P(x) in terms of factors?
2 Answers
See below.
Explanation:
I think some sign or coefficient are not well fitted because
assuming
Identifying coefficients,
Solving for
Solving now
Concerning
we know that
or
r=0 ,P(x)=2x^3-3x^2-5x+6 q(x)=(2x+3)(x-1) P(x)=(2x+3)(x-1)(x-2)
Explanation:
Using remainder theorem
and therefore
=16-12-10+6=0 and
or
=2x^3-3x^2-5x+6
=2x^2(x-2)+x(x-2)-3(x-2)
=(2x^2+x-3)(x-2)
=(2x^2+3x-2x-3)(x-2)
=(x(2x+3)-1(2x+3))(x-2)
=(2x+3)(x-1)(x-2)
and