Question

Find the remainder when f(x) is divided by (x - k)

f(x) = 4x3 - 6x2 + 3x + 1; k= -2

Answer 1

this is simply a case of using the remainder theorem

so find

f(k)

which becomes

f(-2) by substituting -2 for x

Answer 2

Thanks!! do you know how to use the rational zeros therom to answer this though Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = -2x4 + 4x3 + 3x2 + 18

Answer 3

find all the factors of the constant 18 call them p

find all the factors of the coefficient of the leading term -2 call them q

then the rational roots come from p/q

so \[18: \pm1, \pm2, \pm3, \pm6, \pm9, \pm18\]

and

\[-2: \pm 1, \pm2\]

so the rational roots are any combination such as 18/-1 9/-2, -3/2 etc