Question

find the polynomial f of x is equal to X ^ 4 + 2 x cube _13 x square - 14 x + 24​

Answer 1

Step-by-step explanation:

Let f(x)=x4−2x3−13x2+14x+24

By the rational root theorem, any rational roots of f(x)=0 must be of the form pq for some integers p and q with p as factor of the constant term 24 and q a factor of the coefficient 1 of the leading term.

That means that the only possible rational zeros are:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Try the first few in turn:

f(1)=1−2−13+14+24=24

f(−1)=1+2−13−14+24=0

f(2)=16−16−52+28+24=0

So x=−1 and x=2 are zeros and (x+1) and (x−2) are factors:

x4−2x3−13x2+14x+24