Question

use factor theorem,factorise the polynomial, x⁴ + 2 x³ -13 x² -14 x+24

Answer 1

this is the answer to your question. i hope it may be helpful.

Answer 2

Answer:

(x+1) (x-2) (x-4) (x+3)

Step-by-step explanation:

Use the rational root theorem to help find the first two factors, then divide and factor the remaining quadratic to find:

y=x4−2x3−13x2+14x+24

=(x+1)(x−2)(x−4)(x+3)

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

=(x+1)(x3−3x2−10x+24)

=(x+1)(x−2)(x2−x−12)

To factor the remaining quadratic, find a pair of factors of 12 that differ by 1. The pair 4,3 works, hence we find:

=(x+1)(x−2)(x−4)(x+3)

Hope it helps you friend :)