Question

help with factoring this polynomial

Answer 1

\[x^{4} - 6x^{3} + 13x^{2} -24 x +36\]

Answer 2

i dont see a gcf and im a bit rusty with factoring... i can't group em, so what should i do?

Answer 3

explain please

Answer 4

by?

Answer 5

isn't usually the (x-c) form that i need to fully divide?

Answer 6

Yes, you should try divisors of the coefficient 36. For example, +3, so the division you could try is by x-3.

Answer 7

whatchu talking about?

Answer 8

why would i just use the constant? 36? how did you get 3 from 36?

Answer 9

i know synthetic division, just tell me whyyyyyy!?

Answer 10

By the Newton's formula it is known that the indepdent factor of the polinomy is the product of all the roots. You can also try the Ruffini decomposition.

Answer 11

im sorry mate, im in a trig/precal hybrid class, my knowledge of mathematical formals are limited.

Answer 12

There is a web page that can also helps you,

http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

Answer 13

awful, just awful.

Answer 14

The fact that you should try the factor x+3 is the following. In the easy way, suppose you have an order 2 polinomy,

\[(x-a)(x-b)\]
Expand the product,
\[(x-a)(x-b)=x^2-(a+b)x+a\cdot b\]
Then, you see that the factor that has no x, is the product of all the roots of your polinomy. So you always should try by divisors of this coefficient. In this case, for 36, you can try by: +1,-1,+2,-2,+3,-3, +4, -4, +9, -9, ...

Answer 15

nope. but thanks.

Answer 16

here's a medal for your effort, also you have my gratitude..

Answer 17

Anyway if you need it, the answer is the following,
\[(x-3)^2(x^2+4)\]
Hope it helps.