Question

How do I factor this HUGE polynomial? Gotta be an easy way to do that right? 6x^5 + 11x^4 – 59^x3 – 6x^2 + 80x – 32

Answer 1

have you heard of the remainder theorem and the factor theorem?

Answer 2

Yeah I have heard of the remainder theorem.

Answer 3

do you know how to apply it here?

Answer 4

The remainder theorem is when you plug in the opposite of what you are dividing by into x right? So if I was dividing by x+2 I would plug in -2 for x to find the remainder. I don't know how to apply that here because I'm not dividing anything.

Answer 5

No, but you ARE factorising. Which is basically dividing the expression into its factors

Answer 6

which in comes the FACTOR THEOREM. if you plug in -2 into the equation and get 0, then (x+2) is a factor.

Answer 7

that means you need to use either long division or synthetic division to find out the quotient of the equation after you have divided it by (x+2)

Answer 8

So I should just plug in random numbers till I get 0?

Answer 9

not just random numbers, factors of -32 because if (x-a) is a factor of P(x), then a must be a FACTOR of the term independent of x, which is -32.

Answer 10

you'll need to repeat this process until you get 5 brackets, because it is a polynomial of degree 5.

Answer 11

1,2,4,8 and 32 then.
And I do this for the first coefficient as well?
1,2,3,6

Answer 12

no, just the end coefficient. You also forgot 16, as well as the negative counterparts.
when you get down to the last two brackets you should be able to factorise the 6 from the 1st coeff.