36x^2-9x^3-x^4?

Question

please show step by step

Answer 1

Factor the expression... 36x^2-9x^3-x^4

*The expression has to be written in alpha descending order.

- x^4 - 9x^3 + 36x^2

First: the first coefficient has to be positive... factor out (-1).

- 1 (x^4 + 9x^3 - 36x^2)

Sec: find the Least Common Factor which is, x^2.

- 1*x^2 (x^2 + 9x - 36)
-x^2 (x^2 +9x -36)

Third: factor the expression - multiply the 1st & 3rd term to get -36. find two numbers that give you -36 when multiplied & 9 (2nd term) when added/subtracted. the numbers are
(-3 & 12). rewrite the expression with the new middle terms.

x^2 -3x +12x - 36

*Group "like" terms & factor both sets of parenthesis.

(x^2 - 3x) + (12x - 36)
x(x - 3) + 12(x - 3)
(x - 3)(x + 12) or, (x+12)(x-3)

and the final result includes the Least Common factor (-x^2).

-x^2(x-3)(x+12) or, -x^2(x+12)(x-3)

Answer 2

Assuming you want that factored:

First, factor out -x^2. x^2 since all the terms have a degree of x two or greater, and negative since the highest degree of x (-x^4) is negative:

-x^2 (x^2 + 9x - 36)

Now factor the remainder. What two numbers have a difference of +9, and when multiplied yield -36? The answer is 12 and -3:

-x^2 (x - 3)(x + 12)

Assuming you wanted it factored, that's it.