Factor trinomial w^3-3w^2-54w Everything I have tried doesn't work on the check...?

w^3-3w^2-54w
=w(w^2-3w-54)
=w(w+6)(w-9) answer @(^_^)@

w³ - 3w² - 54w = 0
w(w² - 3w - 54) = 0

w² - 3w = 54
w² - 3/2w = 54 + (- 3/2)
w² - 3/2w = 216/4 + 9/4
(w - 3/2)² = 225/4
w - 3/2 = 15/2

Factors:
= w - 3/2 - 15/2; = w - 18/2; = w - 9
= w - 3/2 + 15/2; w + 12/2; = w + 6

Answer: w(w - 9)(w + 6) are the factors.

Proof (F.O.I.L.):
= w(w - 9)(w + 6)
= w(w² + 6w - 9w - 54)
= w(w² - 3w - 54)
= w³ - 3w² - 54w

w^3 - 3w^2 - 54w
= w(w^2 - 3w - 54)
= w(w^2 + 6w - 9w - 54)
= w[(w^2 + 6w) - (9w + 54)]
= w[w(w + 6) - 9(w + 6)]
= w(w + 6)(w - 9)

w³ - 3w² - 54w =

Look at each term's factors.
w³ = w * w * w
-3w² = -1 * 3 * w * w
-54w = -1 * 2 * 3 * 3 * 3 * w

The LCD is w, so factor that out.
w³ - 3w² - 54w =
w(w² - 3w - 54) =

Replace the polynomial with 2 sets of parentheses.
w(_______)(_______) =

Look at the first term's factors.
w² = w * w

Write w at the beginning of each set of parentheses.
w(w_______)(w_______) =

Look at the last term's factors. You want the pair that will add up to the middle term -3w when multiplied by the 2 w's you already have.
1 * -54 ===> (1w * 1) + (1w * -54) = 1w + -54w = -53w <=== wrong pair
2 * -27 ===> (1w * 2) + (1w * -27) = 2w + -27w = -25w <=== wrong pair
3 * -18 ===> (1w * 3) + (1w * -18) = 3w + -18w = -15w <=== wrong pair
6 * -9 ===> (1w * 6) + (1w * -9) = 6w + -9w = -3w <=== right pair
9 * -6 ===> (1w * 9) + (1w * -6) = 9w + -6w = 3w <=== wrong pair
18 * -3 ===> (1w * 18) + (1w * -3) = 18w + -3w = 15w <=== wrong pair
27 * -2 ===> (1w * 27) + (1w * -2) = 27w + -2w = 25w <=== wrong pair
54 * -1 ===> (1w * 54) + (1w * -1) = 54w + -1w = 53w <=== wrong pair

6 * -9 is the right pair.

Write + 6 and - 9 in the remaining blanks.
w(w + 6)(w - 9)

ANSWER: w(w + 6)(w - 9)

ok your answer to factoring the trinomial w^3-3w^2-54w is:

w[(w+6)(w-9)]

CHECK:

w[w^2-9w+6w-54]

w[w^2-3w-54] then you multiply the w through

w^3-3w^2-54w this is your original answer so the check proves that the top answer is correct!

Hope I helped!!

An obvious factor is w. Divide out w and you have a quadratic. Use the quadratic solution formula or factor on sight
(w - 9)(w + 6)

w(w^2-3w-54)
w(w-9)(w+6)

Always take out the common factor first, if there is one:

w(w^2 -3w - 54) is the result. Then factor more, if possible:

w(w-9)(w+6)

(w+6)(w-9)(w)

Take out a w and use quadratic eqn.