Home > Algebra > Factor Polynomials Using Special Products

How do you factor #w^3-3w^2-9w+27#?

Answer 1

#(w^3-3w^2-9w+27)=color(blue)((x-3)(x-3)(x+3))#

Writing #w^3-3w^2-9w+27# as #color(white)("XXX")w^3-3w^2-3^3w+3^3# makes it fairly clear that #color(white)("XXX")w=3# is a zero of this expression.

That is #(w-3)# is a factor of #(w^3-3w^2-9w+27)#

If we divided #(w^3-3w^2-9w+27)# by #(w-3)# (either by polynomial long division or synthetic division) we find #color(white)("XXX")(x^2-9)# is also a factor

...but #(x^2-9)=(x^2-3^2)=(x-3)(x+3)#

So a complete factoring is #color(white)("XXX")(w^3-3w^2-9w+27)=(x-3)(x-3)(x+3)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Nathan Axel

To factor the expression ( w^3 - 3w^2 - 9w + 27 ), you can use the factor theorem or synthetic division to find one root and then factor the expression further using polynomial long division or synthetic division. Once you have factored out one root, you can then use the quadratic formula or other methods to factor the remaining quadratic expression.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.