How do you write the following polynomial as a product of its factors?

Question

#x^3+27#

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Answer 1 · 2018-03-26T12:11:42

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

We can write:

#27=3^3#

#:.#

#x^3-3^3#

This is the difference of two cubes. This can be expressed as:

#(a^3-b^3)=(a+b)(a^2-ab+b^2)#

#:.#

#(x^3+3^3)=(x+3)(x^2-(x)(3)+3^2)#

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

We can not factor #(x^2-3x+9)# further:

These are common identities and should be memorised.

#(a^3-b^3)=(a+b)(a^2-ab+b^2)#

#(a^3+b^3)=(a-b)(a^2+ab+b^2)#

#(a^2-b^2)=(a+b)(a-b)#