Which of the following is the correct factorization of the polynomial below? x^3-12

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

Step-by-step explanation:

Question is incomplete (options are missing);

However, I'll factorize the polynomial using identity

Given

x³ - 12

This can be factorized using the following identity

a³ - b³ = (a - b)(a² + ab + b²)

By comparison,

a³ = x³ and b³ = 12

a = x and b = ∛12

Replace a with x and b with ∛12 in the above equation

a³ - b³ = (a - b)(a² + ab + b²) becomes

x³ - 12 = (x - ∛12)(x² + x∛12 + ∛12²)

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

This is as far as it can be factorized

So, the factorization of x³ - 12 using identity is (x - ∛12)(x² + x∛12 + 12²/³)

the answer to this question is yes

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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