Respuesta :

Answer:

option-A

(5)

Step-by-step explanation:

we are given

[tex]5x^3-135[/tex]

Firstly, we can factor out 5

[tex]5x^3-5\times 27[/tex]

[tex]5(x^3-27)[/tex]

[tex]5(x^3-3^3)[/tex]

now, we can use formula of factor

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

we can compare

a=x , b=3

now, we can plug this into formula

[tex]5(x^3-3^3)=5(x-3)(x^2+3\times x+3^2)[/tex]

[tex]5(x^3-3^3)=5(x-3)(x^2+3x+9)[/tex]

so, we get

[tex]5x^3-135=5(x-3)(x^2+3x+9)[/tex]

so, only factor 5 matches

alinakincsem

Answer:

The correct answer option is A) 5.

Explanation:

We are given the following expression and we are to factorize it:

[tex]5x^3-135[/tex]

If we take the common term out of this, then we are left with:

[tex]5(x^3-27)[/tex]

Now the term [tex](x^3-27)[/tex] can also be written in the form of [tex]x^3-y^3[/tex] as:

[tex]x^3-3^3[/tex]

Next, we will factorize it applying the difference of cubes formula [tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex] to get:

[tex]x^3-3^2= \left(x-3\right)\left(x^2+3x+3^2\right)[/tex]

[tex]=\left(x-3\right)\left(x^2+3x+3^2\right)[/tex]

[tex]=\left(x-3\right)\left(x^2+3x+9\right)[/tex]

Adding the common term back to it to get:

[tex]5\left(x-3\right)\left(x^2+3x+9\right)[/tex]

Therefore, from the given answer options we can see that the option A) 5 is the factor of the given expression 5x^3 - 135.

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