Divide the binomial by the monomial to find the quotient -36x^4y + 144x^2 y^6/ -4x^2y

The way that you would do this is by taking [tex] -4x^{2} [/tex] out of the binomial, or as I like to think about it, 'un-distributing'. :p
[tex] -4x^{2} [/tex] out of [tex] -36x^{2}y [/tex], you end up with [tex] 12x^{2} [/tex].
When you take [tex] -4x^{2} [/tex] out of [tex] 144x^{2}y{6} [/tex], you get [tex] -36y^{5} [/tex].
Put it together, and the solution is [tex] 12x^{2} [/tex] - [tex] 36y^{5} [/tex].

Hope I helped!!

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lidaralbany lidaralbany · Answer 2 · 2019-06-25T10:56:32+02:00

Answer:

The quotient is:

[tex]9x^2-36y^5[/tex]

Step-by-step explanation:

We are asked to find the quotient when a binomial is divided by the monomial.

The expression is as follows:

[tex]\dfrac{-36x^4y+144x^2y^6}{-4x^2y}[/tex]

on taking out the common factors from the numerator term of the expression we get:

[tex]-36x^4y+144x^2y^6=36x^2y(-x^2+4y^5)[/tex]

Hence, we get:

[tex]\dfrac{-36x^4y+144x^2y^6}{-4x^2y}=\dfrac{36x^2y(-x^2+4y^5)}{-4x^2y}\\\\\\\dfrac{-36x^4y+144x^2y^6}{-4x^2y}=-9(-x^2+4y^5)\\\\\\i.e.\\\\\\\dfrac{-36x^4y+144x^2y^6}{-4x^2y}=9(x^2-4y^5)[/tex]

Hence, the quotient is:

[tex]9x^2-36y^5[/tex]