What is the greatest common monomial factor of this polynomial? 21x4y5z+28x2y4z4 Enter your answer in the box.

Mathematics

1 answer:

jasenka [17]2 years ago

3 0

Answer:

$\boxed{7x^2y^4z}$

Step-by-step explanation:

The greatest common factor of 21=7·3 and 28=7·4 is 7.

The greatest common factor of x^4 and x^2 is x^2 (the term with the smallest exponent).

The greatest common factor of y^5 and y^4 is y^4.

The greatest common factor of z and z^4 is z.

21x^4·y^5·z+28x^2·y^4·z^4 = 7x^2·y^4·z·(3x^2·y + 4z^3)

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Find the following integral. <br> Integrate x + 5/x^2 +10x +26 dx

sweet-ann [11.9K]

Given :

Polynomial , $f(x)=x+\dfrac{5}{x^2}+10x+26$ .

To Find :

Integration of f(x) .

Solution :

We know , integration of $x^n$ is :

$\int x^n \, dx = \dfrac{x^{n+1}}{n+1}+C$

( Here , is C is a constant )

Now ,

$\int f(x)\ dx=\int( x+\dfrac{5}{x^2}+10x+26)dx\\ \\ \int f(x)\ dx= \int x\ dx+\int 5x^{-2}\ dx+\int 10 x \ dx +26\ dx\\ \\ \int f(x)\ dx=\dfrac{x^2}{2}+\dfrac{5\times x^{-1}}{(-1)}+\dfrac{10x^2}{2}+26x+C\\\\ \int f(x)\ dx=\dfrac{11x^2}{2}+26x-5x^{-1}+C$