Question 1.) Factor completely
Since
divides all the three terms of the equation, so we take
common out from the equation.
i.e., ![6(2x^{4}+ 1x^{3}+3x^{2})](https://tex.z-dn.net/?f=6%282x%5E%7B4%7D%2B%201x%5E%7B3%7D%2B3x%5E%7B2%7D%29)
Now, since
divides all the three terms of the equation, so we take
common out from the equation.
i.e., ![6x^{2}(2x^{2}+ 1x+3)](https://tex.z-dn.net/?f=6x%5E%7B2%7D%282x%5E%7B2%7D%2B%201x%2B3%29)
Now, this cannot be factored further as
is a quadratic equation and taking out discriminant of it is:
![D = (1)^2 - 4(2)(3)\\ \ \ = 1- 24\\ \ \ = -23](https://tex.z-dn.net/?f=D%20%3D%20%281%29%5E2%20-%204%282%29%283%29%5C%5C%20%20%5C%20%5C%20%20%20%3D%201-%2024%5C%5C%20%5C%20%5C%20%3D%20-23%3C0)
Since, the discriminant is less than zero. Therefore, the factored form of the given equation :
is : ![6x^{2}(2x^{2}+ 1x+3)](https://tex.z-dn.net/?f=6x%5E%7B2%7D%282x%5E%7B2%7D%2B%201x%2B3%29)
Question 2.) ![7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}](https://tex.z-dn.net/?f=7x%5E%7B3%7Dy%2B%2014x%5E%7B2%7D%20y%5E%7B3%7D%20-%207x%5E%7B2%7Dy%5E%7B2%7D)
Since
divides all the three terms of the equation, so we take
common out from the equation.
i.e., ![7(x^{3}y+ 2x^{2} y^{3} - x^{2}y^{2})](https://tex.z-dn.net/?f=7%28x%5E%7B3%7Dy%2B%202x%5E%7B2%7D%20y%5E%7B3%7D%20-%20x%5E%7B2%7Dy%5E%7B2%7D%29)
Now, since
divides all the three terms of the equation, so we take
common out from the equation.
i.e., ![7x^{2}y(x+ 2y^{2} - y)](https://tex.z-dn.net/?f=7x%5E%7B2%7Dy%28x%2B%202y%5E%7B2%7D%20-%20y%29)
Therefore, the factored form of the given equation :
is : ![7x^{2}y(x+ 2y^{2} - y)](https://tex.z-dn.net/?f=7x%5E%7B2%7Dy%28x%2B%202y%5E%7B2%7D%20-%20y%29)
Question 3.) What is the Greatest Common Factor of
and
?
The Greatest Common Factor of two numbers is the biggest number which divides both the given numbers completely.
Now, for the expressions
and
:
Since,
divides both the expressions completely and it is the biggest expression which divides both the expressions.
Therefore,
is the Greatest Common Factor of
and ![x^{3}](https://tex.z-dn.net/?f=x%5E%7B3%7D)