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kkurt [141]
3 years ago
15

PLZ HELP ASAP! ILL MARK BRAINLEST!

Mathematics
2 answers:
zmey [24]3 years ago
8 0

Answer:

#2 is definatly B

Step-by-step explanation:

Sav [38]3 years ago
7 0

Question 1.) Factor completely 12x^{4}+ 6x^{3}+18x^{2}

Since 6 divides all the three terms of the equation, so we take 6 common out from the equation.

i.e., 6(2x^{4}+ 1x^{3}+3x^{2})

Now, since x^{2} divides all the three terms of the equation, so we take x^{2} common out from the equation.

i.e., 6x^{2}(2x^{2}+ 1x+3)

Now, this cannot be factored further as 2x^{2}+ 1x+3 is a quadratic equation and taking out discriminant of it is:

D = (1)^2 - 4(2)(3)\\  \ \   = 1- 24\\ \ \ = -23

Since, the discriminant is less than zero. Therefore, the factored form of the given equation :  12x^{4}+ 6x^{3}+18x^{2}  is : 6x^{2}(2x^{2}+ 1x+3)


Question 2.) 7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}

Since 7 divides all the three terms of the equation, so we take 7 common out from the equation.

i.e., 7(x^{3}y+ 2x^{2} y^{3} - x^{2}y^{2})

Now, since x^{2}y divides all the three terms of the equation, so we take x^{2}y common out from the equation.

i.e., 7x^{2}y(x+ 2y^{2} - y)

Therefore, the factored form of the given equation :  7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}  is : 7x^{2}y(x+ 2y^{2} - y)


Question 3.) What is the Greatest Common Factor of x^{6} and x^{3} ?

The Greatest Common Factor of two numbers is the biggest number which divides both the given numbers completely.

Now, for the expressions x^{6} and x^{3}:

Since, x^{3} divides both the expressions completely and it is the biggest expression which divides both the expressions.

Therefore, x^{3} is the Greatest Common Factor of x^{6} and x^{3}



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==============================================================

Work Shown:

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