GCF, LCM, and a polynomial?

Question

Find (A) the GCF and (B) the LCM of the following monomials.
1) 28, 35, 42
2) 9x^2y and 36xy^3

Solve the following equation.
x(x-2)(x+3)=0

MERCI BEAUCOUP!

Answer 1

1)

A) 7
B) 420

2)

A) 9xy
B) 36x²y^3

For the equation:

x = 0 or x = 2 or x = -3

Answer 2

28 = 2*2*7
35 = 5*7
42 = 2*3*7

The only common one is 7, therefore the greatest common factor is 7.
The lowest number that can be divided by any of the three must contain enough prime factors to cover all three:

It needs two 2's, one 3, one 5 and one 7.
LCM = 2*2*3*5*7 = 420

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9x^2y = 3*3*x*x*y
36xy^3 = 2*2*3*3*x*y*y*y
GCF = 3*3*x*y = 9xy
LCM = 2*2*3*3*x*x*y*y*y = 36(x^2)(y^3)

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x(x-2)(x+3)=0
If any one of the factors is zero, then the product is 0.
x=0
0(x-2)(x+3) = 0(-2)(3) = 0
or
(x-2)=0
(-2)(0)(1) = 0
or
(x+3)=0
(3)(1)(0) = 0

Answer 3

1) GCF: 7 LCM: 420

2) GCF: 9xy LCM: 36x^2*y^3 ; I added (*) (which means to multiply) so you wouldn't mistake it as 36x to the power 2y

To solve the last one just find the answer to each x.

x=0 Divide each side by (x-2) and (x+3) to leave "x" by itself.

x=2 Divide each side by (x+3) and x to leave (x-2) by itself. Now add 2 on both sides.

x= -3 Divide each side by (x-2) and x to leave (x+3) by itself. Now subtract 3 on both sides.

That's the answer x= 0, 2, -3

Answer 4

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