simple math question?

Question

I don't understand the below math problem.
Can you explain this logic?

3X³ + 15X² + 18X
= 3X(X² + 5X + 6)
= 3X(X + 2)(X + 3)

Answer 1

First, you're dividing each figure by 3x.
Then you're looking for two numbers that add up to 5 and whose product is 6.

Answer 2

I'll try to explain this:
First off it's called 'factoring', and it is pretty confusing when you start it.
You're starting with 3X³ + 15X² + 18X.
How you then move on to = 3X(X² + 5X + 6) is...
you're dividing the equation by 3X, which 3X(X² + 5X + 6) is equal to 3X³ + 15X² + 18X
...since 3X * X² = 3X³, 5X * 3X² = 15X², and 3X * 6 = 18X.

Then you continue completely factor your equation by factoring the (X² + 5X + 6)
part of it. You do this by taking our the X and placing both X's in (X+_)(X+_)...so far you will get X² since X * X=X²...then (here comes the confusing part)....you have to find two numbers that are the sum of 5 and the product of 6...this just so happens to be 2 and 3 since 2+3=5 and 2*3=6......so you place them in (X+_)(X+_) and get (X+2)(X+3).

Now for background reference to put (X+2)(X+3) into the (X² + 5X + 6) form you use F.O.I.L. (first,outside,inside,last)..which in (X+2)(X+3) you'd multiple First: X * X which is X². Outside:3 * X which is of course 3X. Inside: 2 * X which is 2X and Last: 3 * 2 which is 6. Now you always add Outside and Inside together, which is your 5X. You end up with (X² + 5X + 6).

Anyway you just tack the 3X onto the (X + 2)(X + 3)...therefore when correctly multiplied out, you'll get the original 3X³ + 15X² + 18X.

I hope this helps and makes sense because I can't sleep and have nothing better to do then answer a question in my worst subject. Haha.

Answer 3

In the first step, you've factored out the common factor 3x. Every term in the original expression is a multiple of 3x. You can check to see that the second line is equivalent to the first by multiplying it back out: 3x * x^2 = 3x^3, 3x * 5x = 15x^2, and 3x * 6 = 18x.

The third line is the factoring of the quadratic part of the second line. To factor a quadratic where the coefficient of x^2 is one, you need only to find two numbers whose product is the constant term (6) and whose sum is the coefficient of the linear term (5). These two numbers are 2 and 3, so it factors as (x +2)(x + 3).

To check it, you can multiply the whole thing out. You will arrive at the original expression.

Answer 4

this method is known as splitting the method. in th 2nd step keep the 3x aside what remains is x2 + 5x + 6. the multiples of 6 are 3 & 2. the sum of 3&2 is 5.so 3x(x2 + 2x+3x(because we r expanding 5 with the multiples of 6)+6)
the above answer can be further divided.
3x(x(x+2) +3(x+2)). now x+2 is common. so the answer is 3x(x+2)(x+3)

Answer 5

You are being asked to find a value of X that will satisfy this equation.

Try some values in X (eg. 1, 2 or 3) and work out whether the three equations equal each other.

Answer 6

FIRST OF A WHO REALLY NEEDS THIS KIND OF MATH AND SECOND THE ANSWER IS ONLY IMPORTANT IF ASK THE RIGHT QUESTION...

Answer 7

I kant count past potato.

Answer 8

its all done with mirrors