Question

Quick Question...

Answer 1

How does \[x^3+2x^2-9x-18\]
turn into \[x^2(x+2)-9(x+2)\]
and then into \[(x^2-9)(x+2)\]

Answer 2

I just don't understand how the first equation turns into the second .-.

Answer 3

@Michele_Laino

Answer 4

we have to factor out \(x^2\) between the first and second terms
furthermore, we have to factor out \(-9\) between the third and fourth terms

Answer 5

at the final step, we have to factor out \((x+2)\)

Answer 6

okay...but why (x+2) ?

Answer 7

since \((x+2)\) is the common factor

Answer 8

from \[x^2(x+2)-9(x+2)\]
how get x+2 from x^3+2x^2 ?

Answer 9

here we have:
\(\left( {x + 2} \right)\) is contained as a factor in the term \({x^2}\left( {x + 2} \right)\)
furthermore:
\(\left( {x + 2} \right)\) is also contained as a factor into the term \(9\left( {x + 2} \right)\)
so \(\left( {x + 2} \right)\) is a common factor, and I can factor out it

Answer 10

i know. i dont get HOW you got x+2

Answer 11

now if I apply the distributive property of multiplication over addition, I get this:
\[{x^2}\left( {x + 2} \right) = {x^2} \cdot x + 2 \cdot {x^2}\]

Answer 12

furthermore, if I apply the same property, I can write this:
\[ - 9\left( {x + 2} \right) = - 9x - 2 \cdot 9\]

Answer 13

finally, if we add the right sides of the two expressions above, I get your original expression

Answer 14

...alright i guess. what i understand is that:
\[x^3 \] and \[2x^2\] have \[x^2\] in common. which leaves x+2 left over. is THAT where the (x+2) comes from? if so, why is it also combined with -9?

Answer 15

starting from the expression below:
\[{x^2}\left( {x + 2} \right) - 9\left( {x + 2} \right)\]
I can factor out the quantity \((x+2)\), so I get this:
\[\left( {x + 2} \right)\left( {{x^2} - 9} \right)\]

Answer 16

wipe out the last equation. just totally forget about it.
im talking about:
why is it -9(x+2)? where did the (x+2) come from? i understand the x^2(x+2)...but why -9(x+2)?

Answer 17

because I factored out \(-9\) between the third and fourth term of your original expression, like this:
\[ - 9x - 18 = - 9\left( {x + 2} \right)\]

Answer 18

...I guess I get it...alright well thanks anyway

Answer 19

wow...omg i completely get it now xD sorry for the hassle and THANK YOU FOR YOUR PATIENCE!!

Answer 20

:)