how do i factor this polynomial; 9x^2+6x^3
helper will be rewarded !

Question

anonymous · Answer

first what is common between the two?

arbyj · Answer

they're both divisible by 3

anonymous · Answer

3x^2 is common right?

anonymous · Answer

you group them and 3x^2(3+2x) I guess?

arbyj · Answer

i think so

solomonzelman · Answer

via rules of exponents:
$\color{#000000 }{ \displaystyle x^3=x^{2+1}=x^2\cdot x^1=x^2\cdot x  }$

then,

$\color{#000000 }{ \displaystyle 9x^2+6x^3  }$
$\color{#000000 }{ \displaystyle 3\cdot 3\cdot x^2+3\cdot 2 \cdot x^2 \cdot x }$
$\color{#000000 }{ \displaystyle 3\cdot (3x^2)+ 2x \cdot (3x^2) }$

so the above ws correct

solomonzelman · Answer

the rule is:
$\color{#000000 }{ \displaystyle a\times b+a\times c=(b+c)a }$

solomonzelman · Answer

if you think about it, it makes sense.

Try calculating each side separately,

$\color{#000000 }{ \displaystyle 4\times 3+4\times 5=(3+5)4 }$

arbyj · Answer

okay, thank you all !