## fari321 Group Title One factor of 4x^3+15x^2-31x-30 is x-2. Find the other factors one year ago one year ago

1. freewilly922 Group Title

You could use long division or synthetic division. Your choice.

2. fari321 Group Title

how

3. fari321 Group Title

with long division

4. freewilly922 Group Title

Well to start with you know that $4x^2 \times (x-2) = 4x^3-8x^2$ so just like you would do long division with numbers you can also do it with variables like this. so $4x^3-15x^2 -\bigg[4x^3-8x^2 \bigg]=-7x^2$ you drop the -31x like long division to get $-7x^2 -31x$ and then divide this by (x-2) again $-7x\times (x-2) = -7x^2 +14x$ and so on

5. freewilly922 Group Title

sorry the $-15x^2$ should be positive 15

6. freewilly922 Group Title

so $4x^3+15x^2 -\bigg[4x^3-8x^2 \bigg]=23x^2$ $23x\times (x-2) = 23x^2-46x$ $23x^2-31x -\bigg[23x^2-46x\bigg]=+15x$ $15\times(x-2)=15x-30$ $+15x-30 -\bigg[15x-30 \bigg]=0$ so $4x^3+15x^2-31x-30 \to (x-2)(4x^2+23x+15)$ and you can factor the rest... hopefully

7. freewilly922 Group Title

Explaining how to do long division or synthetic division is a real pain on open study, I would suggest you take the time outside of this to study it from a book with examples. Or go online and search for a youtube video. It isn't hard.

8. fari321 Group Title

thank you