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

1. freewilly922

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

2. fari321

how

3. fari321

with long division

4. freewilly922

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

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

6. freewilly922

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

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

thank you