Question

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

Answer 1

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

Answer 2

how

Answer 3

with long division

Answer 4

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

Answer 5

sorry the
\[-15x^2 \] should be positive 15

Answer 6

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

Answer 7

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.

Answer 8

thank you