How do you divide (6x2+7x−2) by x+4?

1 Answer
George C.
May 28, 2015

The process of synthetic division is somewhat like long division.

First choose a multiplier for (x+4) that will result in an expression whose highest order term matches the highest order term of (6x2+7x−2).

That multiplier is 6x...

6x⋅(x+4)=6x2+24x

Subtract this from the original value to leave a remainder...

(6x2+7x−2)−(6x2+24x)

=6x2+7x−2−6x2−24x

=−17x−2

Now choose a multiplier for (x+4) that will result in an expression whose highest order term matches the highest order term of (−17x−2)

That multiplier is −17

−17(x+4)=−17x−68

Subtract this from the previous remainder to get a new remainder:

(−17x−2)−(−17x−68)

=−17x−2+17x+68

=66

So

(6x2+7x−2)=(x+4)(6x−17)+66

or

6x2+7x−2x+4=(6x−17)+66x+4

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