Question

Use synthetic division to solve (4x3-3x2+5x+6)/(x+6) What is the quotient?

Answer 1

Start by setting synthetic division up:

6 | 3 5 6

Bring the 3 down,

6 | 3 5 6

3

Multiply, rinse and repeat:

6 | 3 5 6

18 138

3 23 144

Separate one term from the right, since this is vanilla synthetic division:

6 | 3 5 6

18 138

3 23 || 144

Use the appropriate polynomial rules to build your equation from there:

3x + 23 + (144/x+6)

As for the quotient I would assume it is referring to the remainder, which is 144/x+6, but that is probably a better thing for you to decide than me.

Answer 2

4x^2 -27x +167

Explanation:

(4x^3-3x^2+5x+6)/(x+6)

WE use synthetic division

x+6 =0 , so x=-6

We divide by -6. Write the coefficient of all terms inside and -6 outside.

Take down 4 as it is. then multiply the bottom number with -6 and put it in the middle. Continue the process.

-6 4 -3 5 6

-24 162 -1002

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4 -27 167 -996 (remainder)

Quotient is 4x^2 -27x +167

Remainder is -996