Use synthetic division to find the quotient and the remainder. (12x^4 + 5x^3 + 3x^2 - 5)/(x + 1)

Question

helder_edwin · Answer

$$\large \begin{array}{c|rrrrr}
               & 12 & 5 & 3 & 0 & -5\
               -1 & & -12 &7 & -10 & 10 \
               \hline
               & 12 & -7 & 10 & -10 & \fbox{5}
            \end{array} $$

anonymous · Answer

So the remainder would be 5?

helder_edwin · Answer

yes

anonymous · Answer

And the quotient is 12,  -7, 10, -10, 5?

helder_edwin · Answer

those r the coefficients, and 5 is the remainder (u said it yourself)

anonymous · Answer

Okay then what is my next step this is the part I am confused on, how to turn the coefficients into the quotient. Thank so much!

helder_edwin · Answer

see how i ordered the coefficients of the original polynomial.

u have now four coefficients. what is the degree of the polynomial?

anonymous · Answer

4?

helder_edwin · Answer

no. the degree is 3.

now from right to left the power goes from 3 to zero. so say u had 7, -4, 6, and 1 then the polynomial would be
$$\large 7x^3-4x^2+6x+1 $$

got it?

anonymous · Answer

so 
$$12^{3}-7x ^{2}+10x-10$$

helder_edwin · Answer

yes. very good

anonymous · Answer

Okay awesome thank you so much for your help!

helder_edwin · Answer

u r very welcome