use synthetic division to solve $(2x^{3}+4x^{2}-35x + 15)div(x - 3)$. what is the quotient?\n$2x^{2}-2x-29+\f…

Explanation:

Step1: Set up synthetic division

The divisor is $x - 3$, so we use $c=3$. The coefficients of the dividend $2x^{3}+4x^{2}-35x + 15$ are $2,4,-35,15$.

Step2: Bring down the first coefficient

Bring down the first coefficient $2$.

Step3: Multiply and add

Multiply $3\times2 = 6$, then add to the second - coefficient: $4 + 6=10$.

Step4: Multiply and add again

Multiply $3\times10 = 30$, then add to the third - coefficient: $-35+30=-5$.

Step5: Multiply and add one more time

Multiply $3\times(-5)=-15$, then add to the fourth - coefficient: $15+( - 15)=0$. The numbers $2,10,-5,0$ represent the coefficients of the quotient polynomial. The quotient is a polynomial of degree one less than the dividend. So the quotient is $2x^{2}+10x - 5$.

Answer:

D. $2x^{2}+10x - 5$