Question

find the quotient and remainder using synthetic division for: $dfrac{x^{3}+10x^{2}+21x + 13}{x + 2}$
the quotient is
the remainder is
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Explanation:

Step1: Identify root of divisor

For $x+2=0$, root is $x=-2$

Step2: List coefficients of dividend

Coefficients: $1, 10, 21, 13$

Step3: Perform synthetic division

Bring down 1. Multiply by -2: $1\times(-2)=-2$. Add to 10: $10+(-2)=8$
Multiply 8 by -2: $8\times(-2)=-16$. Add to 21: $21+(-16)=5$
Multiply 5 by -2: $5\times(-2)=-10$. Add to 13: $13+(-10)=3$

Step4: Form quotient polynomial

The first three results are coefficients of quotient (degree 2): $1x^2 +8x +5$

Answer:

The quotient is $x^2 + 8x + 5$
The remainder is $3$