Question

homework assignment 5.4 dividing polynomials score: 6/8 answered: 6/8 question 7 find the quotient and remainder using synthetic division: $\frac{x^{3}+9x^{2}-97}{x + 5}$ the quotient is the remainder is question help: video read written example message instructor

Explanation:

Step1: Set up synthetic division

The divisor is $x + 5$, so we use $- 5$ in the synthetic - division setup. The dividend is $x^{3}+9x^{2}+0x - 97$, so the coefficients are $1,9,0,-97$.

Step2: Bring down the first coefficient

Bring down the first coefficient $1$.

Step3: Multiply and add

Multiply $-5\times1=-5$, and add to the second coefficient: $9+( - 5)=4$. Then multiply $-5\times4=-20$, and add to the third coefficient: $0+( - 20)=-20$. Then multiply $-5\times(-20) = 100$, and add to the fourth coefficient: $-97 + 100=3$.

Step4: Write the quotient and remainder

The numbers $1,4,-20$ are the coefficients of the quotient polynomial, and $3$ is the remainder. The quotient is $x^{2}+4x - 20$ and the remainder is $3$.

Answer:

The quotient is $x^{2}+4x - 20$
The remainder is $3$