Question

question 5 use synthetic division to divide $x^{3}+4x^{2}-4x + 4$ by $x - 1$. the quotient is: the remainder is: question help: video read written example message instructor

Explanation:

Step1: Set up synthetic division

For dividing by $x - 1$, use $1$ as the divisor. Write the coefficients of the dividend $x^{3}+4x^{2}-4x + 4$ which are $1,4,-4,4$.

Step2: Bring down the first coefficient

Bring down the first coefficient $1$.

Step3: Multiply and add

Multiply the divisor $1$ by the number just brought down ($1$), getting $1\times1 = 1$. Add this to the second - coefficient $4$: $4+1=5$.

Step4: Repeat multiplication and addition

Multiply the divisor $1$ by $5$ getting $5$, add to the third - coefficient $-4$: $-4 + 5=1$.

Step5: Final multiplication and addition

Multiply the divisor $1$ by $1$ getting $1$, add to the fourth - coefficient $4$: $4 + 1=5$.
The synthetic - division setup looks like:

1 |  1  4 -4  4
   |     1  5  1
   |-------------
     1  5  1  5

Answer:

The quotient is $x^{2}+5x + 1$ and the remainder is $5$.