Question

Use synthetic division to divide (x3 + x2 – 40x – 4) ÷ (x – 6).

A. x2 + 7x + 2 R 8
B. x2 + 5x – 2 R 6
C. x3 + 6x – 1 R 2
D. x2 – 7x + 3 R 5
please for help................................

Answer 1

Your answer is A. x^2+7x+2 R 8

Answer 2

The quotient
`x^2+7x+2` and remainder (R) is 8

A is correct

Explanation:

Given: Synthetic division

`(x^3+x^2-40x-4)/ (x-6)`

Synthetic division: First we write coefficient of polynomial of numerator and then divide by bottom number when 0

Set of synthetic division:

6 | 1 1 -40 -4 |

6 42 12

1 7 2 8

First we put 1 down and then multiply it by 6. Write the result below next number. Repeat the step till end.

At last we get number 8. This is remainder.

Rest are coefficient of quotient.

Please find the attachment for steps of synthetic division.

`\text{Quotient } : x^2+7x+2`

`\text{Remainder }: 8`

Hence, The quotient
`x^2+7x+2` and remainder (R) is 8