Question

Simplify the expression (x^4+4x^3-6x-24)÷(x+4) using synthetic division. Show your work just an answer without showing the synthetic division will get a zero grade. After doing the synthetic division, which gives you just coefficients. Convert the coefficient quotient answer, into a polynomial with variable x and the correct exponent powers in it. Convert your coefficient answer into a polynomial.

Hint: remember to fill in any missing degree terms in your dividend with coefficients that are zero to represent missing place holders.

Answer 1

• x³ + 8x² - 32x + 6

Step-by-step explanation:

The procedure of the synthetic division is in the picture attached.

The arrows will help you to understand the following explanation.

The first step is to copy the coefficients of the dividend, x⁴ + 4x³ -6x - 24, placing a zero in the place of x².

So, the coeeficients are: 1 4 0 -6 -24.

In front of those coefficients you have to copy the coefficient of the divisor, changed of sign, this is - 4.

With that, the first line is -4 | 1 4 0 -6 -24

Then, you copy the leading coefficient (1) below the line.

Then, multiply this number by - 4, and carry the result up into the next column and add down the column.

Now, continue multiplying each result of a column by - 4, and carry result up into next column.

At the end, the number down the last column is the remainder. Since it is zero the division is exact.

The resulting numbers before the remainder are the coefficients of the quotient polynomilal, so 1, 8, -32, and 6 are the corresponding coefficients of the polynomial x³ +8x² - 32x + 6, and the remainder is zero.