Question

divide by synthetic division

(h^2-6h+8)/(h-2)

Answer 1

Divide the polynomials using long division.
(t^2+2t-8)/t+4)

Answer 2

To divide using synthetic division, we will set up the equation as follows:

2 │ 1 -6 8

First, write down the coefficient of each term in descending order. The dividend is h^2 - 6h + 8, and the divisor is h - 2.

Next, write down the first coefficient on the top row of the synthetic division box:

2 │ 1 -6 8

Bring down the 1:

2 │ 1 -6 8
|
__________
1

Multiply the divisor (2) by the number on the bottom row and write the product below the next coefficient:

2 │ 1 -6 8
| 2
__________
1

Add the product to the next coefficient in the top row:

2 │ 1 -6 8
| 2
__________
1 -4

Repeat the process of multiplying the divisor by the next number and adding it to the following number until all the coefficients have been processed:

2 │ 1 -6 8
| 2 -8
__________
1 -4 0

The final row represents the quotient of h-2, and the last number (0) represents the remainder. Therefore, the result of dividing (h^2 - 6h + 8) by (h - 2) using synthetic division is:

Quotient: h - 4

Remainder: 0

Answer 3

To divide the polynomials using long division, we will set up the equation as follows:

t + 4 │ t^2 + 2t - 8

First, divide the first term in the numerator (t^2) by the first term in the denominator (t) and write the result above the division line:

-1 │ t^2 + 2t - 8
- t^2 - 4t
____________
6t - 8

Next, multiply the divisor (t + 4) by the result (-1):

-1 │ t^2 + 2t - 8
- t^2 - 4t
____________
6t - 8
- (6t + 24)
_____________
-32

Subtract the product from the remaining terms:

-1 │ t^2 + 2t - 8
- t^2 - 4t
____________
6t - 8
- (6t + 24)
_____________
-32

Since the degree of the resulting polynomial (-32) is less than the degree of the divisor (t + 4), the division is complete.

Therefore, the quotient is -1 and the remainder is -32.