divide by synthetic division
(h^2-6h+8)/(h-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
Divide the polynomials using long division.
(t^2+2t-8)/t+4)
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.
Synthetic division is a method used to divide a polynomial by a linear binomial of the form (x - a). In this case, we want to divide the polynomial h^2 - 6h + 8 by the binomial (h - 2).
To perform synthetic division, follow these steps:
Step 1: Set up the division:
Write the coefficients of the polynomial in descending order (highest power to lowest power), including any missing terms. Our dividend is h^2 - 6h + 8, so the coefficients are 1, -6, and 8.
Step 2: Identify the dividing term:
The binomial divisor is h - 2. We are dividing by (h - 2), so our dividing term is 2.
Step 3: Begin synthetic division:
Start by writing the dividing term (2) outside a long division-like bracket, and then write the coefficients inside the bracket as shown below:
2 | 1 -6 8
Step 4: Bring down the first coefficient:
Bring down the leading coefficient (1) directly below the horizontal line:
2 | 1 -6 8
|
| 1
Step 5: Multiply and subtract:
Multiply the divisor (2) by the number below the horizontal line (which is 1), and write the result under the next coefficient:
2 | 1 -6 8
| 2
-------
| 1
Subtract this result from the next coefficient:
2 | 1 -6 8
| 2
-------
| 1 -4
Step 6: Repeat the process:
Repeat steps 4 and 5 using the new number below the line (which is -4) and the next coefficient (which is -6):
2 | 1 -6 8
| 2 -4
-------
| 1 -4 0
Step 7: Interpret the result:
The answer is the row of numbers on top of the horizontal line, reading from left to right. In this case, the quotient is 1x - 4. This means that the original polynomial h^2 - 6h + 8 is equal to (h - 2)(1x - 4).
Therefore, the quotient of (h^2 - 6h + 8)/(h - 2) is equal to (1x - 4).