The quotient is x² + 3x + 4 and the remainder is 7
Step-by-step explanation:
In the synthetic calculation we use the coefficient of the dividend with
the divisor
1. The dividend is x³ + 5x² + 10x + 15
2. The divisor is x + 2
3. Equate the divisor by 0 to find x
∵ The divisor is x + 2
∴ x + 2 = 0
- Subtract 2 from both sides
∴ x = -2
Now let use use the synthetic division
Step 1 : Write down the coefficients of the dividend , put x = -2 at the left
-2 1 5 10 15
____________
Step 2 : Bring down the first coefficient to the bottom row.
-2 1 5 10 15
_____________
1
Step 3 : Multiply it by -2, and carry the result into the next column.
-2 1 5 10 15
____-2________
1
Step 4 : Add down the column
-2 1 5 10 15
___ -2____________
1 3
Step 5 : Multiply it by -2, and carry the result into the next column
-2 1 5 10 15
___-2__-6____
1 3
Step 6 : Add down the column
-2 1 5 10 15
___-2__-6_____
1 3 4
Step 7 : Multiply it by -2, and carry the result into the next column
-2 1 5 10 15
____-2__-6__-8_
1 3 4
Step 8 : Add down the column
-2 1 5 10 15
___-2___-6__-8_
1 3 4 7
The quotient is 1 degree less than the degree of the dividend
∴ The quotient is (x² + 3x + 4) and the remainder is 7
The quotient is x² + 3x + 4 and the remainder is 7
Learn more:
You can learn more about quotient in brainly.com/question/629998
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