Answer:
2x²+10x-5
Explanation:
Given polynomial: 2x³ + 4x² - 35x + 15
Divisor: x - 3
Step 1: Bring down the coefficient of the highest power of x:
2
Step 2: Multiply the divisor, 3, by the value just brought down (2):
2 * 3 = 6
Step 3: Add the result to the next coefficient in the polynomial (4):
6 + 4 = 10
Step 4: Multiply the divisor, 3, by the new sum (10):
10 * 3 = 30
Step 5: Add the result to the next coefficient in the polynomial (-35):
30 - 35 = -5
Step 6: Multiply the divisor, 3, by the new sum (-5):
-5 * 3 = -15
Step 7: Add the result to the last coefficient in the polynomial (15):
-15 + 15 = 0
The resulting coefficients after synthetic division are: 6, 10, -5, 0.
Therefore, the quotient is 2x² + 10x - 5.