Final answer:
To divide (3x³+2x²-5x+3) by (x+3), you can use polynomial long division. The quotient is 3x²-4x+13.
Step-by-step explanation:
To divide (3x³+2x²-5x+3) by (x+3), we can use polynomial long division.
Step 1: Divide the first term of the numerator (3x³) by the first term of the denominator (x). This gives us 3x².
Step 2: Multiply the entire denominator (x+3) by 3x². This gives us 3x³+9x².
Step 3: Subtract the result obtained in step 2 from the numerator. This gives us (3x³+2x²-5x+3) - (3x³+9x²).
Step 4: Repeat steps 1 to 3 with the new numerator (2x²-5x) and the original denominator (x+3).
Step 5: Continue the process until we can no longer perform division. The quotient is the result obtained after all the divisions. In this case, the quotient is 3x²-4x+13.