Final answer:
To find the quotient and remainder of {x³+2x²-10} divided by {x+3}, you need to perform polynomial long division. The quotient is x²-1 and the remainder is -10.
Step-by-step explanation:
To find the quotient and remainder of {x³+2x²-10} divided by {x+3}, we use polynomial long division.
Step 1: Divide the first term of the dividend, which is x³, by the first term of the divisor, which is x. This gives us x² as the first term of the quotient.
Step 2: Multiply the divisor {x+3} by the quotient term x². This gives us {x³+3x²}.
Step 3: Subtract the product from the dividend. {x³+2x²-10-(x³+3x²)} = -x²-10}.
Step 4: Bring down the next term of the dividend, which is -10.
Step 5: Repeat Steps 1-4 until we have no more terms to bring down.
Step 6: The final quotient is x²-1 and the remainder is -10.