Question

Simplify (4x³ + 8x² + 15x + 14) / (2x + 1) into quotient and remainder:

a) Quotient: 2x² + 4x + 7, Remainder: 7
b) Quotient: 2x² + 4x + 7, Remainder: 0
c) Quotient: 2x² + 4x + 7, Remainder: 14
d) Quotient: 2x² + 4x + 7, Remainder: 1

Answer 1

To simplify the expression (4x³ + 8x² + 15x + 14) / (2x + 1) into quotient and remainder, we can use polynomial long division. The quotient is 2x² + 4x + 7 and the remainder is 0.

Step-by-step explanation:

To simplify the expression (4x³ + 8x² + 15x + 14) / (2x + 1) into quotient and remainder, we can use polynomial long division. Here are the steps:

1. Divide the first term of the numerator (4x³) by the first term of the denominator (2x). This gives us 2x².
2. Multiply the divisor (2x + 1) by the quotient from step 1 (2x²). This gives us 4x³ + 2x².
3. Subtract the result from step 2 (4x³ + 2x²) from the numerator (4x³ + 8x² + 15x + 14). This gives us 6x² + 15x + 14.
4. Repeat steps 1, 2, and 3 with the result from step 3 (6x² + 15x + 14).
5. In the final step, the remaining expression in the numerator is the remainder and the expression obtained so far is the quotient. The remainder is 0 in this case, so the quotient is 2x² + 4x + 7 and the remainder is 0.