Final answer:
The expression 23(2x - (1/2)x² - 2x - 3) simplifies to -23 × 2² after combining like terms, indicating that the value of 'a' is -23. The correct answer is option (d) -23.
Step-by-step explanation:
The task is to simplify the expression 23(2x - (1/2)x² - 2x - 3) and write it in the form a × 2ˣ. To simplify the expression, we need to distribute the 23 and combine like terms.
First, we distribute the 23 across the expression:
23 × 2x = 46x
23 × -(1/2)x² = -11.5x²
23 × -2x = -46x
23 × -3 = -69
After distributing, we can combine the like terms:
46x and -46x cancel out
So we are left with -11.5x² - 69. Multiplying by the base 2, we rewrite -11.5x² as -23 × (1/2)x² to fit the form a × 2ˣ,
This shows that the coefficient a is -23. Therefore, the correct answer is (d) -23.