Final answer:
To solve for k in the equation (21x - 3)(2x + 5) = 8x² + kx, you must expand and simplify the left-hand side to get 42x² + 99x - 15, which, when compared to the right-hand side, shows that k equals 99.
Step-by-step explanation:
To solve for k in the equation (21x - 3)(2x + 5) = 8x² + kx, we must first expand the left-hand side of the equation. The expanded form of the left-hand side will be:
42x² + 105x - 6x - 15 = 8x² + kx
Combining like terms, we get:
42x² + 99x - 15 = 8x² + kx
To find the coefficient k, we need to compare the corresponding terms from both sides of the equation:
42x² = 8x²
99x = kx
Since the x² terms on both sides of the equation already match, we can focus on the x terms. Therefore, k equals 99, as the coefficient in front of x on the left-hand side of the equation is 99 when it's fully expanded and simplified.