Answer:
d. 4x² + 19x + 15.
Explanation:
To simplify the given polynomial expression, we will apply the distributive property and combine like terms.
The expression is:
3x(4x + 5) - 4(-x - 3)(2x - 5)
Let's simplify each term step by step:
Expand the first term, 3x(4x + 5):
= 12x² + 15x
Expand the second term, -4(-x - 3)(2x - 5):
= -4(-x - 3)(2x) + (-4)(-x - 3)(-5)
= 8x² + 12x + 20x + 60
= 8x² + 32x + 60
Now, let's combine like terms:
12x² + 15x - 4x² - 32x - 60
Combining the x² terms and the x terms:
(12x² - 4x²) + (15x - 32x) - 60
= 8x² - 17x - 60
Therefore, the simplified form of the polynomial expression 3x(4x + 5) - 4(-x - 3)(2x - 5) is:
8x² - 17x - 60
Hence, the correct option is d. 4x² + 19x + 15.