Answer:
sum: 5x² - 9/2x + 4
difference: -x² + 7/2x + 4
product: 6x⁴ - 19/2x³ + 14x² - 16x
Explanation:
1. 2x² - 1/2x + 4
2. 3x² - 4x
Sum:
2x² - 1/2x + 4 + 3x² - 4x
= 2x² + 3x² - 1/2x - 4x + 4
= 5x² - 9/2x + 4
Difference:
2x² - 1/2x + 4 - (3x² - 4x)
= 2x² - 1/2x + 4 - 3x² + 4x
= 2x² - 3x² - 1/2x + 4x + 4
= -x² + 7/2x + 4
Product:
(2x² - 1/2x + 4)(3x² - 4x)
= 6x⁴ - 8x³ - 3/2x³ + 4/2x² + 12x² - 16x
= 6x⁴ - 19/2x³ + 14x² - 16x