Question

Find the sum, difference and product of the given polynomials

1. (2x^2 - 1/2x + 4)
2. (3x^2 - 4x)

Answer 1

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