Answer:
f(x) = x⁴ - 7x³ + 7x² + 21x - 30
Explanation:
Given function is f(x) = (x - 2)(x - 5)(x - √3)(x + √3)
f(x) = (x - 2)(x - 5)[(x² - (√3)²] {By using formula, (a - b)(a + b) = a² - b²]
= (x - 2)(x - 5)(x² - 3)
= (x - 2)[x(x² - 3) -5(x² - 3)] [By distributive property]
= (x - 2)(x³ - 3x - 5x² + 15)
= (x - 2)(x³ - 5x² - 3x + 15)
= [x(x³ - 5x² - 3x + 15) - 2(x³ - 5x² - 3x + 15)]
= x⁴ - 5x³- 3x² + 15x - 2x³ + 10x² + 6x - 30
= x⁴ - 7x³ + 7x² + 21x - 30
Therefore, expanded form of the polynomial function will be,
f(x) = x⁴ - 7x³ + 7x² + 21x - 30