Answer :
The factors of the equation [tex]4x^{5}[/tex]+ [tex]4x^{4}[/tex] - [tex]25x^{3}[/tex] +25x² are 0, 1, 2.5 and -2.5.
Given, [tex]4x^{5}[/tex]+ [tex]4x^{4}[/tex] - [tex]25x^{3}[/tex] +25x²
Deduce one factor,
= x²([tex]4x^{3}[/tex] + 4x² - 25x - 25)
Use Middle term splitting,
= x²(4x²(x + 1) - 25(x + 1))
= x²(4x² - 25)(x + 1)
= x²(x + 1)(2x - 5)(2x + 5)
The final factors of x are,
x = 0
x = 1
x = 5 ÷ 2 = 2.5
x = -5 ÷ 2 = -2.5
Polynomial functions are functions that take only non-negative integer powers or positive integer exponents of variables in quadratic, cubic, and other equations.
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