Question

Sa se descompuna polinomul in factori ireductibili ( clase de resturi )

x^4 + 4x - in Z5 [x ]

Answer 1

$x^4 + 4x= x(x^3+4)=x(x^3+5-1) = x(x^3-1) =\\ \\ = x(x-1)(x^2+x+1)</strong><strong> </strong><strong>=</strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>=</strong><strong> </strong><strong>x</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>5</strong><strong>-</strong><strong>1</strong><strong>)</strong><strong>(</strong><strong>x</strong><strong>^</strong><strong>2</strong><strong>+</strong><strong>x</strong><strong>+</strong><strong>1</strong><strong>)</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>=</strong><strong> </strong><strong>x</strong><strong>(</strong><strong>x</strong><strong>+</strong><strong>4</strong><strong>)</strong><strong>(</strong><strong>x^</strong><strong>2</strong><strong>+</strong><strong>x</strong><strong>+</strong><strong>1</strong><strong>)</strong><strong>$

Answer 2

Răspuns:

-4=1  in Z5  deci

Explicație pas cu pas:

x(x³-4)=x(x³+1)= x(x+1)(x²-x+1)