Question

Obter o valor de K, para que o polinômio P(x)=2x4+k³-6x² seja divisivel pelo binômio x-1

Answer 1

$P(x)=2x^4+k^3-6x^2\\D(x)=x-1$
$P(x)=D(x).Q(x)+R(x)\\R(x)=0\\2x^4+k^3-6x^2=(x-1)(ax^3+bx^2+cx+d)\\2x^4+k^3-6x^2=ax^4+bx^3+cx^2+dx-ax^3-bx^2-cx-d\\2x^4+k^3-6x^2=ax^4+(b-a)x^3+(c-b)x^2+(d-c)x-d\\2x^4=ax^4\\a=2\\k^3=(b-a)x^3\\k=b-2\\-6x^2=(c-b)x^2\\-6=c-b\\0x=(d-c)x\\0=d-c\\d=c\\0=-d\\d=0=c\\-6=-b\\b=6\\k=6-2=4$