Cho đa thức P( \(x\) ) = \(2x^4\) - \(x^2\) + \(x\) - 2. Tìm Q( \(x\) ); H ( \(x\) ) sao cho:
a) Q( \(x\) ) + P( \(x\) ) = \(3x^4\) + \(x^3\) + \(2x^2\) + \(x\) + 1
b) P( \(x\) ) - H( \(x\) ) = \(x^4\) - \(x^3\) + \(x^2\) -...
Đọc tiếp
Cho đa thức P( \(x\) ) = \(2x^4\) - \(x^2\) + \(x\) - 2. Tìm Q( \(x\) ); H ( \(x\) ) sao cho:
a) Q( \(x\) ) + P( \(x\) ) = \(3x^4\) + \(x^3\) + \(2x^2\) + \(x\) + 1
b) P( \(x\) ) - H( \(x\) ) = \(x^4\) - \(x^3\) + \(x^2\) - 2
Lời giải:
a.
$Q(x)=(3x^4+x^3+2x^2+x+1)-P(x)=(3x^4+x^3+2x^2+x+1)-(2x^4-x^2+x-2)$
$=3x^4+x^3+2x^2+x+1-2x^4+x^2-x+2$
$=x^4+x^3+3x^2+3$
b.
$H(x)=P(x)-(x^4-x^3+x^2-2)=(2x^4-x^2+x-2)-(x^4-x^3+x^2-2)$
$=2x^4-x^2+x-2-x^4+x^3-x^2+2$
$=x^4+x^3-2x^2+x$