Question

Cho 2 đa thức P(x)=3x² +2x2 -2x+7-x2 -x Q(x)=-3x3 + x-14- 2x - x2 -1
a) thu gọn 2 đa thức P(x) và Q(x)
b) tìm đa thức M(x)=P(x)+Q(x) ; N(x)=P(x)-Q(x)
c) tìm x để P(x)= -Q(x)

Answer 1

a, P(x) = 3x\(^2\) + 2x\(^2\) -2x + 7 - x\(^2\) - x

= \((3x^2+2x^2-x^2)\) + (-2x - x) + 7

= 4x\(^2\) - 3x + 7

Q(x)=-3x\(^3\) + x - 14 - 2x - x\(^2-1\)

= -3x\(^3\) + (x-2x) +(-14-1) - x\(^2\)

= -3x\(^3\) - x - 15 - x\(^2\)

b, N(x)=P(x)-Q(x) =(4x\(^2\)-3x+7)-(-3x-x-15-x)

= 4x\(^2\)-3x+7 + 3x\(^3\)+x+15+x\(^2\)

= (4x\(^2+x^2\)) + (\(-3x+x\))+(7+15)+3x\(^3\)

= \(5x^2\) - 2x + 12 +3x\(^3\)

M(x)=P(x)+Q(x)

=(4x\(^2\)-3x+7)+(-3x\(^3\)-x-15-x\(^2\))

=4x\(^2\)-3x+7-3x\(^3\)-x-15-x\(^2\)

=(4x\(^2\)-\(x^2\)) + (-3x-x) + (7-15)-3x\(^3\)

= 3 \(x^2\) - 4x - 8 -3x\(^3\)