4)
a/ A(x)= -45-x3+4x2+ 5x+9+4x5-6x2-2
A(x)= -x3-2x2+5x+7
b/ B(x)= -3x4-2x3 +10x2 -8x+5x3-7-2x3+8x
B(x)= -3x4 +x3+10x2 -7
A(x)= -x3-2x2+5x+7
B(x)= -3x4 +x3+10x2 -7
b) P(x) = A(x)+B(x)= -x3-2x2+5x+7-3x4 +x3+10x2 -7= -3x4 +8x2+5x
Q(x)= -x3-2x2+5x+7- (-3x4 +x3+10x2 -7)= -x3-2x2+5x+7 + 3x4-x3 - 10x2 + 7= -2x3-12x2+5x+ 14
c) Thay x= -1 vào đa thức P(x)
P(x)= -3x4 +8x2+5x = -3 x (-1 )4+ 8 x (-1 )2+ 5 x -1= -3 x 1 + 8 x 1 + 5 x -1 = -3 +8 -5 = 0
a) Ta có: \(A=-4x^5-x^3+4x^2+5x+9+4x^5-6x^2-2\)
\(=-x^3-2x^2+5x+7\)
Ta có: \(B=-3x^4-2x^3+10x^2-8x+5x^3-7-2x^3+8x\)
\(=-3x^4+x^3+10x^2-7\)
b) Ta có: P(x)=A(x)+B(x)
\(=-x^3-2x^2+5x+7-3x^4+x^3+10x^2-7\)
\(=-3x^4+8x^2+5x\)
Ta có: Q(x)=A(x)-B(x)
\(=-x^3-2x^2+5x+7+3x^4-x^3-10x^2+7\)
\(=3x^4-2x^3-12x^2+5x+14\)
c) \(P\left(-1\right)=-3\cdot\left(-1\right)^4+8\cdot\left(-1\right)^2+5\cdot\left(-1\right)=-3+8+5=0\)
Vậy: x=-1 là nghiệm của P(x)
