Bài 17.
\(a,A\left(x\right)=-2x^5-x^3-3x^2+5x+9+2x^5-6x^2-2\)
\(=\left(-2x^5+2x^5\right)-x^3+\left(-3x^2-6x^2\right)+5x+\left(9-2\right)\)
\(=-x^3-9x^2+5x+7\)
\(B\left(x\right)=-4x^3+9x^2-2x+4x^3-7+x^3+2x+5\)
\(=\left(-4x^3+4x^3+x^3\right)+9x^2+\left(-2x+2x\right)+\left(-7+5\right)\)
\(=x^3+9x^2-2\)
\(b,P\left(x\right)=A\left(x\right)+B\left(x\right)\)
\(=-x^3-9x^2+5x+7+x^3+9x^2-2\)
\(=\left(-x^3+x^3\right)+\left(-9x^2+9x^2\right)+5x+\left(7-2\right)\)
\(=5x+5\)
\(Q\left(x\right)=A\left(x\right)-B\left(x\right)\)
\(=-x^3-9x^2+5x+7-\left(x^3+9x^2-2\right)\)
\(=-x^3-9x^2+5x+7-x^3-9x^2+2\)
\(=\left(-x^3-x^3\right)+\left(-9x^2-9x^2\right)+5x+\left(7+2\right)\)
\(=-2x^3-18x^2+5x+9\)
\(c,P\left(x\right)=5x+5\)
\(\Rightarrow P\left(-1\right)=5\cdot\left(-1\right)+5\)
\(=-5+5\)
\(=0\)
\(\Rightarrow x=-1\) là nghiệm của đa thức P(x)
`#040911`
`17,`
`a)`
`A(x) = -2x^5 - x^3 - 3x^2 + 5x + 9 + 2x^5 - 6x^2 - 2`
`= (-2x^5 + 2x^5) - x^3 + (-3x^2 - 6x^2) + 5x + (9 - 2)`
`= -x^3 - 9x^2 + 5x + 7`
`B(x) = -4x^3 + 9x^2 - 2x + 4x^3 - 7 + x^3 + 2x + 5`
`= (-4x^3 + 4x^3 + x^3) + 9x^2 + (-2x + 2x) + (-7+5)`
`= x^3 + 9x^2 - 2`
`b)`
`P(x) = A(x) + B(x)`
`= -x^3 - 9x^2 + 5x + 7 + x^3 + 9x^2 - 2`
`= (-x^3 + x^3) + (-9x^2 + 9x^2) + 5x + (7 - 2)`
`= 5x + 5`
`Q(x) = A(x) - B(x)`
`= -x^3 - 9x^2 + 5x + 7 - (x^3 + 9x^2 - 2)`
`= -x^3 - 9x^2 + 5x + 7 - x^3 - 9x^2 + 2`
`= (-x^3 - x^3) + (-9x^2 - 9x^2) + 5x + (7 + 2)`
`= -2x^3 - 18x^2 + 5x + 9`
`c)`
`P(x) = 5x + 5 = 0`
`=> 5*(x + 1) = 0`
`=> x + 1 = 0`
`=> x = -1`
Vậy, `x = -1` là nghiệm của đa thức `P(x).`
`#040911`
`18,`
`a,`
`P(x) = 2x^3 - x^2 + 8x - 1 - 3x^2`
`= 2x^3 + (-x^2 - 3x^2) + 8x - 1`
`= 2x^3 - 4x^2 + 8x - 1`
`Q(x) = -4x^2 + 2x^3 + 3x + 5 + 7x`
`= 2x^3 - 4x^2 + (3x + 7x) + 5`
`= 2x^3 - 4x^2 + 10x + 5`
`b,`
`P(x) + Q(x)`
`= 2x^3 - 4x^2 + 8x - 1 + 2x^3 - 4x^2 + 10x + 5`
`= (2x^3 + 2x^3) + (-4x^2 - 4x^2) + (8x + 10x) + (-1 + 5)`
`= 4x^3 - 8x^2 + 18x + 4`
`c,`
`P(x) - Q(x)`
`= 2x^3 - 4x^2 + 8x - 1 - (2x^3 - 4x^2 + 10x + 5)`
`= 2x^3 - 4x^2 + 8x - 1 - 2x^3 + 4x^2 - 10x - 5`
`= (2x^3 - 2x^3) + (-4x^2 + 4x^2) + (8x - 10x) + (-1-5)`
`= -2x - 6`
Bài 18.
\(a,P\left(x\right)=2x^3-x^2+8x-1-3x^2\)
\(=2x^3+\left(-x^2-3x^2\right)+8x-1\)
\(=2x^3-4x^2+8x-1\)
\(Q\left(x\right)=-4x^2+2x^3+3x+5+7x\)
\(=2x^3-4x^2+\left(3x+7x\right)+5\)
\(=2x^3-4x^2+10x+5\)
\(b,P\left(x\right)+Q\left(x\right)\)
\(=2x^3-4x^2+8x-1+2x^3-4x^2+10x+5\)
\(=\left(2x^3+2x^3\right)+\left(-4x^2-4x^2\right)+\left(8x+10x\right)+\left(5-1\right)\)
\(=4x^3-8x^2+18x+4\)
\(c,P\left(x\right)-Q\left(x\right)\)
\(=2x^3-4x^2+8x-1-\left(2x^3-4x^2+10x+5\right)\)
\(=2x^3-4x^2+8x-1-2x^3+4x^2-10x-5\)
\(=\left(2x^3-2x^3\right)+\left(-4x^2+4x^2\right)+\left(8x-10x\right)+\left(-1-5\right)\)
\(=-2x-6\)
#Urushi☕
17. a) A(x) = -x3 - 9x2 + 5x + 7
B(x) = x3 +9x2 - 2
b) P(x) = 5x + 5
Q(x) = -2x3 - 18x2 + 5x + 9
c) ....................... =) x = -1 là nghiệm của đa thức P(x)
