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a,P(x)=4x\(^3\)+2x\(^2\)-2x+7-x\(^2\)-x
=4x\(^3\)+(2x\(^2\)-x\(^2\))+(-2x-x)+7
=4x\(^3\)+x\(^2\)-3x+7
Q(x)=-4x\(^3\)+x-14-2x-x\(^2\)-1
=-4x\(^3\)-x\(^2\)+(x-2x)+(-14-1)
= -4x\(^3\)-x\(^2\) -x -15
b, P(x)+Q(x)=4x\(^3\)+x\(^2\)-3x+7-4x\(^3\)-x\(^2\) -x -15
=\(\left(4x^3-4x^3\right)\)+\(\left(x^2-x^2\right)\)+(-3x-x)+(7-15)
= -4x-8
P(x)-Q(x)=(4x\(^3\)+x\(^2\)-3x+7)-(-4x\(^3\)-x\(^2\) -x -15)
=4x\(^3\)+x\(^2\)-3x+7+4x\(^3\)+x\(^2\) +x +15
=\(\left(4x^3+4x^3\right)\)+\(\left(x^2+x^2\right)\)+(-3x+x)+(7+15)
= \(8x^3\) + \(2x^2\) - 2x + 22
Bài 1:
2x\(^2\)+3x\(^2\)-\(\dfrac{3}{2}\)x\(^2\)
=(2+3-\(\dfrac{3}{2}\)).x\(^2\)
Bài 2:
a,P(x)=4x\(^3\)+2x\(^2\)-2x+7-x\(^2\)-x
=4x3+(2x\(^2\)-x\(^2\))+(-2x-x)+7
=4x\(^3\)+x\(^2\)-3x+7
Q(x)=-4x\(^3\)+x-14-2x-x\(^2\)-1
=-4x\(^3\)-x\(^2\)+x+(-14-1)
=-4x\(^3\)-x\(^2\)+x-15
b,P(x)+Q(x):
P(x)=4x\(^3\)+x\(^2\)-3x+7
+
Q(x)=-4x\(^3\)-x\(^2\)+x-15
P(x)+Q(x)= -2x-8
P(x)-Q(x):
P(x)=4x\(^3\)+x\(^2\)-3x+7
-
Q(x)=-4x\(^3\)-x\(^2\)+x-15
a. P(x) = 4x3 + 2x2 +7-x2 -x = 4x3+x2-x+7
Q(x) = -4x3+x-(-14) -2x-x2-1 = -4x3+x+14-2x-x2-1 = -4x3 -x2 -x+13
`C(x)=`\(5-8x^4+2x^3+x+5x^4+x^2-4x^3\)
`C(x)= (-8x^4+5x^4)+(2x^3-4x^3)+x^2+x+5`
`C(x)= -3x^4-2x^3+x^2+x+5`
`D(x)=`\(\left(3x^5+x^4-4x\right)-\left(4x^3-7+2x^4+3x^5\right)\)
`D(x)= 3x^5+x^4-4x-4x^3+7-2x^4-3x^5`
`D(x)=(3x^5-3x^5)+(x^4-2x^4)-4x^3-4x+7`
`D(x)=-x^4-4x^3-4x+7`
`P(x)=C(x)+D(x)`
`P(x)=( -3x^4-2x^3+x^2+x+5)+(-x^4-4x^3-4x+7)`
`P(x)=-3x^4-2x^3+x^2+x+5-x^4-4x^3-4x+7`
`P(x)=(-3x^4-x^4)+(-2x^3-4x^3)+x^2+(x-4x)+(5+7)`
`P(x)=-4x^4-6x^3+x^2-3x+12`
`Q(x)=C(x)-D(x)`
`Q(x)=( -3x^4-2x^3+x^2+x+5)-(-x^4-4x^3-4x+7)`
`Q(x)=-3x^4-2x^3+x^2+x+5+x^4+4x^3+4x-7`
`Q(x)=(-3x^4+x^4)+(-2x^3+4x^3)+x^2+(x+4x)+(5-7)`
`Q(x)=-2x^4+2x^3+x^2+5x-2`
`F(x)=Q(x)-(-2x^4+2x^3+x^2-12)`
`F(x)=(-2x^4+2x^3+x^2+5x-2)-(-2x^4+2x^3+x^2-12)`
`F(x)=-2x^4+2x^3+x^2+5x-2+2x^4-2x^3-x^2+12`
`F(x)=(-2x^4+2x^4)+(2x^3-2x^3)+(x^2-x^2)+5x+(-2+12)`
`F(x)=5x+10`
Đặt `5x+10=0`
`\Leftrightarrow 5x=0-10`
`\Leftrightarrow 5x=-10`
`\Leftrightarrow x=-10 \div 5`
`\Leftrightarrow x=-2`
Vậy, nghiệm của đa thức là `x=-2.`
a, \(P\left(x\right)=4x^3+2x-3+2x-2x^2-1\\ =4x^3-2x^2+\left(2x+2x\right)+\left(-3-1\right)\\ =4x^3-2x^2+4x-4\)
Bậc của P(x) là 3
\(Q\left(x\right)=6x^3-3x+5-2x+3x^2\\ =6x^3+3x^2+\left(-3x-2x\right)+5\\ =6x^3+3x^2-5x+5\)
Bậc của Q(x) là 3
b, \(M\left(x\right)=P\left(x\right)+Q\left(x\right)=4x^3-2x^2+4x-4+6x^3+3x^2-5x+5\\ =\left(4x^3+6x^3\right)+\left(-2x^2+3x^2\right)+\left(4x-5x\right)+\left(-4+5\right)\\ =10x^3+x^2-x+1\)
1: P(x)=M(x)+N(x)
=-2x^3+x^2+4x-3+2x^3+x^2-4x-5
=2x^2-8
2: P(x)=0
=>x^2-4=0
=>x=2 hoặc x=-2
3: Q(x)=M(x)-N(x)
=-2x^3+x^2+4x-3-2x^3-x^2+4x+5
=-4x^3+8x+2
P(x)= 4x^3 + 2x^2 - 2x + 7 - x^2 - x
Q(x)= -4x^3 + x- 14 - 2x- x^2 - 1
P(x) = - Q(x)
<=> P(x) + Q(x) = 0
<=> 4x^3 + 2x^2 - 2x + 7 - x^2 - x -4x^3 + x- 14 - 2x- x^2 - 1 = 0
<=> -4x - 8 = 0
<=> -4(x+2) = 0
<=> x = -2