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\(a,N\left(x\right)=x^2+3x^4-2x-x^2+2x^3=3x^4+2x^3+\left(x^2-x^2\right)-2x\\ =3x^4+2x^3-2x\\ P\left(x\right)=-8+5x-6x^3-4x+6=-6x^3+\left(5x-4x\right)+\left(-8+6\right)\\ =-6x^3+x-2\)
Bậc của N(x) là 4
Bậc của P(x) là 3
\(b,P\left(x\right)+N\left(x\right)=3x^4+2x^3-2x-6x^3+x-2\\ =3x^4+\left(2x^3-6x^3\right)+\left(-2x+x\right)-2\\ =3x^4-4x^3-x-2\)
\(c,B\left(x\right)=-2x^2\left(x^3-2x+5x^2-1\right)\\ =\left(-2x^2\right).x^3+\left(-2x^2\right).\left(-2x\right)+\left(-2x^2\right).5x^2+\left(-2x^2\right).\left(-1\right)\\ =-2x^5+4x^3-10x^4+2x^2\\ =-2x^5-10x^4+4x^3+2x^2\)
`@` `\text {Ans}`
`\downarrow`
`a)`
Thu gọn:
`P(x)=`\(5x^4 + 3x^2 - 3x^5 + 2x - x^2 - 4 +2x^5\)
`= (-3x^5 + 2x^5) + 5x^4 + (3x^2 - x^2) + 2x - 4`
`= -x^5 + 5x^4 + 2x^2 + 2x - 4`
`Q(x) =`\(x^5 - 4x^4 + 7x - 2 + x^2 - x^3 + 3x^4 - 2x^2\)
`= x^5 + (-4x^4 + 3x^4) - x^3 + (x^2 - 2x^2) + 7x - 2`
`= x^5 - x^4 - x^3 - x^2 + 7x - 2`
`@` Tổng:
`P(x)+Q(x)=`\((-x^5 + 5x^4 + 2x^2 + 2x - 4) + (x^5 - x^4 - x^3 - x^2 + 7x - 2)\)
`= -x^5 + 5x^4 + 2x^2 + 2x - 4 + x^5 - x^4 - x^3 - x^2 + 7x - 2`
`= (-x^5 + x^5) - x^3 + (5x^4 - x^4) + (2x^2 - x^2) + (2x + 7x) + (-4-2)`
`= 4x^4 - x^3 + x^2 + 9x - 6`
`@` Hiệu:
`P(x) - Q(x) =`\((-x^5 + 5x^4 + 2x^2 + 2x - 4) - (x^5 - x^4 - x^3 - x^2 + 7x - 2)\)
`= -x^5 + 5x^4 + 2x^2 + 2x - 4 - x^5 + x^4 + x^3 + x^2 - 7x + 2`
`= (-x^5 - x^5) + (5x^4 + x^4) + x^3 + (2x^2 + x^2) + (2x - 7x) + (-4+2)`
`= -2x^5 + 6x^4 + x^3 + 3x^2 - 5x - 2`
`b)`
`@` Thu gọn:
\(H (x) = ( 3x^5 - 2x^3 + 8x + 9) - ( 3x^5 - x^4 + 1 - x^2 + 7x)\)
`= 3x^5 - 2x^3 + 8x + 9 - 3x^5 + x^4 - 1 + x^2 - 7x`
`= (3x^5 - 3x^5) + x^4 - 2x^3 - x^2 + (8x + 7x) + (9+1)`
`= x^4 - 2x^3 - x^2 + 15x + 10`
\(R( x) = x^4 + 7x^3 - 4 - 4x ( x^2 + 1) + 6x\)
`= x^4 + 7x^3 - 4 - 4x^3 - 4x + 6x`
`= x^4 + (7x^3 - 4x^3) + (-4x + 6x) - 4`
`= x^4 + 3x^3 + 2x - 4`
`@` Tổng:
`H(x)+R(x)=` \((x^4 - 2x^3 - x^2 + 15x + 10)+(x^4 + 3x^3 + 2x - 4)\)
`= x^4 - 2x^3 - x^2 + 15x + 10+x^4 + 3x^3 + 2x - 4`
`= (x^4 + x^4) + (-2x^3 + 3x^3) - x^2 + (15x + 2x) + (10-4)`
`= 2x^4 + x^3 - x^2 + 17x + 6`
`@` Hiệu:
`H(x) - R(x) =`\((x^4 - 2x^3 - x^2 + 15x + 10)-(x^4 + 3x^3 + 2x - 4)\)
`=x^4 - 2x^3 - x^2 + 15x + 10-x^4 - 3x^3 - 2x + 4`
`= (x^4 - x^4) + (-2x^3 - 3x^3) - x^2 + (15x - 2x) + (10+4)`
`= -5x^3 - x^2 + 13x + 14`
`@` `\text {# Kaizuu lv u.}`
a) A(x) = 2x3 + 5 + x2 - 3x - 5x3 - 4
= 2x3 - 5x3 + x2 - 3x + 5 - 4
= -3x3 + x2 - 3x + 1
B(x) = -3x4 - x3 + 2x2 + 2x + x4 - 4 - x2
= -3x4 + x4 - x3 + 2x2 - x2 + 2x - 4
= -2x4 - x3 + x2 + 2x - 4
b)
H(x) = A(x) - B(x)
H(x) = (-3x3 + x2 - 3x + 1) - (-2x4 - x3 + x2 + 2x - 4)
= -3x3 + x2 - 3x + 1 + 2x4 + x3 - x2 - 2x + 4
= 2x4 - 3x3 + x3 + x2 - x2 - 3x - 2x + 1 + 4
= 2x4 - 2x3 -5x + 5
Bài 1:
a) \(3x^2\left(2x^3-x+5\right)-6x^5-3x^3+10x^2\)
\(=6x^5-3x^3+10x^2-6x^5-3x^3+10x^2\)
\(=10x^2+10x^2\)
\(=20x^2\)
b) \(-2x\left(x^3-3x^2-x+11\right)-2x^4+3x^3+2x^2-22x\)
\(=-2x^4+6x^3+2x^2-22x-2x^4+3x^3+2x^2-22x\)
\(=-4x^4+9x^3+4x^2-44x\)
a) Đặt A(x)=0
\(\Leftrightarrow-4x-5=0\)
\(\Leftrightarrow-4x=5\)
hay \(x=-\dfrac{5}{4}\)
b) Đặt B(x)=0
\(\Leftrightarrow3\left(2x-1\right)-2\left(x+1\right)=0\)
\(\Leftrightarrow6x-3-2x-2=0\)
\(\Leftrightarrow4x=5\)
hay \(x=\dfrac{5}{4}\)
a)⇔A= x4+2x3-5x+9+2x4-2x3= 3x4-5x+9
⇔B= 2x2-6x+2-3x4-2x2+3x-4= -3x4-3x-2
b)A(x)+B(x)= 3x4-5x+9-3x4-3x-2= -8x+7
A(x)-B(x)= 3x4-5x+9+3x4+3x+2= 6x4-2x+1
c)C(x) có hệ số tự do bằng 0 nên có nghiệm bằng 0
d)A(x)+5x= 3x4+9. Tại x bất kì thì 3x4≥0 ⇔ 3x4+9 ≥ 9 ≥ 0
⇒ H(x) vô nghiệm
\(a\\ -5x^2+3x.\left(x+2\right)=-5x^2+3x^2+6x=-2x^2+6x\\ b\\ -2x.\left(1-x^2\right)-2x^3=-2x+2x^3-2x^3=-2x\\ c\\ 4x.\left(x-1\right)-4.\left(x^2+2x-1\right)\\ =4x^2-4x-4x^2-8x+4=-12x+4\)
\(d\\ 6x^3-2x^2.\left(-x^2-3x\right)=6x^3+2x^4+6x^3=2x^4+12x^3\\ e\\ 3x.\left(x-1\right)-\left(1+2x\right).5x\\ =3x^2-3x-5x-10x^2=-7x^2-8x\\ f\\ -5x^2-\left(x-6\right).\left(-2x^2\right)=-5x^2+2x^3-12x^2=2x^3-17x^2\)
cá voi xanh không ? :))))
Ta có : A = -x3(3x - 1) - x(1 + 3x4) - x2(x2 - x - 2)
=> A = x3 - 3x4 - x + 3x5 - x4 - x3 - 2x2
B = -x2(2x2 - 2x - 4) - 2x(2 - 4x4) - 2x3(2x - 2)
=> B = -2x4 + 2x3 + 4x2 - 4x - 8x5 - 4x4 - 4x3
* Rút gọn : A = x3 - 3x4 - x + 3x5 - x4 - x3 - 2x2
=> A = (x3 - x3) + (-3x4 - x4) - x + 3x5 - 2x2
=> A = -4x4 - x + 3x5 - 2x2
B = -2x4 + 2x3 + 4x2 - 4x - 8x5 - 4x4 - 4x3
=> B = (-2x4 - 4x4) + (2x3 - 4x3) + 4x2 - 4x - 8x5
=> B = -6x4 - 2x3 + 4x2 - 4x - 8x5
* Tính A - B
A = 3x5 - 4x4 - 2x2 - x
B = - 8x5 - 6x4 - 2x3 + 4x2 - 4x
-------------------------------------------------------
A - B = 11x5 + 2x4 + 2x3 - 6x2 + 3x
=> A - B = 11x5 + 2x4 + 2x3 - 6x2 + 3x
* Tính B - A
B = -8x5 - 6x4 - 2x3 + 4x2 - 4x
A = 3x5 - 4x4 - 2x2 - x
------------------------------------------------
B - A = -11x5 - 2x4 - 2x3 + 6x2 - 5x
* Tính A + B
A = 3x5 - 4x4 - 2x2 - x
B = -8x5 - 6x4 - 2x3 + 4x2 - 4x
---------------------------------------------------
A + B = -5x5 - 10x4 - 2x3 + 2x2 - 5x
Và cái cuối cùng tự làm nhé
Nếu không biết làm cách 2 thì làm cách 1 trong sách