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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: A(x)=x^4+3x^3-2x^2+x+1
B(x)=2x^4-x^3+3x^2-4x-5
b: A(x)+B(x)
=x^4+3x^3-2x^2+x+1+2x^4-x^3+3x^2-4x-5
=3x^4+2x^3+x^2-3x-4
A(x)-B(x)
=x^4+3x^3-2x^2+x+1-2x^4+x^3-3x^2+4x+5
=-x^4+4x^3-5x^2+5x+6
A(x)+B(x)=2x-3x3+2x2+1+4x3+2x2-5
= x3+4x2+2x-4
thay x=1 vào B(x) ta được
B(x)=4.13+2.13-5
=4+2-5
=1
\(A\left(x\right)+B\left(x\right)=\left(x+2\right)\left(x^2+2x-2\right)\)
thay x=1 \(=>A\left(1\right)+B\left(1\right)=3\left(1+2-2\right)=3\)
\(a,A\left(x\right)=2x^3-3x^2+2x+1\\ B\left(x\right)=3x^3+2x^2-x-5\\ b,A\left(x\right)+B\left(x\right)=\left(2x^3+3x^3\right)+\left(2x^2-3x^2\right)+\left(2x-x\right)+\left(1-5\right)=5x^3-x^2+x-4\\ A\left(x\right)-B\left(x\right)=\left(2x^3-3x^3\right)+\left(-3x^2-2x^2\right)+\left(2x+x\right)+\left(1-5\right)=-x^3-5x^2+3x-4\)
a)
\(A\left(x\right)=3x^3+3x^2+2x-1\)
Bậc của A(x) là 3
Hệ số tự do A(x) là -1
Hệ số cao nhất của A(x) là 3
Tại A(-2)
\(A=3.\left(-2\right)^3+3.\left(-2\right)^2+2.\left(-2\right)-1\)
\(=-17\)
b)
\(B\left(x\right)=5x^4+6x-2x^2+4-5x^4-5x\)
\(=\left(5x^4-5x^4\right)+\left(-2x^2\right)+\left(6x-5x\right)+4\)
\(=-2x^2+x+4\)
c)
\(A\left(x\right)-B\left(x\right)=3x^3+3x^2+2x-1-\left(-2x^2+x+4\right)\)
\(=3x^3+3x^2+2x-1+2x^2-x-4\)
\(=3x^3+\left(3x^2+2x^2\right)+\left(2x-x\right)+\left(-1-4\right)\)
\(=3x^3+5x^2+x-5\)
d)
\(C\left(x\right)-2.\left(-2x^2+x+4\right)=3x^3+3x^2+2x-1\)
\(C\left(x\right)=3x^3+3x^2+2x-1+2.\left(-2x^2+x+4\right)\)
\(C\left(x\right)=3x^3+3x^2+2x-1-4x^2+2x+8\)
\(C\left(x\right)=3x^3+\left(3x^2-4x^2\right)+\left(2x+2x\right)+\left(-1+8\right)\)
\(C\left(x\right)=3x^3-x^2+4x+7\)
chúc bạn học giỏi
`a,A(x)=2x^3+2x-3x^2+11`
`=2x^3-3x^2+2x+11`
`B(x)=2^2+3x^3-x-5`
`=3x^3+2x^2-x-5`
`b, A(x)+B(x)=(2x^3-3x^2+2x+11)+(3x^3+2x^2-x-5)`
`=2x^3-3x^2+2x+11+3x^3+2x^2-x-5`
`=(2x^3+3x^3)+(-3x^2+2x^2)+(2x-x)+(11-5)`
`=5x^3 -x^2 +x+6`
`c,A(x)-B(x)=(2x^3-3x^2+2x+11)-(3x^3+2x^2-x-5)`
`=2x^3-3x^2+2x+11- 3x^3 -2x^2+x+5`
`=(2x^3-3x^3)+(-3x^2-2x^2)+(2x+x)+(11+5)`
`=-x^3 -5x^2+3x+16`
a/\(A\left(x\right)=2x^3+2x-3x^2+11\)
\(=2x^3-3x^2+2x+11\)
\(B\left(x\right)=2x^2+3x^3-x-5\)
\(=3x^3+2x^2-x-5\)
b/\(A\left(x\right)+B\left(x\right)=\left(2x^3-3x^2+2x+11\right)+\left(3x^3+2x^2-x-5\right)\)
\(=2x^3-3x^2+2x+11+3x^3+2x^2-x-5\)
\(=\left(2x^3+3x^3\right)-\left(3x^2-2x^2\right)+\left(2x-x\right)+\left(11-5\right)\)
\(=5x^3-x^2+x+6\)
c/\(A\left(x\right)+B\left(x\right)=\left(2x^3-3x^2+2x+11\right)-\left(3x^3+2x^2-x-5\right)\)
\(=2x^3-3x^2+2x+11-3x^3-2x^2+x+5\)
\(=\left(2x^3-3x^3\right)-\left(3x^2+2x^2\right)+\left(2x+x\right)+\left(11+5\right)\)
\(=-x^3-5x^2+3x+16\)
#DarkPegasus
Ta đặt và thực hiện phép tính P(x) + Q(x) và P(x) – Q(x) có
Vậy: P(x) + Q(x) = – 6 + x + 2x2 – 5x3 + 2x5 – x6
P(x) – Q(x) = – 4 – x – 3x3 + 2x4 - 2x5 – x6
\(A\left(x\right)=x^5+3x^3-x^5+x-1=3x^3+x-1\)
Bậc : 4
\(B\left(x\right)=3x^3-2x^2-1\)
Bậc : 5
\(A\left(x\right)+B\left(x\right)=3x^3+x-1+3x^3-2x^2-1\)
\(=6x^3-2x^2+x-2\)
P(x) = 3x2 – 5 + x4 – 3x3 – x6 – 2x2 – x3
= – x6 + x4 + (– 3x3 – x3) + (3x2 – 2x2) – 5
= – x6 + x4 – 4x3 + x2 – 5.
= – 5+ x2 – 4x3 + x4 – x6
Và Q(x) = x3 + 2x5 – x4 + x2 – 2x3 + x –1
= 2x5 – x4 + (x3 – 2x3) + x2 + x –1
= 2x5 – x4 – x3 + x2 + x –1.
= –1+ x + x2 – x3 – x4 + 2x5
\(\left(x+3\right)\left(x-1\right)=x\left(x-1\right)+3\left(x-1\right)=x^2-x+3x-3=x^2+2x-3\)
\(\left(3x^3-2x^2\right):3x^2=3x^3:3x^2-2x^2:3x^2=x-\dfrac{2}{3}\)