Bài 1: Làm tính chia
\(\left(2x^3-9x^2+19x-15\right):\left(x^2-3x+5\right)\)
Những câu hỏi liên quan
Thực hiện phép tính
a, \(\left(3x^4-8x^3-10x^2+8x-5\right):\left(3x^2-2x+1\right)\)
b,\(\left(2x^3-9x^2+19x-15\right):\left(x^2-3x+5\right)\)
c,\(\left(8x^3-y^3\right)\left(4x^2-y^2\right):\left(2x+y\right)\left(4x^2-4xy+y^2\right)\)
\(\frac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)
\(=\frac{x^2\left(3x^2-2x+1\right)-2x\left(3x^2-2x+1\right)-5\left(3x^2-2x+1\right)}{3x^2-2x+1}\)
\(=\frac{\left(3x^2-2x+1\right)\cdot\left(x^2-2x-5\right)}{3x^2-2x+1}\)
\(=x^2-2x-5\)
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\(\frac{2x^3-9x^2+19x-15}{x^2-3x+5}\)
\(=\frac{2x\left(x^2-3x+5\right)-3\left(x^2-3x+5\right)}{x^2-3x+5}\)
\(=\frac{\left(x^2-3x+5\right)\left(2x-3\right)}{x^2-3x+5}\)
\(=2x-3\)
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\(\frac{\left(8x^3-y^3\right)\left(4x^2-y^2\right)}{\left(2x+y\right)\left(4x^2-4xy+y^2\right)}\)
\(=\frac{\left(2x-y\right)\left(4x^2+2xy+y^2\right)\left(2x-y\right)\left(2x+y\right)}{\left(2x+y\right)\left(2x-y\right)^2}\)
\(=4x^2+2xy+y^2\)
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Thực hiện phép tính
a,\(\left(3x^4-8x^3-10x^2+8x-5\right):\left(3x^2-2x+1\right)\)
b,\(\left(2x^3-9x^2+19x-15\right):\left(x^2-3x+5\right)\)
c,\(\left(8x^3-y^3\right)\left(4x^2-y^2\right):\left(2x+y\right)\left(4x^2-4xy+y^2\right)\)
a)làm tính nhân: (x+2)\(\left(x^2+3x+1\right)\)
b)Làm tính chia: \(\left(2x^3+10x^2+9x+4\right):\left(x+4\right)\)
a) (x + 2)(x2 + 3x + 1)
= x.x2 + x.3x + x.1 + 2.x2 + 2.3x + 2.1
= x3 + 3x2 + x + 2x2 + 6x + 2
= x3 + 5x2 + 7x + 2
b) (2x3 + 10x2 + 9x + 4) : (x + 4)
= (2x3 + 8x2 + 2x2 + 8x + x + 4) : (x + 4)
= [(2x3 + 8x2) + (2x2 + 8x) + (x + 4)] : (x + 4)
= [2x2(x + 4) + 2x(x + 4) + (x + 4)] : (x + 4)
= (x + 4)(2x2 + 2x + 1) : (x + 4)
= 2x2 + 2x + 1
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Làm tính chia :
a) \(\left(2x^5-5x^3+x^2+3x-1\right):\left(x^2-1\right)\)
b) \(\left(5x^5-2x^4-9x^3+7x^2-18x-3\right):\left(x^2-3\right)\)
giải pt:
a,\(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{-4x^2+16x-15}\)
b,\(\left(9x-2\right)\sqrt{3x-1}+\left(10-9x\right)\sqrt{3-3x}-4\sqrt{-9x^2+12x-3}=4\)
c, \(\left(6x-5\right)\sqrt{x+1}-\left(6x+2\right)\sqrt{x-1}+4\sqrt{x^2-1}=4x-3\)
Tìm x:a) 3xleft(3x-8right)-9x^2+80b)6x-15-xleft(5-2xright)0c) x^3-16x0d) 2x^2+3x-50e) 3x^2-xleft(3x-6right)36f) left(x+2right)^2-left(x-5right)left(x+1right)17g) left(x-4right)^2-xleft(x+6right)9h) 4xleft(x-1000right)-x+10000i) x^2-360j) x^2y-2+x+x^2-2y+xy0k) xleft(x+1right)-left(x-1right).left(2x-3right)0l) 3x^3-27x0
Đọc tiếp
Tìm x:
a) \(3x\left(3x-8\right)-9x^2+8=0\)
b)\(6x-15-x\left(5-2x\right)=0\)
c) \(x^3-16x=0\)
d) \(2x^2+3x-5=0\)
e) \(3x^2-x\left(3x-6\right)=36\)
f) \(\left(x+2\right)^2-\left(x-5\right)\left(x+1\right)=17\)
g) \(\left(x-4\right)^2-x\left(x+6\right)=9\)
h) \(4x\left(x-1000\right)-x+1000=0\)
i) \(x^2-36=0\)
j) \(x^2y-2+x+x^2-2y+xy=0\)
k) \(x\left(x+1\right)-\left(x-1\right).\left(2x-3\right)=0\)
l) \(3x^3-27x=0\)
Bài 1 : Ko thực hiện phép chia , hãy xem phép chia sau đây có là phép chia hết ko và tìm đa thức dư trong trg hợp ko chia hết :
a) \(\left(x^3+2x^2-3x+9\right):\left(x+3\right)\)
b) \(\left(9x^4-6x^3+15x^2+2x+1\right):\left(3x^2-2x+5\right)\)
b)\(\frac{9x^4-6x^3+15x^2+2x+1}{3x^2-2x+5}=\frac{3x^2.\left(3x^2-2x+5\right)+2x+1}{3x^2-2x+5}=3x^2+\frac{2x+1}{3x^2-2x+5}\)
=> đa thức dư trong phép chia là 2x+1
\(\frac{x^3+2x^2-3x+9}{x+3}=\frac{x^3+9x^2+27x+27-7x^2-30x-18}{x+3}=\frac{\left(x+3\right)^3-7x^2-30x-18}{x+3}\)
\(\left(x+3\right)^2-\frac{7x^2+21x+9x+18}{x+3}=\left(x+3\right)^2-\frac{7x.\left(x+3\right)+9.\left(x+3\right)-9}{x+3}\)
\(=\left(x+3\right)^2-\frac{\left(7x+9\right).\left(x+3\right)-9}{x+3}=\left(x+3\right)^2-\left(7x+9\right)-\frac{9}{x+3}\)
=> đa thức dư trong phép chia là 9
p/s: t mới lớp 7_sai sót mong bỏ qua :>
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25 tháng 2 2023 lúc 14:40
Tính:
\(a)\left(-2x^2\right)\cdot\left(3x-4x^3+7-x^2\right)\)
\(b)\left(x+3\right)\cdot\left(2x^2-3x-5\right)\)
\(c)\left(-6x^5+7x^4-6x^3\right):3x^3\)
\(d)\left(9x^2-4\right):\left(3x+2\right)\)
\(e)\left(2x^4-13x^3+15x^2+11x-3\right):\left(x^2-4x-3\right)\)
a: \(=-2x^2\cdot3x+2x^2\cdot4X^3-2x^2\cdot7+2x^2\cdot x^2\)
\(=8x^5+2x^4-6x^3-14x^2\)
b: \(=2x^3-3x^2-5x+6x^2-9x-15\)
\(=2x^3+3x^2-14x-15\)
c: \(=\dfrac{-6x^5}{3x^3}+\dfrac{7x^4}{3x^3}-\dfrac{6x^3}{3x^3}=-2x^2+\dfrac{7}{3}x-2\)
d: \(=\dfrac{\left(3x-2\right)\left(3x+2\right)}{3x+2}=3x-2\)
e: \(=\dfrac{2x^4-8x^3-6x^2-5x^3+20x^2+15x+x^2-4x-3}{x^2-4x-3}\)
=2x^2-5x+1
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giải pt :
a,\(\left(6x-5\right)\sqrt{x+1}-\left(6x+2\right)\sqrt{x-1}+4\sqrt{x^2-1}=4x-3\)
b, \(\left(9x-2\right)\sqrt{3x-1}+\left(10-9x\right)\sqrt{3-3x}-4\sqrt{-9x^2+12x-3}=4\)
c, \(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{-4x^2+16x-15}\)