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a) (x3 – 7x + 3 – x2) : (x – 3)
b) (2x4 – 3x2 – 3x2 – 2 + 6x) : (x2 – 2)
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a: \(=\dfrac{x^4-6x^3+12x^2-14x+3}{x^2-4x+1}\)
\(=\dfrac{x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3}{x^2-4x+1}\)
\(=x^2-2x+3\)
b: \(=\dfrac{x^5-3x^4+5x^3-x^2+3x-5}{x^2-3x+5}=x^2-1\)
c: \(=\dfrac{2x^4-5x^3+2x^2+2x-1}{x^2-x-1}\)
\(=\dfrac{2x^4-2x^3-2x^2-3x^3+3x^2+3x+x^2-x-1}{x^2-x-1}\)
\(=2x^2-3x+1\)
1, \(\left(2x^4-5x^2y^2+3xy^3\right)\left(5x^3+x^2y-y^3\right)\)
\(=10x^7-25x^5y^2+15x^4y^3+2x^6y-5x^4y^3+5x^2y^5+3xy^6\)
2, a, \(4-2x+5x^2-4x^2\&5x-3+x^2\)
Sắp xếp: \(4-2x+5x^2-4x^2=5x^2-4x^2-2x+4=x^2-2x+4\)
\(5x-3+x^2=x^2+5x-3\)
- \(\left(x^2-2x+4\right)\left(x^2+5x-3\right)=x^4+3x^3-9x^2-14x-12\)
b, Làm tương tự câu a
1 ) \(\left(2x^4-5x^2y^2+3xy^3\right)\left(5x^3+x^2y-y^3\right)\)
\(=2x^4\left(5x^3+x^2y-y^3\right)-5x^2y^2\left(5x^3+x^2y-y^3\right)+3xy^3\left(5x^3+x^2y-y^3\right)\)\(=10x^7+2x^6y-2x^4y-25x^5y^2-5x^4y^3+5x^2y^5+15x^4y^3+3x^3y^4-3xy^6\)2 ) a ) \(4-2x+5x^2-4x^2=x^2-2x+4\)
\(5x-3+x^2=x^2+5x-3\)
\(\left(x^2-2x+4\right)\left(x^2+5x-3\right)\)
\(=x^4-2x^3+4x^2+5x^3-10x^2+20x-3x^2+6x-12\)
\(=x^4+3x^3-9x^2+26x-12\)
b ) \(10-x^4+3x-4x^2=-x^4-4x^2+3x+10\)
\(2x+x^3-1=x^3+2x-1\)
\(\left(-x^4-4x^2+3x+10\right)\left(x^3+2x-1\right)\)
\(=-x^4\left(x^3+2x-1\right)-4x^2\left(x^3+2x-1\right)+3x\left(x^3+2x-1\right)+10\left(x^3+2x-1\right)\)\(=-x^7-2x^5+x^4-4x^5-8x^3+4x^2+3x^4+6x^2-3x+10x^3+20x-10\)\(=-x^7-\left(2x^5+4x^5\right)+\left(3x^4+x^4\right)+\left(10x^3-8x^3\right)+\left(4x^2+6x^2\right)+\left(20x-3x\right)-10\)\(=-x^7-6x^5+4x^4+2x^3+10x^2+17x-10\)
C1: Gọi đa thức thương là Q(x)
Vì x^4 : x^2 = x^2
=> đa thức có dạng x^2+mx+n
Đề x^4 - 3x^2 + ax+b chia hết x^2 - 3x + 2
=> x^4 - 3x^2 + ax + b = (x^2 - 3x + 2)(x^2 + mx + n)
x^4+ 0x^3 - 3x^2 +ax+b = x^4 +mx^3 +(x^2)n -3x^3 -3mx^2 - 3xn + 2x^2 + 2mx + 2n
x^4 + 0x^3 -3x^2 + ax+b = x^4 + x^3(m-3) - x^2(3m - n -2) +x(2m - 3n) +2n
<=>| 0 = m-3 <=> | m = 3
| 3=3m-n-2 | b= 8
| a=2m-3n | n = 4
| b = 2n | a = -6
Vậy a= -6, b= 8
a: \(P\left(x\right)=-2x^5+x^4+3x^3-x-\dfrac{1}{2}\)
\(Q\left(x\right)=\dfrac{-2}{3}x^5-x^4-2x^3+\dfrac{1}{2}x\)
b: \(P\left(x\right)+Q\left(x\right)=-2x^5+x^4+3x^3-x-\dfrac{1}{2}-\dfrac{2}{3}x^5-x^4-2x^3+\dfrac{1}{2}x\)
\(=\dfrac{-8}{3}x^5+x^3-\dfrac{1}{2}x-\dfrac{1}{2}\)
b: \(P\left(x\right)-Q\left(x\right)=-2x^5+x^4+3x^3-x-\dfrac{1}{2}+\dfrac{2}{3}x^5+x^4+2x^3-\dfrac{1}{2}x\)
\(=-\dfrac{4}{3}x^5+2x^4+5x^3-\dfrac{3}{2}x-\dfrac{1}{2}\)
2x4 – 3x3 – 3x2 – 2 + 6x = 2x4 – 3x3 – 3x2 + 6x – 2
Thực hiện phép chia:
Vậy (2x4 – 3x3 – 3x2 + 6x – 2) : (x2 – 2) = 2x2 – 3x + 1.