Bài 1. Cho hai đa thức \(f\)(\(x\))= 5\(x\)4+4\(x\)2-2\(x\)+7 và \(g\)(\(x\))=4\(x\)4-2\(x\)3+3\(x\)2+4\(x\)-1
Tính \(f\)(\(x\)) + \(g\)(\(x\)) và \(f\)(\(x\)) - \(f\)(\(x\))
Bài 2. Thực hiện phép nhân.
a) (\(x\) + 3).(\(x\) - 1) b) (4\(x\) + 3).(\(x\)- 2)
c) (2\(x\) + 3).(\(x\) + 1) d) (5\(x\)-2).(\(x\)2- 3\(x\) + 1)
Bài 3. Tính giá trị biểu thức.
a) M=3\(x\)2-2\(x\).(\(x\)-5)+\(x\).(\(x\)-7) tại \(x\)=5
b) J=-3\(x\)2+4\(x\)-5.(\(x\)-2) tại \(x\)=-5
c) N=4\(x\).(2\(x\)-3)-5\(x \).(\(x\)-2) tại\(x\)=1
`1,`
`f(x)+g(x)=(5x^4+4x^2-2x+7)+(4x^4-2x^3+3x^2+4x-1)`
`= 5x^4+4x^2-2x+7+4x^4-2x^3+3x^2+4x-1`
`=(5x^4+4x^4)-2x^3+(4x^2+4x^2)+(-2x+4x)+(7-1)`
`= 9x^4-2x^3+8x^2+2x+6`
Đề phải là `f(x)-g(x)` chứ nhỉ :v?
`f(x)-g(x)=(5x^4+4x^2-2x+7)-(4x^4-2x^3+3x^2+4x-1)`
`= 5x^4+4x^2-2x+7-4x^4+2x^3-3x^2-4x+1`
`= (5x^4-4x^4)+2x^3+(-2x-4x)+(4x^2-3x^2)+(7+1)`
`= x^4+2x^3-6x+x^2+8`
`2,`
`a, (x+3)(x-1)`
`= x(x-1)+3(x-1)`
`= x*x+x*(-1)+3*x+3*(-1)`
`=x^2-x+3x-3`
`= x^2+2x-3`
`b, (4x+3)(x-2)`
`= 4x(x-2)+3(x-2)`
`= 4x*x+4x*(-2)+3*x+3*(-2)`
`= 4x^2-8x+3x-6`
`c, (2x+3)(x+1)`
`= 2x(x+1)+3(x+1)`
`= 2x*x+2x*1+3*x+3*1`
`= 2x^2+2x+3x+3`
`= 2x^2+5x+3`
`d, (5x-2)(x^2-3x+1)`
`= 5x(x^2-3x+1)+(-2)(x^2-3x+1)`
`= 5x*x^2+5x*(-3x)+5x*1+(-2)*x^2+(-2)*(-3x)+(-2)*1`
`= 5x^3-15x^2+5x-2x^2+6x-2`
`= 5x^3-17x^2+11x-2`
`3,`
`a, M=`\(3x^2-2x(x-5)+x(x-7)\)
`M=3x^2-(2x^2-10x)+x^2-7x`
`M=3x^2-2x^2+10x+x^2-7x`
`M=2x^2+3x`
Thay` x=5`
`-> M=2*5^2+3*5=2*25+15=50+15=65`
`b,`
`J=-3x^2+4x-5(x-2)`
`J=-3x^2+4x-(5x-10)`
`J=-3x^2+4x-5x+10`
`J=-3x^2-x+10`
Thay `x=-5`
`-> J=-3*(-5)^2-(-5)+10=-3*25+5+10=-75+5+10=-70+10=-60`
`c,`
`N=4x(2x-3)-5x(x-2)`
`N=4x*2x+4x*(-3)-[5x*x+5x*(-2)]`
`N=8x^2-12x-(5x^2-10x)`
`N=8x^2-12x-5x^2+10x`
`N=3x^2-2x`
Thay `x=1`
`-> N=3*1^2-2*1=3-2=1`