a) \(\left(x^2+2x+1\right)\left(x+1\right)\)

\(=x^3+x^2+2x^2+2x+x+1\)

\(=x^3+3x^2+3x+1\)

b) Ta có: \(\left(x^3-x^2+2x-1\right)\left(5-x\right)\)

\(=5x^3-x^4-5x^2+x^3+10x-2x^2-5+5x\)

\(=-x^4+6x^3-7x^2+15x-5\)

Ta có: \(\left(x-5\right)\left(x^3-x^2+2x-1\right)\)

\(=-\left(5-x\right)\left(x^3-x^2+2x-1\right)\)

\(=x^4-6x^3+7x^2-15x+5\)

= 5.x³ - 2 x².5 + x.5 - 1.5 x.x³ -2x².x+ x.x-1.x

=5x³ - 10x² + 5x - 5 -x⁴ - 2x³ + x^{2- x}

= x⁴ + 3x³ - 9x² + 4x

a,\(\left(x+2x+1\right)\left(x+1\right)\)

\(=\left(3x+1\right)\left(x+1\right)\)

\(=3x^2+3x+x+1\)

\(=3x^2+4x+1\)

b,\(\left(x^3-x^2+2x-1\right)\left(5-x\right)\)

\(=5x^3-5x^2+10x-5-x^4+x^3-2x^2+x\)

\(=-x^4+6x^3-7x^2+11x-5\)

a) \(\left(x+2x+1\right)\left(x+1\right)\)

\(=\left(3x+1\right)\left(x+1\right)\)

\(=3x^2+3x+x+1\)

\(=3x^2+4x+1\)

b) \(\left(x^3-x^2+2x-1\right)\left(5-x\right)\)

\(=5x^3-5x^2+10x-5-x^4+x^3-2x^2+x\)

\(=-x^4+6x^3-7x^2+11x-5\)

=x³-x²-2x²+2x+x-1

=x³-3x²+3x-1

=(x-1)³

=> (x^3-2x^2+x-1)(x-5) = x^4-7x^3+11x^2-6x+5

mai em cần rồi, em cản ơn nhiều!

Nếu thực hiện chia theo lược đồ Hoocne thì kết quả như thế này:

\(f\left(x\right)=\left(x^2+2x-3\right)\left(x^3-2x^2+7x-23\right)+68\)

Hay \(f\left(x\right)\) chia \(x^2+2x-3\) được thương \(x^3-2x^2+7x-23\) và dư \(68\)

`a)`

`A(x) + B(x) = 2x - 4x^2 + 1 + x^3 - 4x^2 + 5 - 2x`

                  `= x^3 - ( 4x^2 + 4x^2 ) + ( 2x - 2x ) + ( 1+ 5 )`

                  `= x^3 - 8x^2 + 6`

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`b)`

    `P(x) + B(x) = A(x)`

`=>P(x) = A(x) - B(x)`

`=>P(x) = 2x - 4x^2 + 1 + x^3 + 4x^2 - 5 + 2x`

`=>P(x) = x^3 + ( -4x^2 + 4x^2 ) + ( 2x + 2x ) + ( 1 - 5 )`

`=>P(x) = x^3 + 4x - 4`