What is (z^4-3z^3+2z^2-4z+4)(z-1)^{-1} ?

The solution to (z^4-3z^3+2z^2-4z+4)(z-1)^{-1} is z^3-2z^2-4

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simplify (z^4-3z^3+2z^2-4z+4)(z-1)^{-1}

simplify

(z^{4} - 3 z^{3} + 2 z^{2} - 4 z + 4) (z - 1)^{- 1}

z^{3} - 2 z^{2} - 4

Solution steps

(z^{4} - 3 z^{3} + 2 z^{2} - 4 z + 4) (z - 1)^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

(z - 1)^{- 1} = \frac{1}{z - 1}

= (z^{4} - 3 z^{3} + 2 z^{2} - 4 z + 4) \frac{1}{z - 1}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( z ^{4} - 3 z ^{3} + 2 z ^{2} - 4 z + 4 ) \cdot 1}{z - 1}

Apply rule:

a \cdot 1 = a

(z^{4} - 3 z^{3} + 2 z^{2} - 4 z + 4) \cdot 1 = (z^{4} - 3 z^{3} + 2 z^{2} - 4 z + 4)

= \frac{z ^{4} - 3 z ^{3} + 2 z ^{2} - 4 z + 4}{z - 1}

Factor

z^{4} - 3 z^{3} + 2 z^{2} - 4 z + 4 : (z - 1) (z^{3} - 2 z^{2} - 4)

= \frac{( z - 1 ) ( z ^{3} - 2 z ^{2} - 4 )}{z - 1}

Cancel the common factor:

z - 1

= z^{3} - 2 z^{2} - 4

j^{2} (j + 1)^{2}

(x + 1)^{- 1}

(0.045 x^{750}) x^{4}

(6.67 \cdot 1 0^{- 11}) (58.8) (5.97 \cdot 1 0^{24})

(25 - x^{2})^{2}

What is (z^4-3z^3+2z^2-4z+4)(z-1)^{-1} ?
The solution to (z^4-3z^3+2z^2-4z+4)(z-1)^{-1} is z^3-2z^2-4