What is (a^4+5a^3+2a^2-6a+4)(a+2)^{-1} ?

The solution to (a^4+5a^3+2a^2-6a+4)(a+2)^{-1} is a^3+3a^2-4a+2

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simplify (a^4+5a^3+2a^2-6a+4)(a+2)^{-1}

simplify

(a^{4} + 5 a^{3} + 2 a^{2} - 6 a + 4) (a + 2)^{- 1}

a^{3} + 3 a^{2} - 4 a + 2

Solution steps

(a^{4} + 5 a^{3} + 2 a^{2} - 6 a + 4) (a + 2)^{- 1}

Apply exponent rule:

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

(a + 2)^{- 1} = \frac{1}{a + 2}

= (a^{4} + 5 a^{3} + 2 a^{2} - 6 a + 4) \frac{1}{a + 2}

Apply the fraction rule:

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

= \frac{( a ^{4} + 5 a ^{3} + 2 a ^{2} - 6 a + 4 ) \cdot 1}{a + 2}

Apply rule:

a \cdot 1 = a

(a^{4} + 5 a^{3} + 2 a^{2} - 6 a + 4) \cdot 1 = (a^{4} + 5 a^{3} + 2 a^{2} - 6 a + 4)

= \frac{a ^{4} + 5 a ^{3} + 2 a ^{2} - 6 a + 4}{a + 2}

Factor

a^{4} + 5 a^{3} + 2 a^{2} - 6 a + 4 : (a + 2) (a^{3} + 3 a^{2} - 4 a + 2)

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

Cancel the common factor:

a + 2

= a^{3} + 3 a^{2} - 4 a + 2

x \cdot 1 - x^{2}

2.7489 \cdot 1 0^{8} \cdot e^{- \frac{4278.6}{273 + 20 + 242.79}}

(5 + 26) (5 - 26)

(3 r^{2}) (6 rs) (- 2 r) (- 4 s^{2})

(- 3)^{n} (- \frac{1}{3})^{n}

What is (a^4+5a^3+2a^2-6a+4)(a+2)^{-1} ?
The solution to (a^4+5a^3+2a^2-6a+4)(a+2)^{-1} is a^3+3a^2-4a+2