What is factor x^4+3x^3-20x^2-84x-80 ?

The solution to factor x^4+3x^3-20x^2-84x-80 is (x+2)^2(x+4)(x-5)

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factor x^4+3x^3-20x^2-84x-80

factor

x^{4} + 3 x^{3} - 20 x^{2} - 84 x - 80

(x + 2)^{2} (x + 4) (x - 5)

Solution steps

x^{4} + 3 x^{3} - 20 x^{2} - 84 x - 80

Use the rational root theorem

= (x + 2) \frac{x ^{4} + 3 x ^{3} - 20 x ^{2} - 84 x - 80}{x + 2}

\frac{x ^{4} + 3 x ^{3} - 20 x ^{2} - 84 x - 80}{x + 2} = x^{3} + x^{2} - 22 x - 40

= (x + 2) (x^{3} + x^{2} - 22 x - 40)

Factor

x^{3} + x^{2} - 22 x - 40 : (x + 2) (x + 4) (x - 5)

= (x + 2) (x + 2) (x + 4) (x - 5)

Apply exponent rule:

aa = a^{2}

(x + 2) (x + 2) = (x + 2)^{2}

= (x + 2)^{2} (x + 4) (x - 5)

(3 x - 1)^{2} = 22

9 x + 5 > 23

(5 x)^{- \frac{5}{4}}

x^{2} (x - 2) < 0

\frac{x + 4}{x + 9} < 2

What is factor x^4+3x^3-20x^2-84x-80 ?
The solution to factor x^4+3x^3-20x^2-84x-80 is (x+2)^2(x+4)(x-5)