What is factor x^4+6x^3+10x^2+6x+9 ?

The solution to factor x^4+6x^3+10x^2+6x+9 is (x+3)^2(x^2+1)

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factor x^4+6x^3+10x^2+6x+9

factor

x^{4} + 6 x^{3} + 10 x^{2} + 6 x + 9

(x + 3)^{2} (x^{2} + 1)

Solution steps

x^{4} + 6 x^{3} + 10 x^{2} + 6 x + 9

Use the rational root theorem

= (x + 3) \frac{x ^{4} + 6 x ^{3} + 10 x ^{2} + 6 x + 9}{x + 3}

\frac{x ^{4} + 6 x ^{3} + 10 x ^{2} + 6 x + 9}{x + 3} = x^{3} + 3 x^{2} + x + 3

= (x + 3) (x^{3} + 3 x^{2} + x + 3)

Factor

x^{3} + 3 x^{2} + x + 3 : (x + 3) (x^{2} + 1)

= (x + 3) (x + 3) (x^{2} + 1)

Apply exponent rule:

aa = a^{2}

(x + 3) (x + 3) = (x + 3)^{2}

= (x + 3)^{2} (x^{2} + 1)

- x^{3} 48 - 2 3 x^{6}

\frac{- 7 x - 8}{4} + \frac{x + 5}{4}

(3 k + 1)^{2}

3 \cdot 48

What is factor x^4+6x^3+10x^2+6x+9 ?
The solution to factor x^4+6x^3+10x^2+6x+9 is (x+3)^2(x^2+1)