What is factor x^4-14x^3+34x^2+114x+65 ?

The solution to factor x^4-14x^3+34x^2+114x+65 is (x+1)^2(x^2-16x+65)

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factor x^4-14x^3+34x^2+114x+65

factor

x^{4} - 14 x^{3} + 34 x^{2} + 114 x + 65

(x + 1)^{2} (x^{2} - 16 x + 65)

Solution steps

x^{4} - 14 x^{3} + 34 x^{2} + 114 x + 65

Use the rational root theorem

= (x + 1) \frac{x ^{4} - 14 x ^{3} + 34 x ^{2} + 114 x + 65}{x + 1}

\frac{x ^{4} - 14 x ^{3} + 34 x ^{2} + 114 x + 65}{x + 1} = x^{3} - 15 x^{2} + 49 x + 65

= (x + 1) (x^{3} - 15 x^{2} + 49 x + 65)

Factor

x^{3} - 15 x^{2} + 49 x + 65 : (x + 1) (x^{2} - 16 x + 65)

= (x + 1) (x + 1) (x^{2} - 16 x + 65)

Apply exponent rule:

aa = a^{2}

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

= (x + 1)^{2} (x^{2} - 16 x + 65)

12 = 12 + \frac{v - 8}{2}

\frac{3 x - 32}{5} = - 4

2 y + 9 = 8 y + 21

4 = x + 1

1.5 x^{2} - 15.06 x + 0.6 = 0

What is factor x^4-14x^3+34x^2+114x+65 ?
The solution to factor x^4-14x^3+34x^2+114x+65 is (x+1)^2(x^2-16x+65)