What is factor 3x^4-4x^3+1 ?

The solution to factor 3x^4-4x^3+1 is (x-1)^2(3x^2+2x+1)

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factor 3x^4-4x^3+1

factor

3 x^{4} - 4 x^{3} + 1

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

Solution steps

3 x^{4} - 4 x^{3} + 1

Use the rational root theorem

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

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

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

Factor

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

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

Apply exponent rule:

aa = a^{2}

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

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

(x + 5)^{2} - 3

10 + (- 2)

10 + (- 7)

- 4 \times 7

- \frac{1}{4} - 3

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