What is factor 2x^4+3x^3-9x^2+x+3 ?

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

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factor 2x^4+3x^3-9x^2+x+3

factor

2 x^{4} + 3 x^{3} - 9 x^{2} + x + 3

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

Solution steps

2 x^{4} + 3 x^{3} - 9 x^{2} + x + 3

Use the rational root theorem

= (x - 1) \frac{2 x ^{4} + 3 x ^{3} - 9 x ^{2} + x + 3}{x - 1}

\frac{2 x ^{4} + 3 x ^{3} - 9 x ^{2} + x + 3}{x - 1} = 2 x^{3} + 5 x^{2} - 4 x - 3

= (x - 1) (2 x^{3} + 5 x^{2} - 4 x - 3)

Factor

2 x^{3} + 5 x^{2} - 4 x - 3 : (x - 1) (2 x + 1) (x + 3)

= (x - 1) (x - 1) (2 x + 1) (x + 3)

Apply exponent rule:

aa = a^{2}

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

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

∣ 3 x + 5 ∣ \geq 1

- 2 x^{2} + 5 x + 6 = 4 x^{2} + 5 x

2 (3)^{- 2}

3 ∣ x + 10 ∣ + 6 = 8

\frac{2}{3} x - 5 = 4

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