Question

Factorize

6x⁴-5x³-38x²-5x+6

Answer 1

Hey there! Thanks for the awesome questions.Looks complicated,but it is easy.

6x⁴-5x³-38x²-5x+6
=6x⁴+12x³-17x³-34x²-4x²-8x+3x+6
=(6x⁴+12x³)-(17x³+34x²)-(4x²+8x)+(3x+6)
=6x³(x+2)-17x²(x+2)-4x(x+2)+3(x+2)
=(x+2)(6x³-17x²-4x+3)
=(x+2)(6x³-18x²+x²-3x-x+3)
=(x+2)[(6x³-18x²)+(x²-3x)-(x-3)]
=(x+2)[(6x²(x-3)+x(x-3)-(x-3)]
=(x+2)(x-3)(6x²+x-1)
=(x+ 2)(x+3)(3x-1)(2x+1)

Hope helped! ^^

Answer 2

Hey sup!
Equation to be factorized,
6x⁴-5x³-38x²-5x+6

Step-by-Step factorization of the above given equation,
6x⁴+12x³-17x³-34x²-4x²-8x+3x+6

(6x⁴+12x³)-(17x³+34x²)-(4x²+8x)+(3x+6)

6x³(x+2)-17x²(x+2)-4x(x+2)+3(x+2)

(x+2)(6x³-17x²-4x+3)

(x+2)(6x³-18x²+x²-3x-x+3)

(x+2)[(6x³-18x²)+(x²-3x)-(x-3)]

(x+2)[(6x²(x-3)+x(x-3)-(x-3)]

(x+2)(x-3)(6x²+x-1)

So we get our final answer,
(x+ 2)(x+3)(3x-1)(2x+1)


Hope helps