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

$\huge\underline\blue{Question\:}$ ↪

Factorize

6x⁴-5x³-38x²-5x+6

$\huge{\fbox{\fbox{\bigstar{\underline{\green{Solution}}}}}}$

↪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)