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svetoff [14.1K]
3 years ago
8

Factor (x-1)^3 (4x-9) - (16x+9) (x+1)^2 ? Please explain steps, I'm stuck !

Mathematics
1 answer:
Lapatulllka [165]3 years ago
5 0

(x-1)^3 (4x-9) - (16x+9) (x+1)^2

= (x^3-3x^2+3x-1) (4x-9) - (16x+9) (x^2+2x+1)

= (4x^4-12x^3+12x^2-4x-9x^3-27x^2-27x+9)-(16x^3+32x^2+16x+9x^2+18x+9)

= (4x^4-21x^3+39x^2-31x+9)-16x^3-32x^2-16x-9x^2-18x-9

= 4x^4-21x^3+39x^2-31x+9-16x^3-32x^2-16x-9x^2-18x-9

= 4x^4-37x^3-2x^2-65x

= x(4x^3-37x^2-2x-65)

hence final factor is x(4x^3-37x^2-2x-65)

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