What is factor (x-2)^4(3x+2)^3-10(x-2)+9 ?

The solution to factor (x-2)^4(3x+2)^3-10(x-2)+9 is 27x^7-162x^6+252x^5+152x^4-496x^3-96x^2+310x+157

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factor (x-2)^4(3x+2)^3-10(x-2)+9

factor

(x - 2)^{4} (3 x + 2)^{3} - 10 (x - 2) + 9

27 x^{7} - 162 x^{6} + 252 x^{5} + 152 x^{4} - 496 x^{3} - 96 x^{2} + 310 x + 157

Solution steps

(x - 2)^{4} (3 x + 2)^{3} - 10 (x - 2) + 9

(x - 2)^{4} : x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16

= (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16) (3 x + 2)^{3} - 10 (x - 2) + 9

(3 x + 2)^{3} : 27 x^{3} + 54 x^{2} + 36 x + 8

= (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16) (27 x^{3} + 54 x^{2} + 36 x + 8) - 10 (x - 2) + 9

Expand

(x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16) (27 x^{3} + 54 x^{2} + 36 x + 8) : 27 x^{7} - 162 x^{6} + 252 x^{5} + 152 x^{4} - 496 x^{3} - 96 x^{2} + 320 x + 128

= 27 x^{7} - 162 x^{6} + 252 x^{5} + 152 x^{4} - 496 x^{3} - 96 x^{2} + 320 x + 128 - 10 (x - 2) + 9

Expand

- 10 (x - 2) : - 10 x + 20

= 27 x^{7} - 162 x^{6} + 252 x^{5} + 152 x^{4} - 496 x^{3} - 96 x^{2} + 320 x + 128 - 10 x + 20 + 9

Simplify

27 x^{7} - 162 x^{6} + 252 x^{5} + 152 x^{4} - 496 x^{3} - 96 x^{2} + 320 x + 128 - 10 x + 20 + 9 : 27 x^{7} - 162 x^{6} + 252 x^{5} + 152 x^{4} - 496 x^{3} - 96 x^{2} + 310 x + 157

= 27 x^{7} - 162 x^{6} + 252 x^{5} + 152 x^{4} - 496 x^{3} - 96 x^{2} + 310 x + 157

52 t - 16 t^{2}

2 r - 1 > 17

(1 + \frac{1}{10})^{10}

4 y^{2} + y - 5

928

What is factor (x-2)^4(3x+2)^3-10(x-2)+9 ?
The solution to factor (x-2)^4(3x+2)^3-10(x-2)+9 is 27x^7-162x^6+252x^5+152x^4-496x^3-96x^2+310x+157