Algebra 2, Problem#17: Find all zeros of the polynomial function f(x) = x^5 ? 4x^3 ? 2x^2 + 3x + 2

I have from my teacher that the answers are

-1 (multiplicity 3), 1 , 2

However, I need help with the steps on how to get all these roots. My work is shown in the picture attached, with this Problem # 17 highlighted in red. Thanks

Write a polynomial function f of least degree, in standard form, that has a leading coefficient of 1 and the given zeros. 11. -1, 3, -5 12. 1, -2 - V5 7 ( x + 1) ( x - 3) (xx 5) (x - 1) ( x-(2 - JS )( x-(2+-25)) (x 2 - 2x- 3) (x +5 ) ( x + 21 +15 ) ( 1x - 2)- 255 ) x 3 - 2x 2- 3x 15x 3/-10x-15 ( x - 2 ) - 5 / x 3 + 3 x 2 + 1 x - 15 x. - 4 x + 4 - 5 13 . - 2 , 4 + i x 3 - 6 * 2 - * +15 ( x - 1) ( x2 -4x -1) ( x + 2 ) ( x - 1 4+ z ) (x-(4 -i )) ( x - 41 - 2 ) (1 - shti ) x 3 5 - 4 x 2 - 1 X ( x + 2 ) ( x - 4 R - 1) 1 X3 - 8 x 2 +15 y - x - + 4x + 1 x-8x+16 - 1 12 * 2 - 16 * +15 1x 3- 5x 2 + 3x+1( (x + 2 ) ( x28 x +15) Based on the Fundamental Theorem of Algebra, list how many zeros each polynomial function has. Then find all zeros of the polynomial function. + 6 32 1 $ 8421 14. f(x) = x4+ x3- 7x2 - x+ 6 15. 8 (x) = 15 + 4x4 + x3- 14x2 - 20x - 8 X = 2,1 - M - 1 1 141-14 - 20 -3 - 1 1 - 3 (X- 2 ) (x4+ 6 * 3 +73 * 2712x+4) 2 12 26 24 8 . 2 - 6 2 - 5 - 6 ( x - 2 ) ( x + 2 ) ( x 3 + 4 1 x 2 + 5x+2) 1 6 13 12- 4 0 ( X - 1 ) ( x 3 + 2 x 2 - 5 x - 6 ) 1 2 8 6 ( x- 2 ) ( x + 2 ) ( x+ 2) (x2+2x+1 ) - 2- 8 -10 1 1 6 13 12 4 ( x - 1) ( x - 2 ) ( x 2 + 4 x + 3 ) (x -2) ( * +2 )* +z)(x+1 )2 14 5 ( x - 1) ( x - 2 ) ( x + 1 ) ( x +3 ) X = 2 x =-2 x-- 2 X=-1 4 + 18 9 6 321 - 4 -2 16. f (x) = x4+ x3 -11x2 - 9x + 18 17. 8(x) = 15 - 4x3 - 2x2 + 3x + 2 1 2 10 ( x - 3 ) ( x 3 + 4 x 2 + x - 6) 31 1 1 - 11-918 3 12 3 - 18 (x - 1) ( * 4 +x 3- 3x25x-2) - 21 (X - 3)(x+ 3 ) (x2+ 1 x -2x ) 14 1- 60 ( x - 1) ( x - 2) ( x 3 +3 x 2 + 3x + 1 ) 2 1 1 - 01 -4- 232 31 1 4 1 - 1 1- 3 - 5-2 ( *+2) (x -1) L- 3- 3 6 1- 3 - 6 2 0 1- 2 O x = 3, 1 , - 2,-3 2 1 1 1 1 - 3 - 5 - 2 2 6 . 6 2 3 3 Factor the polynomial completely. 20. 2x9 - 16x6 - 1/1 3 3 18. x3 - 64 19. 8x3 + 343 (2x + 47) 2*6/ x3- 8) 21 (x- 4) (x2+4 x +16) (4x 2 - 14 x + 40) 2x6 ( x- 2) ( x2+2x+4)