 be the second derivative of -n**8/420 + n**7/42 - 4*n**6/45 + 2*n**5/15 - 9*n**3/2 - 9*n. Let o(h) be the second derivative of i(h). Factor o(y).
-4*y*(y - 2)**2*(y - 1)
Suppose -17*b + 34 = -0*b. Factor -426*c**2 + 428*c**b + 3*c - 15*c.
2*c*(c - 6)
Let c = 98 - 93. Let v(g) be the second derivative of g**4 - 3/20*g**c + 3*g**2 + 0 - 5/2*g**3 + 5*g. Factor v(t).
-3*(t - 2)*(t - 1)**2
Let 6*k**5 - 5*k**5 + 10*k**3 - 2*k**2 + 7*k**4 + 0*k**3 + 6*k - 5 - 17*k = 0. Calculate k.
-5, -1, 1
Let c(s) be the first derivative of 0*s - 5/3*s**3 - 1/1080*s**6 - 1 - 1/8*s**4 + 0*s**2 + 1/60*s**5. Let q(a) be the third derivative of c(a). Factor q(d).
-(d - 3)**2/3
Let h(w) = w**2 + 8*w + 7. Let g be h(-7). Let u be g/(-1 + (2 - 3)). Factor u*l**3 + 6/5*l**4 - 8/5*l**2 + 0*l - 2/5*l**5 + 0.
-2*l**2*(l - 2)**2*(l + 1)/5
Let m = -12 + 8. Let y be 1/(m/((-12)/1)). Determine o so that -o**2 - 2*o**5 + y*o**3 - o**5 + 4*o**2 + 0*o**5 - 3*o**4 = 0.
-1, 0, 1
Let f = -3141 - -3141. Determine z so that 3/5*z**5 + 0*z + 0 + f*z**3 - 7/5*z**4 + 4/5*z**2 = 0.
-2/3, 0, 1, 2
Let c(b) be the first derivative of b**3/9 - 25*b**2/6 + 46*b/3 - 15. Let c(o) = 0. What is o?
2, 23
Let s be 1/(-5) + ((-186)/(-30) - 4). Suppose 3*y**2 - 27*y**s - 9*y + 0*y = 0. Calculate y.
-3/8, 0
Let d(j) be the first derivative of 41*j + 10 + 5*j**3 - 41*j - 5*j**2. Suppose d(m) = 0. Calculate m.
0, 2/3
Factor -28/5 - 2/5*q**2 + 18/5*q.
-2*(q - 7)*(q - 2)/5
Let q(z) be the first derivative of 2*z**5 + 45*z**4/4 + 35*z**3/3 - 15*z**2 - 15. Suppose q(b) = 0. Calculate b.
-3, -2, 0, 1/2
Suppose -b = -l - 4, 5*l - 38 = -b - 4. Let h = 13 - b. What is o in o + o - 2*o**3 + 0*o**2 - 4 + h*o**2 = 0?
-1, 1, 2
Let g(n) be the third derivative of n**7/735 - n**6/70 - n**5/30 - n**2 - 900*n. Solve g(v) = 0 for v.
-1, 0, 7
Let g(j) be the first derivative of -j**4/84 + j**3/21 + 3*j**2/14 - 34*j + 29. Let s(q) be the first derivative of g(q). Let s(d) = 0. What is d?
-1, 3
Let k(h) = h**2 - 2*h + 1. Let u be k(-1). Factor -1 + 4080*d**4 - 4079*d**u + 17 - 8*d**2.
(d - 2)**2*(d + 2)**2
Let l = 866 + -865. Factor -1/4*m**4 + 3/4*m**2 - 1/2*m**3 + m - l.
-(m - 1)**2*(m + 2)**2/4
Determine u so that 10*u - 10*u**3 + 26/3*u**2 - 28/3 + 2/3*u**4 = 0.
-1, 1, 14
Suppose -70*q + 60 = -290. Factor 2/3*n**4 + 4/3*n**2 + 0 + 4/9*n + 1/9*n**q + 13/9*n**3.
n*(n + 1)**2*(n + 2)**2/9
Let s(n) be the second derivative of 0 + 5/2*n**2 + 5/12*n**4 - 13*n - 5/3*n**3. Factor s(f).
5*(f - 1)**2
Let c(h) be the first derivative of -h**6/270 - 4*h**5/45 - 8*h**4/9 - 128*h**3/27 + 9*h**2 - 19. Let g(s) be the second derivative of c(s). Factor g(x).
-4*(x + 4)**3/9
Suppose 6*l = 9*l - 18. Determine y so that 2*y**2 - 2*y**2 + 0 - 2*y**2 - 4 - l*y = 0.
-2, -1
Let p = 119 - 78. Let w be 4 - 7 - p/(-11). Suppose 0 + w*l**2 - 2/11*l + 10/11*l**3 = 0. Calculate l.
-1, 0, 1/5
Let z(d) be the third derivative of -d**5/40 + d**4/8 + 2*d**3 - 19*d**2 - 3. Suppose z(t) = 0. Calculate t.
-2, 4
Suppose -4*m - 18 = -2*o, 3*m + 0 = 4*o - 21. Let r be m/7*(8/6)/(-1). Solve 6/7*v**3 + 4/7*v**2 - 6/7*v - r = 0.
-1, -2/3, 1
Suppose 0*j = -j + k + 21, j - 18 = 4*k. Factor 4*h**3 + 5*h**4 - j*h**2 + 8 + 10*h**2 - 4*h - h**4.
4*(h - 1)**2*(h + 1)*(h + 2)
Let x(n) be the third derivative of 2*n**7/35 + 27*n**6/40 + 53*n**5/20 + 21*n**4/8 - 9*n**3/2 + 264*n**2. Suppose x(k) = 0. Calculate k.
-3, -1, 1/4
Let p be (-9)/12 - (-127)/4. Let v = p + -8. Factor -16*s**3 + s + 4*s**4 - s + v*s**2 - 7*s**2.
4*s**2*(s - 2)**2
Factor -1/5*t**3 + 4/5*t**2 + 0 - 4/5*t.
-t*(t - 2)**2/5
Let n(v) be the first derivative of 3*v**4/4 - 7*v**3 - 34. Factor n(l).
3*l**2*(l - 7)
Let c(i) be the second derivative of i**5/4 + 25*i**4/12 + 35*i**3/6 + 15*i**2/2 - 2*i - 132. Factor c(x).
5*(x + 1)**2*(x + 3)
Suppose -152 = -8*y - 0*y. Factor 90 - 10*j**4 + y*j**3 - 45 - 8*j**2 - j - 45.
-j*(j - 1)**2*(10*j + 1)
Let r = 2641 + -2640. Let w(b) be the first derivative of -1/16*b**4 + 0*b - 1/12*b**3 + 0*b**2 + r. Determine u so that w(u) = 0.
-1, 0
Let t = -7 + 11. Suppose 5*q = 2*z + 3*q - 104, -5*z - 4*q + 260 = 0. Find a, given that -z*a**3 - 97*a - 5 - 251 - t*a**4 - 240*a**2 - 351*a = 0.
-4, -1
Let o(r) be the first derivative of r**8/840 - r**6/90 + r**4/12 + 7*r**3 - 31. Let k(b) be the third derivative of o(b). Find h, given that k(h) = 0.
-1, 1
Determine v so that -219*v**2 + 115746*v + 5*v**3 - 21559681 + 677754*v - 3231*v**2 - 39275319 = 0.
230
Let h = 205133/66 + -3108. Let c(b) be the second derivative of h*b**4 - 2*b + 0 + 0*b**2 + 1/11*b**3. Suppose c(t) = 0. What is t?
-3/5, 0
Let o(b) be the third derivative of -b**5/210 + b**4/4 + 22*b**3/21 - 139*b**2. What is g in o(g) = 0?
-1, 22
Let h(b) = b**3 + 6*b**2 - 10*b - 4. Suppose 0*w - 40 = 4*w + 4*g, -26 = 5*w - 3*g. Let m be h(w). Factor -m*z**2 + 34*z**2 + 2 + 3*z - 22*z**2.
-(z - 1)*(5*z + 2)
Find u, given that 2/11*u**2 - 2/11*u - 4/11 = 0.
-1, 2
Factor -25*z**5 + 160*z**2 + 40*z**4 - 23*z + 26*z**5 + 150*z**3 + 78*z - 6*z**5.
-5*z*(z - 11)*(z + 1)**3
Let d(q) be the first derivative of -1/180*q**5 + 0*q + 0*q**3 + 1/72*q**4 + 5 - q**2. Let j(f) be the second derivative of d(f). Factor j(a).
-a*(a - 1)/3
Let l(n) be the third derivative of -n**10/30240 - n**9/7560 - n**8/6720 + n**4/6 + 10*n**2. Let j(x) be the second derivative of l(x). Let j(v) = 0. What is v?
-1, 0
Let y(b) be the third derivative of -b**8/84 - 6*b**7/35 - 11*b**6/15 + 16*b**4/3 + 92*b**2 - b. Determine c, given that y(c) = 0.
-4, -2, 0, 1
Let m(w) = w**2 - w - 24. Let x be m(8). Suppose 10 - 2 = 4*u. Factor 4 - x*j**2 - 14*j**5 - 52*j**4 - 24*j**3 + u*j - 16*j**3 - 28*j**3.
-2*(j + 1)**4*(7*j - 2)
Let a = 6 + -6. Suppose s - 3*o - 30 = -0*s, 2*s - o - 45 = a. Let s + 21*x**2 + 13 - 7 - 45*x + 2*x**3 - 5*x**3 = 0. What is x?
1, 3
Let m(g) be the third derivative of g**7/420 + 7*g**6/120 - 2*g**5/15 - 7*g**4/24 + 5*g**3/4 - 3*g**2 + 18*g. Factor m(j).
(j - 1)**2*(j + 1)*(j + 15)/2
Let k(m) be the first derivative of 20*m + 0*m**4 - 25/3*m**3 + 0*m**2 + 18 + m**5. Suppose k(z) = 0. Calculate z.
-2, -1, 1, 2
Let n(t) be the second derivative of 0*t**2 - 1/160*t**5 - 57*t - 1/96*t**4 + 0 + 1/24*t**3. Factor n(p).
-p*(p - 1)*(p + 2)/8
Let y = -127 + 133. Let h = 9 - y. Factor -1/2*g - g**2 + 1/4 + 2*g**h.
(2*g - 1)**2*(2*g + 1)/4
Let o = 7823039 - 2698945907/345. Let k = o - 6/115. Factor -1/3 - 8*y**3 - k*y**2 - 3*y**4 - 8/3*y.
-(y + 1)**2*(3*y + 1)**2/3
Factor -2*d + 1/2*d**2 + 1/2*d**3 - 2.
(d - 2)*(d + 1)*(d + 2)/2
Suppose 3*h = 3*y + 6, 4*h = -5 + 21. Suppose -y*c - 16 = -2*v - 0*v, 3*v - 5*c - 34 = 0. What is z in 1/2*z**2 - 1/2*z**v + 1/2*z + 0 - 1/2*z**4 = 0?
-1, 0, 1
Let y(c) be the second derivative of c**7/21 - 2*c**6/15 - 3*c**5/5 + 2*c**4/3 + 13*c**3/3 + 6*c**2 + 5*c - 7. Solve y(t) = 0 for t.
-1, 2, 3
Factor -5*t**3 - 240 + 6*t + 26*t + 13*t + 5*t + 25*t**2 - 10*t.
-5*(t - 4)**2*(t + 3)
Let w(x) be the first derivative of -x**5/15 + 5*x**4/12 + 8*x**3/3 + 2*x**2/3 - 32*x/3 + 689. What is u in w(u) = 0?
-2, 1, 8
Let v = -214407/7 + 30657. Factor 144/7 - v*j + 52/7*j**2 - 4/7*j**3.
-4*(j - 6)**2*(j - 1)/7
Let j be 30*8/540*1*9. What is g in -1/3*g**5 + 0*g**2 + 0*g + 1/3*g**3 + 0*g**j + 0 = 0?
-1, 0, 1
Let x be (-244)/854*(-14)/80. Let d(h) be the second derivative of -x*h**5 - 1/24*h**4 - 1/8*h**2 + 1/40*h**6 - 6*h + 0 + 1/6*h**3. Factor d(b).
(b - 1)**2*(b + 1)*(3*b - 1)/4
Let s(r) be the first derivative of -5*r - 5/3*r**3 + 5*r**2 - 1. Suppose s(l) = 0. Calculate l.
1
Let p(s) be the first derivative of s**6/90 + s**5/60 - s**4/6 - 2*s**3/9 + 4*s**2/3 - 32*s - 18. Let w(y) be the first derivative of p(y). Factor w(z).
(z - 2)*(z - 1)*(z + 2)**2/3
Let v(g) be the third derivative of -g**6/72 + 5*g**4/24 - 5*g**3/3 + 12*g**2. Let u(y) be the first derivative of v(y). Factor u(k).
-5*(k - 1)*(k + 1)
Let l = 17675 - 53021/3. Let 7/3*v - v**5 + 8/3*v**4 - l*v**3 - 2/3 - 2*v**2 = 0. What is v?
-1, 2/3, 1
Let r = 209 + -203. Let t(b) be the third derivative of 0*b + 1/36*b**4 - 1/180*b**r + 0 - 1/9*b**3 + 1/90*b**5 - b**2. Factor t(n).
-2*(n - 1)**2*(n + 1)/3
Let k(q) be the first derivative of -q**3/3 + 55*q**2 - 3025*q + 87. Let k(f) = 0. What is f?
55
Let l = 59 + -25. Determine x so that -12*x**3 - 130*x - 52*x - l*x + 15 + 99