**4 = 0.
0, 1
Let f(c) be the third derivative of c**6/960 + c**5/160 + c**4/96 - 3*c**2 + 3. Factor f(z).
z*(z + 1)*(z + 2)/8
Let d(i) = -i**3 + 9*i**2 + 10*i + 2. Let s be d(10). Determine k, given that 5*k**2 - k**2 - s*k**2 - 2*k**3 + 136*k - 132*k = 0.
-1, 0, 2
Let k be (-9)/(11 - 2) - -7 - 6. Solve k + 2*h**2 - 2/3*h + 8/3*h**3 = 0.
-1, 0, 1/4
Let f(o) = o**2 - 13*o - 4. Let k(h) = 4*h**2 - 3*h**2 - 25*h - 1 - 2 - 4. Let a(p) = -7*f(p) + 4*k(p). Factor a(x).
-3*x*(x + 3)
Let l = 1927/420 + 1/84. Let i(o) be the second derivative of -2*o**4 - 10*o + l*o**5 + 0 + 0*o**3 - 14/15*o**6 + 0*o**2. Solve i(y) = 0.
0, 2/7, 3
Factor -258052/3*v**2 - 262144/3 + 174080*v - 680*v**3 - 4/3*v**4.
-4*(v - 1)**2*(v + 256)**2/3
Let z(t) be the second derivative of -26*t - 5/12*t**4 + 0 - 25/6*t**3 + 0*t**2. Factor z(k).
-5*k*(k + 5)
Let o(m) = -m**2 - 11*m - 12. Let x be o(-9). Suppose i - x*i = -10. Let -c + 2*c**i + 4 - 6 + c = 0. What is c?
-1, 1
Factor 0*g - 56/5*g**3 + 0 - 6/5*g**5 + 88/5*g**4 + 0*g**2.
-2*g**3*(g - 14)*(3*g - 2)/5
Let k(m) be the second derivative of 7*m + 0*m**2 + 0 + 1/45*m**3 + 4/45*m**4. Factor k(f).
2*f*(8*f + 1)/15
Let s be (2 + -3)*(-3 - 2). Let y(a) be the third derivative of -1/4*a**4 + 0*a - 2/3*a**3 + 0 - 1/30*a**s + a**2. Factor y(h).
-2*(h + 1)*(h + 2)
Suppose 1/2 + a**2 + 5/4*a + 1/4*a**3 = 0. What is a?
-2, -1
Let t(a) be the second derivative of -a**7/4200 + a**5/600 - a**3/2 - 3*a. Let g(f) be the second derivative of t(f). Factor g(m).
-m*(m - 1)*(m + 1)/5
Let p(o) = -22*o**3 + 5*o**2 + 3 - 26*o**2 + 21*o**3. Let c be p(-21). Factor 92*f + 49/3*f**4 + 12 + 613/3*f**2 + 322/3*f**c.
(f + 3)**2*(7*f + 2)**2/3
Find o, given that 35/6*o - 5/2 - 25/6*o**2 + 5/6*o**3 = 0.
1, 3
What is o in -5/3*o**3 - 20 + 5/3*o**2 + 40/3*o = 0?
-3, 2
Let w(v) be the third derivative of 0*v**3 + 0*v**7 + 0*v**4 + 0*v + 1/1512*v**8 - 1/180*v**6 + 0 - 1/135*v**5 + 22*v**2. Factor w(a).
2*a**2*(a - 2)*(a + 1)**2/9
Let f = -23293404/19 + 292798152253/238830. Let q = f - 1/838. Factor 0 + q*h**2 + 2/15*h + 2/15*h**3.
2*h*(h + 1)**2/15
Let t = -90 + 96. Solve 67 - t*f - 15*f**2 - 38 - 38 - 3*f**3 - 15*f = 0.
-3, -1
Let v(s) = -s**2 - 29*s + 6 + 9 + 17*s. Let j be v(-13). Factor 1/4 - 1/2*p + 1/4*p**j.
(p - 1)**2/4
Suppose 17*a - 14*a - 9 = 0. Factor -34*g**4 + 22*g**4 - 90*g**a - 40*g - 5*g**5 + 100*g**2 + 47*g**4.
-5*g*(g - 2)**3*(g - 1)
Let i(z) be the second derivative of -z**6/40 - 9*z**5/80 + 3*z**4/8 + 7*z**3/2 + 9*z**2 + 7*z + 1. Determine v so that i(v) = 0.
-2, 3
Let b(x) be the third derivative of 0*x + 0*x**3 + 1/40*x**6 + 50*x**2 - 1/8*x**4 + 0*x**5 + 0. Let b(s) = 0. Calculate s.
-1, 0, 1
Factor -8*z - 10/7*z**2 + 24/7.
-2*(z + 6)*(5*z - 2)/7
Find a, given that -2*a**4 - 12*a**4 + 74*a**3 - 62*a**2 + 36 + 108*a - 222*a = 0.
-1, 2/7, 3
Let v(r) = 9*r**4 + 150*r**3 - 9*r**2 - 129*r - 21. Let a(j) = -j**4 - 15*j**3 + j**2 + 13*j + 2. Let q(y) = 21*a(y) + 2*v(y). Factor q(o).
-3*o*(o - 1)*(o + 1)*(o + 5)
Suppose -14*z + 15*z = j - 2, 5*j = -5*z + 40. Factor 0 + 2/5*n**z + 0*n + 2*n**2.
2*n**2*(n + 5)/5
Suppose 3*c - 6 = -5*f, -4*f + 1 = 4*c - 7. Let -12*r + 103 + c*r**2 - 8*r - 53 = 0. What is r?
5
Suppose -2*c + 5*m = -15, -c - 4*c + 2*m + 48 = 0. Suppose 2*o = 2*u - 4, -3*u - 2*u + c = 2*o. Determine f so that -5/2*f**u - 5 + 15/2*f = 0.
1, 2
Let n(p) = -13*p**3 - 21*p**2. Let t(q) = 19*q**3 + 31*q**2. Let z(s) = -7*n(s) - 5*t(s). Let z(r) = 0. What is r?
-2, 0
Factor -w**2 + 396*w - 3*w**2 - 404*w.
-4*w*(w + 2)
Let s = 15 - -19. Let m be -5*(3 + s/(-10)). Factor -14/9*k**4 + m*k**3 + 0 - 4/9*k**2 + 0*k.
-2*k**2*(k - 1)*(7*k - 2)/9
Suppose -36*i - 13*i + 147 = 0. Let w(h) be the first derivative of h**4 - 1/3*h**6 + 9 + 8/3*h**i - 4*h - 4/5*h**5 - h**2. Solve w(z) = 0.
-2, -1, 1
Let w(o) be the third derivative of -2/27*o**4 + 0 + 0*o + 1/180*o**6 - 4/27*o**3 + o**2 - 1/270*o**5. Suppose w(h) = 0. Calculate h.
-1, -2/3, 2
What is w in -52*w + 10 - 6*w**4 + 85/2*w**2 + 47/2*w**3 = 0?
-2, 1/4, 2/3, 5
Let c(n) = 8*n**2 + 16*n + 17. Let t(v) = 6*v**2 + 16*v + 16. Let h(r) = -2*c(r) + 3*t(r). Solve h(q) = 0 for q.
-7, -1
Factor 31/2*t**3 + 0 + 9/2*t - 7/2*t**4 - 33/2*t**2.
-t*(t - 3)*(t - 1)*(7*t - 3)/2
Suppose 6*p = 16*p - 20. Solve -5*a**p - 31*a - 30 - 20 - 21*a - 3*a = 0.
-10, -1
Factor -13*q - 9*q + 6*q + 2*q**2 - 19*q + 7*q.
2*q*(q - 14)
Let k = 8/243 + -479/17010. Let v(j) be the third derivative of 0*j + 0*j**4 + k*j**6 - 5/392*j**8 + 0*j**5 + 1/735*j**7 + 0*j**3 + 0 - 3*j**2. Factor v(l).
-2*l**3*(3*l + 1)*(5*l - 2)/7
Let r = -78 + 80. Factor 69 - 15*n**3 + 15*n + 16*n**4 - 72 - 9*n**r - 4*n**4.
3*(n - 1)**2*(n + 1)*(4*n - 1)
Let u(m) be the third derivative of -m**5/140 + 5*m**4/14 - 19*m**3/14 + 224*m**2. Solve u(z) = 0.
1, 19
Find l, given that -85*l**3 + 82*l + 18 - l**4 - 98 + 3*l + 6*l**4 + 75*l**2 = 0.
-1, 1, 16
Suppose 0 = -r - d - 42, 0*r + r - 4*d = -32. Let v = 67 + r. Determine u so that v*u**4 - 24*u**4 + u**3 - 2*u**3 = 0.
0, 1/3
Let t(i) = 15*i**4 - 19*i**3 + 7*i**2 + 19*i - 22. Let b(f) = -7*f**4 + 9*f**3 - 3*f**2 - 9*f + 10. Let g(y) = 9*b(y) + 4*t(y). Factor g(l).
-(l - 1)**2*(l + 1)*(3*l - 2)
Let n(q) be the third derivative of q**8/80640 - q**7/3360 + 19*q**5/60 - 12*q**2. Let h(u) be the third derivative of n(u). Factor h(o).
o*(o - 6)/4
Let w(f) = -19*f**2 - 712*f - 41770. Let x(a) = 84*a**2 + 2850*a + 167079. Let y(b) = 9*w(b) + 2*x(b). What is t in y(t) = 0?
-118
Let o(t) be the first derivative of -3*t**5/160 + 3*t**4/32 - t**3/8 + 13*t - 15. Let z(s) be the first derivative of o(s). Suppose z(m) = 0. What is m?
0, 1, 2
Let l(z) = z**3 + 67*z**2 + 1031*z - 41. Let r be l(-43). Find c such that 0*c**r - 2/5*c + 0 + 2/5*c**3 = 0.
-1, 0, 1
Solve -13/4*q + 0 + 1/4*q**5 + 5/2*q**4 - 9*q**3 + 19/2*q**2 = 0.
-13, 0, 1
Determine x so that 2/5*x**2 - 264/5*x + 8712/5 = 0.
66
Factor -5 + 101*w**2 - 119*w + 39*w - 16*w**2.
5*(w - 1)*(17*w + 1)
Suppose g + g = -o - 54, -4*g - 120 = 5*o. Let c be 3 - (0 - g/35). What is m in 684/7*m**2 + 810/7*m**3 + c + 184/7*m = 0?
-2/5, -2/9
Let i be (0/(42/7))/1. What is g in -2/7*g**3 + 8/7*g**2 + 0 + i*g = 0?
0, 4
Suppose -45 = 3*o + 2*b - 61, -b + 5 = 0. Solve -4/9 + 6*k - 128/3*k**4 - 88/3*k**o + 544/9*k**3 = 0.
1/4, 2/3
Let j(p) be the first derivative of 3*p**5/10 - p**4/8 - 8*p**3 + 4*p**2 - 948. Suppose j(d) = 0. Calculate d.
-4, 0, 1/3, 4
Let 108*i**2 - 38*i - 183*i - 222*i**2 - 211*i + 115*i**2 + 46656 = 0. Calculate i.
216
Let q be (1 + -2)*-2*(-1 + 3). Suppose q*j - n = -0*j + 8, -3*j = -n - 6. Factor 6/5 + 2/5*h**j + 8/5*h.
2*(h + 1)*(h + 3)/5
Let s(g) = -2*g**2 - 12*g + 16. Let o be s(-7). Find q such that 3 + 3/2*q - 3/2*q**o = 0.
-1, 2
Let j = -11697/20 - -2423/5. Let b = j + 101. Find m such that 0 + 0*m - 3/4*m**3 + b*m**2 = 0.
0, 1
Let i(q) = q**2 - 5*q + 5. Let y be i(5). Suppose -5*b + 4*b = -5*u - 3, y*b - 15 = -5*u. Factor u*r - 2*r**3 - r**2 + 9*r**2 - 5*r - 3*r.
-2*r*(r - 2)**2
Suppose 3*k + 122 - 101 = 3*v, k = -5*v + 11. Determine m so that 0*m**2 - 3/2*m**4 + v*m**3 + 3/2 - 3*m = 0.
-1, 1
Let w(n) be the first derivative of -3*n - 1/2*n**3 + 9/4*n**2 - 6. Factor w(d).
-3*(d - 2)*(d - 1)/2
Let n(j) = -35*j**2 - 88*j + 87. Let t(z) = -29*z**2 - 88*z + 87. Let w(y) = -5*n(y) + 6*t(y). Factor w(v).
(v - 87)*(v - 1)
Let m(s) be the first derivative of -20*s**3/3 - 6*s**2 + 8*s - 10. Let n(g) = -7*g**2 - 4*g + 3. Let w(o) = -3*m(o) + 8*n(o). Factor w(b).
4*b*(b + 1)
Let j(p) = p**3 - 11*p**2 - p + 14. Let s be j(11). Factor 16*k**s + 3*k**5 + 12*k**4 + k**3 - 2*k + k**3 + 12*k**2 + 5*k.
3*k*(k + 1)**4
Factor 17/4*t - 21 + 1/4*t**2.
(t - 4)*(t + 21)/4
Let b be (4/23)/(456/5244). Factor 0*i + 15/4*i**3 - 3/2*i**b + 21/4*i**4 + 0.
3*i**2*(i + 1)*(7*i - 2)/4
Let h be (4 + 0)*(656/(-256)*-8 + -20). Factor 4/5 + 3/5*x - 1/5*x**h.
-(x - 4)*(x + 1)/5
Let l(y) be the first derivative of -y**4/34 - 8*y**3/51 - 5*y**2/17 - 4*y/17 - 19. Find f such that l(f) = 0.
-2, -1
Let k(r) be the second derivative of 2*r**7/7 - 12*r**6/5 + 147*r**5/20 - 45*r**4/4 + 19*r**3/2 - 9*r**2/2 + 138*r. What is d in k(d) = 0?
1/2, 1, 3
Let t(x) be the second derivative of -x**4/42 - 6*x**3/7 - 17*x**2/7 - 485*x. Factor t(u).
-2*(u + 1)*(u + 17)/7
Factor -1610*i - 2940 - 215/3*i**2 - 5/