5/3*w**2 = 0. Calculate w.
-4, 0
Factor 1/5*w**2 + 3/5*w + 2/5.
(w + 1)*(w + 2)/5
Let r = 78 + -50. Let k = -5 + r. Suppose 20 + k - b - 41 - b**2 = 0. What is b?
-2, 1
Suppose -2 = 2*q + 6. Let t be q/(-2)*-1 + 2. What is o in -4/11*o**2 + t + 0*o**4 + 2/11*o**5 - 6/11*o**3 + 0*o = 0?
-1, 0, 2
Find o, given that 5*o**3 + 16*o**3 - 3*o**2 - 4*o**5 + 23*o**3 + 27*o**2 + 16*o**4 = 0.
-1, 0, 6
Let p(c) be the first derivative of 1/16*c**4 + 1/4*c - 1/12*c**3 + 42 - 1/8*c**2. Factor p(k).
(k - 1)**2*(k + 1)/4
Let v(x) = -14*x**3 + 114*x**2 - 254*x + 64. Let j(h) = -h**2 + 0*h**2 + 0*h + 6*h - 5*h. Let y(t) = 2*j(t) - v(t). Suppose y(w) = 0. Calculate w.
2/7, 4
Let l(y) be the third derivative of -y**7/210 + y**6/120 + y**5/60 - y**4/24 + 2*y**2 - 16. Let l(w) = 0. Calculate w.
-1, 0, 1
Let c(n) be the first derivative of -n**7/84 - n**6/20 - n**5/20 + n**4/12 + n**3/4 + n**2/4 - 10*n + 42. Let f(j) be the first derivative of c(j). Factor f(h).
-(h - 1)*(h + 1)**4/2
Let j(b) be the third derivative of -b**8/504 + 8*b**7/105 - 11*b**6/30 + 32*b**5/45 - 7*b**4/12 - 96*b**2. Let j(y) = 0. What is y?
0, 1, 21
Let r = -1841 + 1841. Factor -2/3*t - 2/3*t**2 + r.
-2*t*(t + 1)/3
Let l(m) = 6*m**5 - 63*m**4 - 348*m**3 - 426*m**2 + 348*m + 486. Let b(a) = -3*a**5 + a**4 + a. Let u(s) = 3*b(s) + l(s). Determine c, given that u(c) = 0.
-9, -2, -1, 1
Let i(p) = p**3 + 3*p**2 - 7*p. Let u be i(2). Let w be (-20)/u - 28/(-7). Solve 0*x**2 + 0 + 0*x + 0*x**4 + w*x**5 - 2/3*x**3 = 0.
-1, 0, 1
Let x(l) be the first derivative of -2*l**6/135 - l**5/60 + l**4/108 - 6*l - 5. Let p(o) be the first derivative of x(o). Factor p(d).
-d**2*(d + 1)*(4*d - 1)/9
Let s(c) be the second derivative of -1/36*c**4 - 1/90*c**6 + 0*c**2 + 0 + 10*c + 1/30*c**5 + 0*c**3. Solve s(z) = 0.
0, 1
Suppose -2*v = -2 + 14. Let w be 2/(6 - (2 + v)). Let -1/5*r**2 + w*r + 0 = 0. Calculate r.
0, 1
Let u = 547/815 + -11/2445. Suppose 1/3*j**4 + 1/3*j**2 + 0 - u*j**3 + 0*j = 0. What is j?
0, 1
Let z be 1953/196 - (-2)/(-8). Let p = -197/21 + z. Factor -1/3 - p*q**2 - 2/3*q.
-(q + 1)**2/3
Let w(f) be the second derivative of f**5/4 + 25*f**4/4 - 2*f + 4. Solve w(y) = 0.
-15, 0
Let g(w) be the second derivative of 0*w**2 + 0*w**4 + 0 + 1/35*w**5 + w + 0*w**3 + 1/147*w**7 - 1/35*w**6. Let g(b) = 0. Calculate b.
0, 1, 2
Factor 4*o**4 + 7*o**2 + 639*o**3 + 5*o**2 - 2*o**2 + o**4 - 624*o**3.
5*o**2*(o + 1)*(o + 2)
Let g(b) be the third derivative of 7*b**2 - 8/3*b**3 - 1/15*b**5 + 0*b + 2/3*b**4 + 0. Determine p so that g(p) = 0.
2
Let v be ((-1071)/135)/(-17) - ((-24)/(-9) - 3). Solve 2/5*n**3 + 2*n - v - 8/5*n**2 = 0 for n.
1, 2
Let b(k) = -171*k**2 + 397*k - 194. Let w(i) = 115*i**2 - 265*i + 130. Let x(g) = 5*b(g) + 8*w(g). Determine o, given that x(o) = 0.
1, 14/13
Let j(g) = 2*g**2 - 2*g - 1. Let d be j(2). Suppose -2*v = -11 + 3. Factor -6*q**2 + d*q**v - 24 - 28 + 55.
3*(q - 1)**2*(q + 1)**2
Let l be (-2)/4 - (-99)/22 - 2. Factor 5/2*d**l + 0*d - 5/2.
5*(d - 1)*(d + 1)/2
Let d(v) = -v**2 - 23*v + 59. Let p be d(-19). Let a be 1*5/p*6. Factor -2/9*z**3 + 0*z + a*z**2 + 0.
-2*z**2*(z - 1)/9
Let g = 7 - 5. Factor -7*s**2 + 4*s**4 - 3*s**g + 10*s**2 + s**5.
s**4*(s + 4)
Let g(l) be the third derivative of -l**6/600 + l**5/600 + 13*l**4/240 + l**3/10 - 3*l**2 + 8*l. Factor g(p).
-(p - 3)*(p + 2)*(2*p + 1)/10
Suppose -5*h - 4 = 2*o + 2*o, -4*h - 2 = 2*o. Let s(d) be the third derivative of 0*d**4 + 1/100*d**6 + h*d + 0 + 3/100*d**5 + d**2 - 1/10*d**3. Factor s(y).
3*(y + 1)**2*(2*y - 1)/5
Let z(j) be the third derivative of -j**7/336 + j**6/144 + j**5/48 - 5*j**4/48 - 11*j**3/6 - 10*j**2. Let b(i) be the first derivative of z(i). Solve b(s) = 0.
-1, 1
Let m(p) = p**3 + 5*p**2 - 8*p - 3. Let j be m(-6). Factor -5 - 5*v**4 + 9 - 8*v**2 + j*v**4.
4*(v - 1)**2*(v + 1)**2
Let w(v) be the third derivative of -v**6/210 - v**5/35 + 3*v**4/7 + 67*v**2. Suppose w(p) = 0. Calculate p.
-6, 0, 3
Let b be 2/8 - (-10)/8. Suppose -64*z + 3*a = -66*z + 19, -5*z - a = -15. Factor b*h - 3/4*h**z + 0.
-3*h*(h - 2)/4
Let a(x) be the first derivative of x**3/3 - x**2 + 3. Let s be a(3). Factor -s + v - v + 3*v**4 + 4*v**3 + 2*v**3 - 6*v.
3*(v - 1)*(v + 1)**3
Let i = -2/50201 - -100412/251005. Solve 8/5*l - 8/5*l**2 + 8/5*l**4 - 6/5*l**3 + 0 - i*l**5 = 0 for l.
-1, 0, 1, 2
Let x = 29198/25585 - -6/3655. Factor 2/7*g**4 + 16/7 - x*g + 2/7*g**3 - 12/7*g**2.
2*(g - 2)*(g - 1)*(g + 2)**2/7
Factor 2/13*f**2 - 22/13*f + 60/13.
2*(f - 6)*(f - 5)/13
Let x(b) be the second derivative of b**5/100 + b**4/20 - b**3/3 + 43*b. Factor x(n).
n*(n - 2)*(n + 5)/5
Let x be ((-1260)/250 + 0 + 5)*-5. Find c such that -2/5*c - x - 1/5*c**2 = 0.
-1
Let w(v) be the second derivative of 0*v**2 - 13/20*v**5 - 1/3*v**3 - 3*v - 25/24*v**4 + 11 - 1/12*v**6. Factor w(c).
-c*(c + 1)*(c + 4)*(5*c + 1)/2
Let r(s) be the second derivative of s**7/14 - 3*s**5/4 + 2*s**3 + 70*s. Let r(z) = 0. What is z?
-2, -1, 0, 1, 2
Let t = 67/174 - 3/58. Let g be (5/6 - 1)*-2. Factor g*l**2 + 0 + t*l.
l*(l + 1)/3
Let b = -4806 - -4830. Suppose b*k + 44/3*k**2 + 14/3*k**5 + 16/3 - 50/3*k**3 - 8*k**4 = 0. What is k?
-1, -2/7, 2
Let s(r) be the first derivative of -5/6*r**4 - 8/3*r + 4*r**2 - 26 - 2/3*r**3. Solve s(k) = 0 for k.
-2, 2/5, 1
Let h = 70 - 53. Suppose 0 = -h*b + 26*b. Factor 1/4*t - 1/4*t**2 + b.
-t*(t - 1)/4
Let j(q) = 2*q**2 - 4*q + 3. Let z = 21 + -19. Let i be j(z). Factor 3*u + 7*u**i - 3*u**2 - u**4 + 4*u**4 - 10*u**3.
3*u*(u - 1)**2*(u + 1)
Let s(f) be the first derivative of -f**6/24 - f**5/20 - 24. Factor s(n).
-n**4*(n + 1)/4
Let f(x) be the third derivative of 0*x + 0 + 1/6*x**4 - 1/30*x**6 + 4/3*x**3 - 1/5*x**5 + 2/105*x**7 - 5*x**2. Suppose f(d) = 0. What is d?
-1, 1, 2
Suppose -8 = -2*i + 4*w + 2, 0 = -w - 1. Let -17*s**3 - 35*s**2 - 9*s + 2*s**i + 45*s**2 - 20 + 34*s = 0. Calculate s.
-4/3, 1
Let i be (810/12)/5*-14. Let r = -566/3 - i. Factor -4/3 + r*f**2 + 0*f.
(f - 2)*(f + 2)/3
Suppose 0 = 5*k + 24*k - 58. Let w(s) be the first derivative of 1/7*s**3 - 9/7*s**k + 15/7*s + 11. Let w(t) = 0. Calculate t.
1, 5
Let d(h) = 41*h - 120. Let p be d(3). Let n(f) be the third derivative of -1/21*f**3 + 0 + p*f**2 + 0*f + 0*f**4 + 1/210*f**5. Factor n(s).
2*(s - 1)*(s + 1)/7
Let o(h) be the third derivative of h**9/12096 - h**8/6720 - h**7/3360 + h**6/1440 - 10*h**3/3 - 23*h**2. Let a(m) be the first derivative of o(m). Factor a(w).
w**2*(w - 1)**2*(w + 1)/4
Solve 18/13*v**2 - 2/13*v - 18/13 + 2/13*v**3 = 0 for v.
-9, -1, 1
Let s(g) be the second derivative of g**4/66 + 58*g**3/33 + 57*g**2/11 + 78*g. Factor s(z).
2*(z + 1)*(z + 57)/11
Let d = 616/933 + 2/311. Factor 2/9*z**3 + 2/9 + 2/3*z + d*z**2.
2*(z + 1)**3/9
Let x be (-8)/(-20) - 893/2820. Let q(t) be the third derivative of -1/12*t**4 - 1/420*t**7 - x*t**3 - 1/20*t**5 + 5*t**2 + 0*t - 1/60*t**6 + 0. Factor q(r).
-(r + 1)**4/2
Let u be 2 - -5 - (-55)/(-8). Let k(y) be the first derivative of 9/16*y**2 - u*y**3 - 5 - 3/4*y. What is c in k(c) = 0?
1, 2
Let l be (-5 - 0/(-2))/(110/(-88)*1). Find r, given that 3/2*r**l + 3/2 - 3*r**2 + 3/2*r**3 - 3/4*r**5 - 3/4*r = 0.
-1, 1, 2
Let v = -2/4167 - -11126/29169. Factor -8/21*u - 2/21*u**2 - v.
-2*(u + 2)**2/21
Suppose 0 = 20*n - 17*n - 15. Suppose -4*d - 16 = -x, 0 = 5*x + n*d - 3 + 23. Let 0*k + 0*k**2 + x*k**4 + 0 + 1/2*k**5 - 1/2*k**3 = 0. What is k?
-1, 0, 1
Let t(c) be the third derivative of c**9/90720 - c**8/20160 + c**7/15120 - c**4/3 + 27*c**2. Let z(y) be the second derivative of t(y). Factor z(g).
g**2*(g - 1)**2/6
Let y be 290/(-42)*9/12. Let h = y - -38/7. Find j, given that -h*j**2 + 0 + 1/4*j = 0.
0, 1
Let g(j) = 17*j + 68. Let u be g(-4). Let b(w) be the third derivative of 0*w - 1/150*w**5 + 0*w**3 + u + 0*w**4 + 2*w**2. Factor b(o).
-2*o**2/5
Let u = 41 - 41. Let x(m) be the third derivative of u*m**3 + 1/2*m**4 + 0 - 1/20*m**5 - 7*m**2 + 0*m. Factor x(z).
-3*z*(z - 4)
Let g be (-4)/(3*2/12). Let h = -4 - g. Find v, given that -5*v**5 - v**4 + 2*v**h + 6*v**5 = 0.
-1, 0
Let b(k) be the first derivative of 3*k**4/16 - 3*k**2/8 + 216. Solve b(r) = 0 for r.
-1, 0, 1
Let i(v) be the first derivative of v**7/560 - v**6/120 - 3*v**5/80 + v**3 - 7. Let j(a) be the third derivative of i(a). Factor j(n).
3*n*(n - 3)*(n + 1)/2
Let g(t) be the f