1)/3
Let y(h) be the third derivative of -h**8/70560 - h**7/1764 - 5*h**6/504 + h**5/4 + h**2. Let b(l) be the third derivative of y(l). Find p, given that b(p) = 0.
-5
Let u(h) = h - 12. Let y be u(11). Let a be (8/(-2) - y) + (-10)/(-3). Suppose -a*p**2 - 2/3*p + 0 = 0. What is p?
-2, 0
Determine b so that -15/7*b + 0 - 3/7*b**2 = 0.
-5, 0
Let y(l) = 17*l**5 - 8*l**4 - 8*l**3. Let z(t) = -t**5 + t**3 - t**2. Suppose -7 = -5*n - 12. Let f(s) = n*z(s) - y(s). Solve f(i) = 0.
-1/4, 0, 1
Suppose -4*j = 2*u - 3*j - 10, -14 = -5*u + 3*j. Factor 0*y**5 + 3*y**5 + 15*y**3 + 2*y**u + 10*y**4 - 6*y**3.
3*y**3*(y + 1)*(y + 3)
Let g = 7/57 - -23/19. Solve 0*t + t**2 - g - 1/3*t**3 = 0.
-1, 2
Let x(t) = 3*t**2 - 28*t + 12. Let g(m) = m**2. Let l(k) = -2*g(k) + x(k). Let a(h) = -h**2 + 19*h - 8. Let b(q) = -7*a(q) - 5*l(q). Factor b(d).
(d + 4)*(2*d - 1)
Let 40/7*d**3 + 0*d**2 - 8/7*d**5 - 32/7*d - 12/7 + 12/7*d**4 = 0. What is d?
-1, -1/2, 1, 3
Factor -16/3 - 2/3*w**3 - 4*w**2 - 8*w.
-2*(w + 2)**3/3
Let s(w) be the third derivative of 1/20*w**5 - 1/160*w**6 + 0*w**3 - 1/280*w**7 - 16*w**2 + 1/8*w**4 + 0*w + 0. Factor s(a).
-3*a*(a - 2)*(a + 1)*(a + 2)/4
Let m be (1636/(-2863))/(2 + -1 + (-18)/14). Determine r, given that 3/5*r**m + 12/5*r + 0 = 0.
-4, 0
Let w(u) be the second derivative of u**4/24 - 95*u**3/12 - 24*u**2 + 8*u + 21. Factor w(l).
(l - 96)*(l + 1)/2
Let t be ((-10)/(-15))/((-4)/(-90)). Factor -t*x**2 - 2*x + 13*x**2 - 4*x + 20.
-2*(x - 2)*(x + 5)
Let t(b) be the second derivative of 1/2*b**2 + 0*b**3 + 1/4*b**4 - 1/40*b**6 + 0 - 1/20*b**5 + 2*b. Let v(a) be the first derivative of t(a). Factor v(d).
-3*d*(d - 1)*(d + 2)
Let v = -233 + 177. Let h be 92/115*-10*2/v. Factor 2/7*j + 0 + h*j**2.
2*j*(j + 1)/7
Let o = -20 + 15. Let b be o/2*-1*9/15. Suppose b - 21/2*s**2 - 9/4*s + 45/4*s**3 = 0. Calculate s.
-2/5, 1/3, 1
Let f be (36/(-14))/((-18)/63). Let m(t) = -12*t + 110. Let b be m(f). Find h such that 0*h**b - 2/7*h**5 + 0*h - 8/7*h**3 + 0 - 8/7*h**4 = 0.
-2, 0
Let k(q) be the second derivative of -q**6/60 - q**5/4 + 11*q**4/24 - 2*q + 87. Solve k(i) = 0.
-11, 0, 1
Let h(k) be the third derivative of 0*k**4 + 0*k**3 + 0*k + 1/300*k**5 + 0 - 1/1050*k**7 + 0*k**6 + 6*k**2. Solve h(l) = 0.
-1, 0, 1
Let u(d) = -d**3 - 6*d**2 - 8*d + 4. Let v be u(-4). Let m(q) be the first derivative of 4/5*q**2 + 1/20*q**v - 4/5*q + 5 - 1/3*q**3. Factor m(g).
(g - 2)**2*(g - 1)/5
Let h(u) be the first derivative of u**5/4 - u**4/2 - u**3/2 - 9*u**2/2 - 9. Let g(y) be the second derivative of h(y). Suppose g(n) = 0. What is n?
-1/5, 1
Let f(b) be the third derivative of 3/80*b**5 + 1/420*b**7 - 7/480*b**6 - 5/96*b**4 + 0*b + 0 + 1/24*b**3 + 6*b**2. Solve f(a) = 0 for a.
1/2, 1
Let h = -295 + 176. Let j be (-323)/h + 4/14. Factor 0 - 1/3*s - 5*s**j + 7/3*s**2 + 13/3*s**4 - 4/3*s**5.
-s*(s - 1)**3*(4*s - 1)/3
Let p(h) be the first derivative of h**5 - 105*h**4/4 + 200*h**3 - 250*h**2 + 258. What is n in p(n) = 0?
0, 1, 10
Let i(z) be the third derivative of -z**5/39 - 19*z**4/52 + 6*z**3/13 + 656*z**2. Factor i(a).
-2*(a + 6)*(10*a - 3)/13
Let o(y) be the first derivative of -4/33*y**3 + 4/33*y**4 + 1/30*y**5 + 0*y - 1 - y**2 - 3/220*y**6. Let c(l) be the second derivative of o(l). Solve c(x) = 0.
-1, 2/9, 2
Let 3/2*x**5 + 0*x - 4*x**4 + 0 - 3/2*x**3 + 0*x**2 = 0. What is x?
-1/3, 0, 3
Determine b so that 1/6*b**2 - 14/3*b + 98/3 = 0.
14
Let d(u) be the first derivative of u**7/2100 - u**6/180 + u**5/50 + 19*u**3/3 - 26. Let y(k) be the third derivative of d(k). Factor y(t).
2*t*(t - 3)*(t - 2)/5
Let f(h) = -6*h - h**2 + 4*h + 3*h**4 + 2*h**4 - 2*h**3. Let n(c) = -c**4 + 2*c - 25*c**3 - 4*c**4 + 28*c**3. Let u(l) = 5*f(l) + 4*n(l). Factor u(t).
t*(t - 1)*(t + 1)*(5*t + 2)
Let n be 16/6 - (-6)/(-9). Find z, given that 4*z**3 - 2*z - z**4 - 3 - z**4 - 2 + 4*z**n + 3 - 2*z**5 = 0.
-1, 1
Suppose 435*r - 457*r + 44 = 0. Factor -8/5 - 6/5*a**r - 12/5*a - 1/5*a**3.
-(a + 2)**3/5
Suppose 5*x + 57 = -u, -5*x - 2*u = 3*u + 45. Let y be 3 + -4 + x/(-9). Factor 5/3*q**3 + 0*q - 2/3*q**2 - 4/3*q**4 + y*q**5 + 0.
q**2*(q - 2)*(q - 1)**2/3
Suppose -42*r**3 - 66 - 39*r - 60*r + 3*r**5 + 96*r**2 - 30*r**4 + 138*r = 0. Calculate r.
-2, -1, 1, 11
Let v(s) = s**2 + 6*s + 2. Let p be v(-6). Suppose 0 = 9*g - 10 - 8. Factor 2*a**p - 18*a - a**g - 27 - 4*a**2.
-3*(a + 3)**2
Let p(g) be the first derivative of -2*g**5/25 + 9*g**4/10 - 58*g**3/15 + 39*g**2/5 - 36*g/5 + 197. Suppose p(h) = 0. Calculate h.
1, 2, 3
Let c(h) = -h**3 - 6*h**2 + 3*h - 26. Let z be c(-7). What is l in -11*l**5 + 6*l**5 + 10*l**3 + 7*l - 10*l**z - 10*l**2 + 10 - 12*l + 10*l**4 = 0?
-1, 1, 2
Let g(f) be the second derivative of 1/160*f**5 + 1/4*f**2 - 7/48*f**3 + 1/48*f**4 + 0 - 17*f. Find i such that g(i) = 0.
-4, 1
Let 12/5*d + 0 - 16/5*d**2 + 16/5*d**4 - 8/5*d**3 - 4/5*d**5 = 0. What is d?
-1, 0, 1, 3
Let f(j) = 51*j - 250. Let m be f(5). Determine l, given that 2/11*l**m + 32/11 - 32/11*l - 14/11*l**4 - 16/11*l**2 + 32/11*l**3 = 0.
-1, 2
Let u = -137 - -150. Suppose -20 = -2*h - 0. Factor -20*g**2 - 7*g - h + 8*g**3 - u*g**3 - 18*g.
-5*(g + 1)**2*(g + 2)
Suppose 9 - 42 = -11*f. Suppose -s = 3*i - 3, i = -f*s - 4 - 3. Factor -1/2*r + 0 - 1/4*r**i.
-r*(r + 2)/4
Let h(r) be the first derivative of 1/2*r**4 + 1/9*r**3 - 7 + 0*r**2 + 3/5*r**5 + 2/9*r**6 + 0*r. Factor h(k).
k**2*(k + 1)**2*(4*k + 1)/3
Let o be 9/(-3) + -2 - -102. Let c = o + -97. Let 0*m**2 + c - 1/2*m**3 + 0*m = 0. Calculate m.
0
Let -212*t**4 - 4*t**5 + 101*t**3 - 601*t**3 - 2200*t**3 + 2916*t**2 = 0. What is t?
-27, 0, 1
Let n(k) be the second derivative of k**6/480 - 13*k**5/80 + 169*k**4/32 - 4*k**3 - 20*k. Let q(p) be the second derivative of n(p). Factor q(d).
3*(d - 13)**2/4
Suppose -d + 5*a = -4 + 12, 0 = 4*d - a - 6. Factor -147 + 137 - d*q - 5*q - 8*q + 5*q**3.
5*(q - 2)*(q + 1)**2
Let z be (-206)/(-208) + (-10)/(480/18). Let 6/13*o**2 + 8/13*o**3 + 2/13*o**4 - 8/13*o - z = 0. What is o?
-2, -1, 1
Let c(k) be the third derivative of k**5/50 + 99*k**4/40 + 49*k**3/10 + 63*k**2 + 2*k. Factor c(o).
3*(o + 49)*(2*o + 1)/5
Let k = 130 + -105. Suppose 0 = -k*g + 20*g. Let g*l + l**4 + 1/3 + 2/3*l**3 - 4/3*l**2 - 2/3*l**5 = 0. What is l?
-1, -1/2, 1
Let -147*r**3 - 8250*r**2 - 29851 - 23276 + 772*r**3 + 36300*r - 113 = 0. Calculate r.
22/5
Let q(t) be the second derivative of -1/15*t**3 - 1/60*t**4 - 2*t + 0*t**2 + 0. Solve q(j) = 0.
-2, 0
Let i(o) = o**5 - o**3 - o**2 + o. Let t(f) = -87*f**4 - 807*f**3 - 1923*f**2 + 4803*f + 6000. Let c(q) = 3*i(q) - t(q). Factor c(z).
3*(z - 2)*(z + 1)*(z + 10)**3
Let n be -2*57/18 - -7. Let t(j) be the first derivative of 6 - 4/3*j**2 - 4/3*j**3 + 0*j + n*j**4. Determine f so that t(f) = 0.
-1/2, 0, 2
Let b = -251 - -253. Let k(z) be the third derivative of -1/2*z**3 - 5*z**b - 1/4*z**4 + 0 + 0*z - 1/160*z**6 - 1/16*z**5. Factor k(q).
-3*(q + 1)*(q + 2)**2/4
Let k(z) be the first derivative of z**5/20 - 9*z**4/16 + 23*z**3/12 - 15*z**2/8 - 222. Suppose k(r) = 0. Calculate r.
0, 1, 3, 5
Let h be 5624/(-1628) + (-8)/(-2). Factor 0 + 18/11*n - h*n**2.
-6*n*(n - 3)/11
Let u(p) be the third derivative of 0 + 0*p + 32/1155*p**7 + 1/11*p**3 - 8/55*p**6 - 4*p**2 - 1/55*p**5 + 17/132*p**4. Suppose u(v) = 0. Calculate v.
-1/4, 1/2, 3
Let n = 1381/5 + -276. Let z(g) be the second derivative of n*g**2 + 0 - 1/30*g**3 - 1/60*g**4 + 2*g. Factor z(i).
-(i - 1)*(i + 2)/5
Let s(d) be the second derivative of 0 - 6*d**2 + 0*d**3 + 9/20*d**5 + 30*d + 7/4*d**4. What is m in s(m) = 0?
-2, -1, 2/3
Let c be 21/7 + 0 + 1. Suppose 4*p + 2*n = 2, c*p = -n - 0*n + 7. Factor -4*x**3 - 12 + 9*x**2 + 0*x**3 - 12*x + 5*x**3 - 3*x**4 + 5*x**p.
-3*(x - 2)**2*(x + 1)**2
Let m(x) be the third derivative of x**6/20 + 29*x**5/60 - 7*x**4/24 - 5*x**3/3 - 10*x**2 + 11*x. Find y such that m(y) = 0.
-5, -1/2, 2/3
Let j = 92 - 87. Solve -14 - 156*i**2 + 120*i**2 + 40*i + 3*i**3 + j*i**3 + 2*i**4 = 0.
-7, 1
Let f = 33 - 57. Let q be 6/f + 3/4. Suppose 3/4*d + 1/4*d**2 + q = 0. Calculate d.
-2, -1
Let g(n) be the first derivative of 0*n**3 + 1/48*n**4 - 1/8*n**2 + n - 3. Let m(s) be the first derivative of g(s). Factor m(t).
(t - 1)*(t + 1)/4
Let m(u) be the first derivative of 1/2*u**4 - 2*u**3 + 2*u**2 + 0*u + 44. Factor m(s).
2*s*(s - 2)*(s -