t o be l(1). Let z(j) be the third derivative of 0*j + 5/8*j**4 + 5/3*j**3 - 11*j**o + 1/12*j**5 + 0. Factor z(g).
5*(g + 1)*(g + 2)
Let q be (((-12)/(-21))/(-2))/(2/(-28)). Let b(k) be the first derivative of 1/26*k**q + 2 - 4/39*k**3 + 0*k + 1/13*k**2. Factor b(o).
2*o*(o - 1)**2/13
Let n(w) = -6*w**3 + 6*w**2 + 54*w - 54. Let y(b) = 3*b**3 - 3*b**2 - 27*b + 27. Let f(q) = -4*n(q) - 7*y(q). What is g in f(g) = 0?
-3, 1, 3
Let k = -1513/33 - -684/11. Suppose 190/3*x**2 + 17/3*x**4 + 161/3*x + 1/3*x**5 + k + 94/3*x**3 = 0. Calculate x.
-7, -1
Let v(x) = -7*x**3 + 4*x**2 + 6*x + 2. Let b be v(-1). Let l(z) be the first derivative of -6*z - 3/4*z**4 + b - 4*z**3 - 15/2*z**2. Factor l(t).
-3*(t + 1)**2*(t + 2)
Factor -36/7 + 10/7*u**3 - 62/7*u**2 + 86/7*u + 2/7*u**4.
2*(u - 2)*(u - 1)**2*(u + 9)/7
Let c(v) be the first derivative of -5*v**4/4 + 20*v**3 + 5*v**2/2 - 60*v - 419. What is f in c(f) = 0?
-1, 1, 12
Solve 4/3*h**3 - 4*h**2 + 8/3*h + 0 = 0 for h.
0, 1, 2
Let o(m) be the first derivative of -m**7/189 - 2*m**6/135 + m**5/30 - 7*m + 8. Let u(d) be the first derivative of o(d). Factor u(b).
-2*b**3*(b - 1)*(b + 3)/9
Let p be 20/(-9)*(-72)/60. Solve 10/3*t**2 + 0*t**3 - p + 0*t - 2/3*t**4 = 0.
-2, -1, 1, 2
Let a be 4*3/(-42) - 258/(-21). Let z(r) be the first derivative of 0*r**2 - 1/8*r**4 + 0*r + a - 1/3*r**3. Find j, given that z(j) = 0.
-2, 0
Let f(k) be the third derivative of k**7/10 - k**6/20 - 72*k**2. Factor f(i).
3*i**3*(7*i - 2)
Let j be ((-282)/(-235))/(21/30). Find c such that -9/7*c**4 - j*c**5 - 6/7*c**2 + 0*c + 0 + 27/7*c**3 = 0.
-2, 0, 1/4, 1
Let x(i) be the first derivative of -3*i**2 - i**3 - 1/2*i**6 + 3/5*i**5 - 11 + 9/4*i**4 + 0*i. Find q such that x(q) = 0.
-1, 0, 1, 2
Suppose 4*b - n = -2*n + 22, 10 = 5*n. Let f(c) be the first derivative of 0*c**2 - 6 + 0*c - 1/4*c**4 + 1/6*c**6 + 1/5*c**b - 1/3*c**3. Factor f(w).
w**2*(w - 1)*(w + 1)**2
Let p(x) be the third derivative of -2/315*x**7 - 8/9*x**3 + 0 - 1/15*x**6 - 13/45*x**5 - 2/3*x**4 + 0*x - 9*x**2. Solve p(s) = 0 for s.
-2, -1
Suppose 0 = -4*w - t - 19, w - 4*t - t = -10. Let h = w - -8. Factor -15*n**2 - 3*n + 10*n**h + 5 - 2 - 19*n**3.
-3*(n + 1)**2*(3*n - 1)
Let g = -735 + 738. Let b(l) be the first derivative of 0*l**4 + 0*l + 1/7*l**2 + 3 + 4/21*l**g - 1/21*l**6 - 4/35*l**5. Factor b(j).
-2*j*(j - 1)*(j + 1)**3/7
Let x(z) = z**5 + 2*z**2 - z + 1. Let g(b) = -15*b**5 + 42*b**4 - 58*b**3 + 20*b**2 + b - 5. Let k(w) = -g(w) - 5*x(w). Suppose k(c) = 0. What is c?
0, 1/5, 1, 2
Let x(h) be the first derivative of 3*h**5/5 - 9*h**4/2 - 9*h**3 + 21*h**2 + 226. Factor x(l).
3*l*(l - 7)*(l - 1)*(l + 2)
Let r(x) = 5*x**4 + 16*x**3 + 28*x**2 + 14*x + 5. Let l(j) = j**4 + j**2 - j + 1. Let p(o) = 2*l(o) - r(o). Solve p(m) = 0.
-3, -1, -1/3
Let i be 4/20 + 63/210. Find d such that 1/2*d**2 + 1/2*d**3 - i - 1/2*d = 0.
-1, 1
Let d(i) be the third derivative of 11*i**4/24 - 7*i**3 - 64*i**2. Let h be d(4). Solve 0 + 2/9*g**h + 2/9*g - 4/9*g**3 = 0 for g.
-1/2, 0, 1
Let v be (-27)/2*6/(-9). Suppose -v - 6 = -3*s. Solve 24*r**4 + 8 - 5*r**5 + 71*r**2 + r**s - 36*r - 7*r**2 - 37*r**3 - 19*r**3 = 0.
1, 2
Let h(y) = 3*y**2 - 30*y + 49. Let u(i) = -65*i**2 + 660*i - 1080. Let s(r) = -45*h(r) - 2*u(r). Factor s(j).
-5*(j - 3)**2
Suppose 0 = 5*q - 15 - 5. Solve -f**3 - q*f**2 - 2*f**3 + 9*f**2 - 8*f**2 = 0.
-1, 0
Suppose 0 = 4*b - 3*k - 15, 4*b - 7*k + 5*k = 14. Let j(g) be the third derivative of 0*g**b - 5*g**2 + 1/330*g**5 + 0 + 0*g + 1/132*g**4. Solve j(l) = 0.
-1, 0
Let n(j) be the third derivative of j**6/24 - 19*j**5/12 + 50*j**4/3 + 250*j**3/3 + 30*j**2. Factor n(v).
5*(v - 10)**2*(v + 1)
Let g(h) be the second derivative of -2/11*h**2 + 0 + 8*h - 5/33*h**3 + 2/33*h**4 + 3/110*h**5. Determine x so that g(x) = 0.
-2, -1/3, 1
Let x be 25*-8*2/(-20). Suppose -5 + 0*p**3 + 10*p**3 - 10*p + x*p**2 + 67*p**4 - 82*p**4 = 0. What is p?
-1, -1/3, 1
Let w(c) = c**2 + 2. Let z be w(2). Suppose 28 = d + z*d. Factor 1 - 7/2*h - h**3 + 1/2*h**5 + 4*h**2 - h**d.
(h - 1)**4*(h + 2)/2
Let q = 831 - 827. Let b(w) be the first derivative of -5/9*w**2 + 2/3*w + 1/18*w**q + 9 + 2/27*w**3. Factor b(x).
2*(x - 1)**2*(x + 3)/9
Let p(c) be the first derivative of 9*c**7/280 - 13*c**6/120 + c**5/9 - c**4/18 + 16*c**3/3 + 8. Let b(u) be the third derivative of p(u). Factor b(t).
(t - 1)*(9*t - 2)**2/3
Factor -4*p**3 - 3*p - 2*p + 15*p**2 + 2*p**3 + 7*p**3 - 15.
5*(p - 1)*(p + 1)*(p + 3)
Suppose 5*i = -3*p + 2, 28 = 2*p + 3*p - 4*i. Suppose -p*s + 10 = s. Let -v**3 - 19*v + 8*v + 1 + 12*v - v**s = 0. Calculate v.
-1, 1
Factor -559 + 112*l**3 - 2*l**4 - 112*l + 1043 + 1084 - 1566*l**2.
-2*(l - 28)**2*(l - 1)*(l + 1)
Determine z, given that -53/3*z - 1/3*z**3 - 26/3 - 28/3*z**2 = 0.
-26, -1
Let q(u) be the third derivative of u**10/6048 + u**9/1512 + 7*u**4/24 + 7*u**2. Let k(p) be the second derivative of q(p). Factor k(z).
5*z**4*(z + 2)
What is f in 16*f**2 - 14*f**2 - 821*f + 265*f - 6*f**2 - 552 = 0?
-138, -1
Let n(z) be the first derivative of 1/6*z**6 + 0*z**2 + 0*z + 3/5*z**5 + 2 + 1/2*z**4 + 0*z**3. Determine f so that n(f) = 0.
-2, -1, 0
Let b(g) = -6*g**3 - 13*g**3 + g + g**2 + 3 + 18*g**3. Let i be 1/(1/(-3)*1). Let c(y) = y**3 - 2*y**2 - y - 4. Let z(k) = i*b(k) - 2*c(k). Factor z(a).
(a - 1)*(a + 1)**2
Factor 0*z + 0 - 1/3*z**4 - 55/3*z**2 - 56/3*z**3.
-z**2*(z + 1)*(z + 55)/3
Suppose 24*r = 123 - 123. Let j(k) be the second derivative of 0*k**4 + 2/15*k**6 + r*k**2 + 0 + 0*k**3 + 2/5*k**5 - 9*k. Let j(y) = 0. Calculate y.
-2, 0
Suppose 4*b + 2704 - 2680 = 12*b. Find z, given that 0 + 2/13*z + 0*z**2 - 2/13*z**b = 0.
-1, 0, 1
What is i in -186/13*i**2 - 59582/13 - 5766/13*i - 2/13*i**3 = 0?
-31
Let i be (-8)/(-52) - 84/546. Let o = -1/5 + 7/10. Factor i*l + o*l**2 + 0.
l**2/2
Suppose 34*w - 36 = 31*w. Let -4*p + p**2 - w + 18 - p = 0. What is p?
2, 3
Let v be (-19)/4 + 5 - (-705)/(-4). Let c = v - -1238/7. Determine k, given that 8/7*k + 2/7*k**2 + c = 0.
-3, -1
Let p(h) be the second derivative of h**6/120 + h**5/20 + h**4/16 - 7*h - 1. Factor p(w).
w**2*(w + 1)*(w + 3)/4
Let s(h) be the third derivative of h**5/300 + 41*h**4/60 + 1681*h**3/30 + 6*h**2 + 28. Suppose s(a) = 0. Calculate a.
-41
Suppose z + z - 6 = 0. Let l = 23 + -39. Let s(k) = -2*k**2 - 2*k + 1. Let j(d) = -10*d**2 - 10*d + 4. Let h(x) = l*s(x) + z*j(x). Factor h(i).
2*(i - 1)*(i + 2)
Let d(h) be the first derivative of h**3/7 + 129*h**2/14 - 270*h/7 + 146. Factor d(j).
3*(j - 2)*(j + 45)/7
Let m be (264 - 263)*(-9)/(-4). Let g = -32/3 - -137/12. Suppose g*c**3 + m*c**2 + 3/4 + 9/4*c = 0. What is c?
-1
Let w = -813 + 5695/7. What is q in -2/7*q**2 + w*q - 2/7 = 0?
1
Let v be 1 + (2/4)/(2/16). Suppose -3*o - k + 9 = -2*k, 0 = -v*o - 5*k - 5. Solve 8/3*h - 7/6*h**o - 2/3 = 0.
2/7, 2
Determine q so that 2*q**3 + 1623 + 326 + 726*q + 66*q**2 + 713 = 0.
-11
Let h = 70586/15 + -14110/3. Suppose h*i + 2/5*i**2 + 16/5 = 0. Calculate i.
-4, -2
Suppose 42 = 5*l + 12*b - 13*b, -l + 3*b = -14. Let i(p) be the second derivative of 0*p**2 + 0 + 1/16*p**4 - 1/2*p**3 - l*p. Factor i(t).
3*t*(t - 4)/4
Let c(j) = j**3 + 5*j**2 - 23*j + 10. Let v(b) = -b - 31. Let d be v(-23). Let k be c(d). Suppose -1/8*r**k + 1/8*r**3 - 5/8*r - 3/8 = 0. Calculate r.
-1, 3
Let p(l) = l**2 - l - 12. Let n be p(6). Suppose 0 = 21*v - n*v - 6. Factor 6*r**3 + 8*r**3 + v*r + 2*r**2 - 16*r**3 - 2*r**4.
-2*r*(r - 1)*(r + 1)**2
Let u(y) be the second derivative of 0*y**3 + 0*y**4 - 1/126*y**7 + 24*y - 1/45*y**6 + 0 + 0*y**2 + 1/20*y**5. Find g such that u(g) = 0.
-3, 0, 1
Let h(q) be the second derivative of -q**4/78 + 4*q**3/39 + 12*q**2/13 - q + 47. Factor h(u).
-2*(u - 6)*(u + 2)/13
Find h such that -2880*h + 5184/7 + 4192/7*h**2 + 33056/7*h**3 + 3620/7*h**4 + 100/7*h**5 = 0.
-18, -1, 2/5
Let k(d) be the first derivative of -4*d**2 - 4 - 1/10*d**5 + 0*d**3 + 2*d + 1/2*d**4. Let h(g) be the first derivative of k(g). Suppose h(a) = 0. What is a?
-1, 2
Let v(x) be the second derivative of -75*x**7/14 - 117*x**6/2 - 511*x**5/4 - 685*x**4/12 + 200*x**3/3 + 30*x**2 + 564*x. Suppose v(d) = 0. What is d?
-6, -1, -2/15, 1/3
Let q(j) = -j**2 - 6*j**2 + 9*j**2 + 14*j + 35 - 3*j**2. Let n be q(16). Let -1/2*o + 0 + 1/4*o**n + 1/4*o**2 = 0. What is o?
-2, 0, 1
Suppose -2*