*s**2 - 3/2 = 0. Calculate s.
-1/2, 1
Let m(d) be the first derivative of 21 + 5/4*d + 5/8*d**4 - 15/8*d**2 + 5/24*d**6 - 3/4*d**5 + 5/6*d**3. Find u, given that m(u) = 0.
-1, 1
Let r(a) = -6*a. Let l be r(-2). Suppose 2*o - l = -o. Factor 3*k**2 - o*k**4 + k**4 - 3*k**2.
-3*k**4
Let n(o) = o**3 - o**2 - 9*o - 14. Let z(q) = q**2. Let h(u) = 3*n(u) + 21*z(u). Find x such that h(x) = 0.
-7, -1, 2
Let y(m) = 5*m + 11. Let x be y(-4). Let f = -7 - x. Suppose 5*c**2 + 3*c**3 - 4*c**3 - f*c**2 = 0. What is c?
0, 3
Let d(t) be the second derivative of -t**5/80 + 7*t**4/24 + 16*t. Factor d(x).
-x**2*(x - 14)/4
Let z(x) = 2*x**2 + 108. Let l be z(0). Suppose -116*y + l*y + 24 = 0. Factor -1/2*k**2 + 0*k + 0 + 1/4*k**y.
k**2*(k - 2)/4
Let a(f) be the first derivative of 5*f**4/4 - 15*f**3 + 15*f**2 + 280*f + 2. What is v in a(v) = 0?
-2, 4, 7
Let v = -56 - -23. Let o(p) = -3*p**3 - 19*p**2 - 21*p - 9. Let z(x) = -24*x**3 - 153*x**2 - 168*x - 72. Let y(i) = v*o(i) + 4*z(i). Factor y(w).
3*(w + 1)**2*(w + 3)
Let t = 1562 - 1562. Factor 6/7*o**3 + t*o**4 - 3/7*o + 0 + 0*o**2 - 3/7*o**5.
-3*o*(o - 1)**2*(o + 1)**2/7
Factor -65 - 229*t**2 + 462*t**2 - 238*t**2 - 70*t.
-5*(t + 1)*(t + 13)
Let o = 72292/9 - 8032. Factor -o*j - 4/9 - 1/9*j**2.
-(j + 2)**2/9
Let t(c) be the third derivative of 5*c**8/84 - 10*c**7/21 + 37*c**6/24 - 5*c**5/2 + 15*c**4/8 - 3*c**2 + 30. Factor t(g).
5*g*(g - 1)**2*(2*g - 3)**2
Let p(w) be the third derivative of 8*w**7/21 - 29*w**6/3 - 119*w**5/12 - 25*w**4/8 - 35*w**2. Suppose p(r) = 0. What is r?
-1/4, 0, 15
Let c(k) = -2*k**2 - 8*k - 3. Let y be c(-6). Let h be y/(-12) - 3/(-4). Find w such that -h*w - 10*w**2 + 0*w - 5*w**2 = 0.
-1/5, 0
Let r = -248/3 - -84. Let u = 13/48 - -1/16. Factor r*y + u*y**2 + 4/3.
(y + 2)**2/3
Let j(d) be the third derivative of d**6/30 + d**5/15 - 2*d**4/3 - 8*d**3/3 - 19*d**2. Factor j(r).
4*(r - 2)*(r + 1)*(r + 2)
Factor 5*g**4 + g**2 + 13*g**3 - 18*g**3 - 6*g**2 + 5*g.
5*g*(g - 1)**2*(g + 1)
Let m(t) = t**2 - 31*t + 54. Let o be m(29). Let p be ((-110)/120 - 1/o)*-3. Solve -2/5*k**4 + 0 + 6/5*k**3 - 8/5*k + 0*k**p = 0 for k.
-1, 0, 2
Let d(t) be the second derivative of -2*t**7/105 + 2*t**6/25 - 3*t**5/25 + t**4/15 + 130*t. Factor d(x).
-4*x**2*(x - 1)**3/5
Let n(f) be the first derivative of f**4/4 - 3*f**3 + 15*f**2/2 - 7*f - 117. Find u such that n(u) = 0.
1, 7
Suppose 304*l + 258 - 162*l**2 + 171*l**2 + 473*l = 0. Calculate l.
-86, -1/3
Let y(i) = 5*i**2 + 19*i + 7. Let f(t) = 2*t**2 + 9*t + 3. Suppose 0 = q, -3*q + 7 = 2*h + 1. Let x(o) = h*y(o) - 7*f(o). Suppose x(k) = 0. Calculate k.
0, 6
Let h be 25/(-100) - 1075/4. Let l = -266 - h. Factor -4/7*d**2 - 2/7*d**5 + 0*d + 0*d**4 + 6/7*d**l + 0.
-2*d**2*(d - 1)**2*(d + 2)/7
Let s = 2113 + -2113. Let p be 20/(-15)*(-3)/5. Find k, given that p - 4/5*k**2 + s*k = 0.
-1, 1
Suppose 0*u + 2*f - 12 = -2*u, -f + 14 = 5*u. Factor -3*l**2 + 9*l + u*l**2 - 2 - 4 - 2*l**2.
-3*(l - 2)*(l - 1)
Let l be (3 - 3)/(1 - -1). Let v be l + 1 + 0 + 77/28. Factor -21/4*t - v*t**2 - 3/2.
-3*(t + 1)*(5*t + 2)/4
Let h be -3 + 0 + 2*362855/241900. Let l = h - -2786687/24190. Find i, given that -162/5*i**4 - 24/5 - 206/5*i**2 - 184/5*i + l*i**3 = 0.
-2/9, 1, 3
Determine c, given that -127/4*c**3 - 63/4*c**5 + 291/4*c**4 + 5/2*c + 2 - 119/4*c**2 = 0.
-1/3, 2/7, 1, 4
Let g(q) be the first derivative of -q**8/112 - q**7/168 + q**6/9 - q**5/6 - 9*q**3 - 30. Let u(x) be the third derivative of g(x). Factor u(b).
-5*b*(b - 1)*(b + 2)*(3*b - 2)
Let z(p) be the second derivative of p**9/12096 + 11*p**8/13440 + p**7/360 + p**6/360 - p**4/6 + 10*p. Let w(b) be the third derivative of z(b). Factor w(n).
n*(n + 2)**2*(5*n + 2)/4
Determine x, given that 3/8*x**3 + 3/2*x**2 + 15/8*x + 3/4 = 0.
-2, -1
Factor -14*a**2 + 21 + 30*a + 61*a**2 - 102*a - 32*a**2 - 36*a.
3*(a - 7)*(5*a - 1)
Let v(t) be the first derivative of -t**6/285 - t**5/190 + t**4/114 + t**3/57 + 2*t + 9. Let o(y) be the first derivative of v(y). Find k such that o(k) = 0.
-1, 0, 1
Let w(x) be the second derivative of -1/8*x**4 - 20*x + 0*x**2 + 0 + 3/80*x**5 + 1/8*x**3. Factor w(f).
3*f*(f - 1)**2/4
Solve 3584*p - 63*p**2 - 3152*p + 3*p**3 + 408 - 1368 = 0 for p.
5, 8
Let f(j) = -2*j + 17*j - 13 + 4. Let a(y) = -10 + 0*y**2 + 14*y - y**2 + 0*y**2. Let x(i) = 3*a(i) - 2*f(i). Let x(v) = 0. Calculate v.
2
Suppose 0 = 27*u - 24*u - 45. Let b be 3/u*(22/6 + -2). Solve b*x**2 - x**5 - 1/3*x**4 + x**3 + 0*x + 0 = 0 for x.
-1, -1/3, 0, 1
Let b(v) be the third derivative of 1/10*v**4 + 1/70*v**7 - 11/100*v**5 + 2/5*v**3 - 1/50*v**6 + 0 - 6*v - 4*v**2 + 1/280*v**8. Let b(d) = 0. What is d?
-2, -1/2, 1
Let z(u) be the third derivative of 0*u**3 + 1/480*u**6 - 5*u**2 + 0*u + 0 + 1/48*u**4 - 1/80*u**5. Factor z(m).
m*(m - 2)*(m - 1)/4
Let u(r) be the first derivative of -r**8/4200 - r**7/2100 + r**6/900 + r**5/300 + 6*r**3 + 9. Let g(o) be the third derivative of u(o). Factor g(h).
-2*h*(h - 1)*(h + 1)**2/5
Suppose -4*o + 12 = -32. Factor -2 + 3*t**2 + 3*t**2 - 2*t**2 - o*t + 8.
(t - 2)*(4*t - 3)
Determine n so that -15 - 17*n**2 + 20*n**2 + 2*n**2 + 10*n = 0.
-3, 1
Let a be 4/(-8)*3 + (-1)/(-2). Let j be -1*(2 + a) - -2*2. Factor -7/3*k**2 + 8/3*k - 5/3*k**j + 4/3.
-(k - 1)*(k + 2)*(5*k + 2)/3
Let p(t) be the second derivative of -t**6/30 + 13*t**5/60 - t**4/9 - 104*t. Determine u so that p(u) = 0.
0, 1/3, 4
Let c(w) = -w**2 - 35*w - 283. Let p be c(-13). Find h, given that -3*h + 0 - p*h**2 - 3/4*h**5 + 9/4*h**3 + 3/2*h**4 = 0.
-1, 0, 2
Find v, given that -465*v**2 + 9 - 355*v**3 - 5*v**5 + 111*v + 185 - 75*v**4 + 355 + 249*v - 9 = 0.
-6, -3, -1, 1
Let u(l) be the second derivative of l**4/4 + 6*l**3 - 39*l**2/2 - 60*l. Factor u(a).
3*(a - 1)*(a + 13)
Let l(d) be the second derivative of -18*d + 3/50*d**5 - 1/5*d**3 + 0 + 1/30*d**4 - 1/5*d**2. Factor l(g).
2*(g - 1)*(g + 1)*(3*g + 1)/5
Let k(h) be the second derivative of -h**7/2016 - h**6/60 + h**5/24 - 9*h**4/2 + 51*h. Let a(u) be the third derivative of k(u). Let a(l) = 0. Calculate l.
-10, 2/5
Let a(c) = -c**2 - 13*c + 6. Let v be a(-6). Factor 1 + 2 + 24*f**2 + 29 + 4*f**3 + v*f.
4*(f + 2)**3
Let g(h) be the third derivative of -1/132*h**4 + 0*h - 4/33*h**3 + 0 - 27*h**2 + 2/165*h**5 + 1/660*h**6. Factor g(a).
2*(a - 1)*(a + 1)*(a + 4)/11
Let -6 - 6*o + 9/2*o**2 + 6*o**3 + 3/2*o**4 = 0. Calculate o.
-2, -1, 1
Let k = 405/4 + -34441/340. Let h = 73/255 - k. Factor -1 - 4/3*l - h*l**2.
-(l + 1)*(l + 3)/3
Let u(c) be the second derivative of c**6/1440 - c**5/160 + c**4/48 - c**3/2 - 14*c. Let d(r) be the second derivative of u(r). Determine g so that d(g) = 0.
1, 2
Let k be 2/(-7) - (192/14 - 2). Let o be 2/4*(-4 + (-64)/k). Factor -2/3 + o*z**2 + 0*z.
2*(z - 1)*(z + 1)/3
Suppose 4*c - 2*u = 20, -49*c + 3*u + 20 = -48*c. Find i, given that -432/7*i - 1728/7 - 1/7*i**3 - 36/7*i**c = 0.
-12
Let d be (1/((-5)/6))/(19 + (-1782)/90). Factor -1/4*l**2 + 0 - d*l.
-l*(l + 6)/4
Let d(v) be the first derivative of 8/9*v**3 + 29 - v**4 + 0*v - 1/3*v**2 + 8/15*v**5 - 1/9*v**6. Factor d(r).
-2*r*(r - 1)**4/3
Let o(h) be the third derivative of 0*h**3 + 1/135*h**7 + 1/54*h**4 + 0*h + 11/270*h**5 + 0 + 4/135*h**6 - 5*h**2. Factor o(n).
2*n*(n + 1)**2*(7*n + 2)/9
Solve 0 + 4*q + 8/3*q**2 - 1/3*q**4 - 1/3*q**3 = 0 for q.
-2, 0, 3
Suppose 5*j + 2*n + 0*n - 32 = 0, j = 2*n + 16. Suppose -25*o + j = -21*o. Factor 2/7*i**o - 10/7*i**3 + 0 + 0*i.
-2*i**2*(5*i - 1)/7
Let g(f) be the first derivative of -3*f**5/40 - 3*f**4/8 + f**3/4 + 9*f**2/4 + 42*f - 46. Let h(z) be the first derivative of g(z). Factor h(c).
-3*(c - 1)*(c + 1)*(c + 3)/2
Let o(t) be the third derivative of -t**9/45360 + t**8/6720 - t**7/3780 + 7*t**4/24 + 8*t**2. Let x(q) be the second derivative of o(q). Factor x(d).
-d**2*(d - 2)*(d - 1)/3
Let i(y) be the first derivative of y**8/1344 + y**7/140 + 3*y**6/160 + y**5/60 + 16*y**2 + 34. Let g(n) be the second derivative of i(n). Factor g(t).
t**2*(t + 1)**2*(t + 4)/4
Let p be 36/6*25/1. Let m = p - 446/3. Factor 1/3*i**2 + 4/3 - m*i.
(i - 2)**2/3
Let o(j) = -j**3 - 9*j**2 - 12*j - 28. Suppose 41 = -4*x + 9. Let r be o(x). Factor 0 - 6/7*c**2 - 2/7*c - 6/7*c**3 - 2/7*c**r.
-2*c*(c + 1)**3/7
Suppose -q - 2*q = 0. Suppose -2*d = -3*v + 85, q*v - 30 = -2*v - 4*d. Let 1 - 8*p**2 - 1