.
r*(r - 1)**2*(r + 1)/2
Let i(c) be the first derivative of c**4/6 + 2*c**3 - 16*c - 36. Let q(n) be the first derivative of i(n). Solve q(h) = 0.
-6, 0
Factor 2/11*c**3 + 70/11*c**2 + 0*c + 0.
2*c**2*(c + 35)/11
Let m(u) be the second derivative of 5776*u**4/3 - 304*u**3/3 + 2*u**2 - 135*u. Solve m(i) = 0 for i.
1/76
Let n(z) be the first derivative of -z**2 - 12 + 2/3*z**3 + 0*z. Factor n(r).
2*r*(r - 1)
Let r(a) be the third derivative of 0 - 1/240*a**6 + 0*a - 1/24*a**3 + 1/840*a**7 + 0*a**5 - 4*a**2 + 1/48*a**4. Let r(s) = 0. Calculate s.
-1, 1
Factor 2/3*x**2 + 4 - 14/3*x.
2*(x - 6)*(x - 1)/3
Let j(s) = s**2 - 2*s - 22. Let m be j(6). Let 58*v**2 + 96*v + 6 + 26*v**m - 196*v**3 + 10 = 0. Calculate v.
-2/7, 1
Let v(u) be the first derivative of -135*u**4/4 + 110*u**3 - 50*u**2 - 40*u + 61. Factor v(d).
-5*(d - 2)*(3*d - 2)*(9*d + 2)
Let x = 9/383 + 721/1915. Find i such that 0 - 16/5*i - x*i**2 = 0.
-8, 0
Let 2/7*q**3 - 4/7*q**4 + 2/7*q**5 + 0*q**2 + 0*q + 0 = 0. What is q?
0, 1
Let y = -27334 - -109341/4. Find d, given that -y*d + 5/4*d**2 - 15/2 = 0.
-2, 3
Let t(k) be the second derivative of -k**7/420 + k**6/45 - k**5/12 + k**4/6 - 7*k**3/6 - 13*k. Let v(c) be the second derivative of t(c). Factor v(u).
-2*(u - 2)*(u - 1)**2
Let j(m) be the first derivative of -1/5*m**2 + 1/6*m**3 + 7/60*m**4 - 3*m + 1. Let u(w) be the first derivative of j(w). What is b in u(b) = 0?
-1, 2/7
Let u be (6/(-8))/(-13 - 19605/(-1560)). Factor u*v**2 + 8/5*v + 4/5*v**3 + 8/15 + 2/15*v**4.
2*(v + 1)**2*(v + 2)**2/15
Let m(n) be the first derivative of -4*n**5/5 - 18*n**4 - 148*n**3/3 + 792*n**2 - 1936*n + 24. Factor m(x).
-4*(x - 2)**2*(x + 11)**2
Let 20*p**2 - 20*p**4 - 154/5*p**5 + 0 + 138/5*p**3 + 16/5*p = 0. Calculate p.
-1, -4/11, -2/7, 0, 1
Let r = 372 - 1111/3. What is u in -3*u - r*u**2 + 2/3 = 0?
-2, 1/5
Let u(y) be the first derivative of -y**3/8 - 141*y**2/16 + 18*y - 75. Factor u(f).
-3*(f - 1)*(f + 48)/8
Let f(u) be the third derivative of u**7/350 - u**6/300 - u**5/100 + u**4/60 - 40*u**2 - 3. Factor f(b).
b*(b - 1)*(b + 1)*(3*b - 2)/5
Let z(c) be the second derivative of -c**6/80 + 27*c**5/40 - 51*c**4/16 + 25*c**3/4 - 99*c**2/16 + 13*c + 1. Factor z(a).
-3*(a - 33)*(a - 1)**3/8
Find h, given that 1/2*h**4 + 2*h**3 + 3/2*h**2 + 0 + 0*h = 0.
-3, -1, 0
Let n(j) be the second derivative of -j**5/20 + 11*j**4/6 - 20*j**3/3 - j + 100. Determine s, given that n(s) = 0.
0, 2, 20
Let m(f) be the second derivative of -f**4/16 + 29*f**3/4 - 2523*f**2/8 + 36*f - 1. Suppose m(a) = 0. Calculate a.
29
Let d(u) = 2*u**4 - u**3 - 3*u**2 + u - 1. Let z(g) = 3*g**4 - 84*g**3 - 155*g**2 - 48*g + 4. Let h(t) = -40*d(t) + 5*z(t). Suppose h(r) = 0. What is r?
-3, -2, -1, 2/13
Let t = -86 - -108. Let r be t/24 + 6/(-9). Let 1/2*k**2 - 3/4*k + k**3 + 0*k**4 - 1/2 - r*k**5 = 0. What is k?
-1, 1, 2
Let i(u) = -4*u**2 - 11*u + 3. Let f be i(-3). Let c(s) be the third derivative of 0*s**3 - 3*s**2 + f + 1/80*s**5 + 0*s - 1/32*s**4. Find r such that c(r) = 0.
0, 1
Let k = 23521/42 + -560. Let j(b) be the second derivative of 0 + 0*b**6 + 0*b**4 + 1/10*b**5 + 4*b - k*b**7 + 0*b**2 - 1/6*b**3. Factor j(p).
-p*(p - 1)**2*(p + 1)**2
Let y(a) be the third derivative of 1/108*a**4 + 0*a**3 + 0*a + 0 + 8*a**2 - 1/540*a**6 + 0*a**5. Factor y(l).
-2*l*(l - 1)*(l + 1)/9
Suppose 9*f + 5*o = 4*f + 5, f = 5*o + 19. Let s(b) be the third derivative of 2/27*b**3 + 1/540*b**6 - 4*b**2 + 5/108*b**f + 0 + 2/135*b**5 + 0*b. Factor s(u).
2*(u + 1)**2*(u + 2)/9
Solve 8/3*l**2 + 578/3 - 136/3*l = 0.
17/2
Let d(j) be the first derivative of j**5/120 - j**4/24 + j**3/12 + 3*j**2/2 - 8. Let a(q) be the second derivative of d(q). Find x, given that a(x) = 0.
1
Let r(q) be the second derivative of -q**6/40 - q**5/4 - q**4 - 2*q**3 + q**2/2 + 9*q. Let u(a) be the first derivative of r(a). Factor u(s).
-3*(s + 1)*(s + 2)**2
Suppose -6*w + 2 + 40 = 0. Let x(g) be the second derivative of -9*g + 0 + 0*g**2 + 1/3*g**6 + 0*g**4 - 5/42*g**w - 1/4*g**5 + 0*g**3. Factor x(r).
-5*r**3*(r - 1)**2
Let j = 1613/1923 + -7/1282. Factor 2/3*b**2 - j*b + 1/6.
(b - 1)*(4*b - 1)/6
Factor 38 - 38 + 9*x + 23*x - 36*x**2 + 4*x**3.
4*x*(x - 8)*(x - 1)
Let d be (1/((-2)/58))/(-1). Find a, given that -a**4 - 9*a**2 + 23*a**3 - 6 - 57*a**3 + 4 - 7*a + d*a**3 = 0.
-2, -1
Let t(v) be the third derivative of -v**6/240 - v**5/30 - v**4/12 + 43*v**2. Factor t(f).
-f*(f + 2)**2/2
Suppose -6 = 4*f + 2. Let z(r) = -r**4. Let x(u) = u**4 - 2*u**3 + 10*u**2 - 6*u. Let k(n) = f*x(n) - 6*z(n). Suppose k(o) = 0. Calculate o.
-3, 0, 1
Let b = 173121/2500 + -277/4. Let n = 3769/11875 + b. Let 6/19*y**2 - n*y - 2/19*y**3 + 2/19 = 0. What is y?
1
Suppose 0 = l + 4*x - 19 + 3, -8 = 2*l - 2*x. Let k(y) be the second derivative of l*y**2 + 1/20*y**5 + y + 0 - 1/3*y**4 + 1/2*y**3. Factor k(w).
w*(w - 3)*(w - 1)
Let w(x) = x**2 - 2*x + 5. Let c = -37 - -57. Let r(l) = l - 1. Suppose -q = -5*g - 26, -18 = 4*g - g - 3*q. Let p(m) = c*r(m) + g*w(m). Factor p(d).
-5*(d - 3)**2
What is h in 2*h + 7*h**2 + 9/2*h**3 - 5/4*h**5 + 0 - 7/4*h**4 = 0?
-2, -1, -2/5, 0, 2
Let c(k) be the second derivative of 1/120*k**6 + 0 - 4*k + 0*k**5 + 1/336*k**7 - 1/48*k**3 + 0*k**2 - 1/48*k**4. Suppose c(g) = 0. Calculate g.
-1, 0, 1
Suppose 0 = 6*z - 9 - 3. Let m(o) be the second derivative of 0*o**z + 0*o**3 + 4*o + 1/45*o**6 + 1/9*o**4 + 0 - 1/10*o**5. Factor m(q).
2*q**2*(q - 2)*(q - 1)/3
Let m(o) be the third derivative of -3/2*o**4 + 0 + 18*o**3 + 1/20*o**5 + 0*o - 5*o**2. Factor m(w).
3*(w - 6)**2
Let x be (1/(-1) - -3)*1. Factor 9*a**2 + 0*a - 8*a**2 + x*a.
a*(a + 2)
Let x be (6/21)/(((-1440)/(-378))/10). Suppose 0 + 5/2*q**3 + 5/2*q**5 + 21/4*q**4 - x*q**2 - 1/2*q = 0. Calculate q.
-1, -1/2, 0, 2/5
Let c = -1/70 + 3/14. Solve -2/5*w**2 + 0*w - c*w**3 + 0 = 0.
-2, 0
Let d be 25/10 + (-2)/4. Suppose -d*l = 3*q + 7 - 30, 6 = -l + 2*q. Let -2*j**2 + 2 - 7*j**2 + 2*j**l + 0*j**2 + 5*j**2 = 0. What is j?
-1, 1
Let v(s) be the first derivative of -4*s**5 + 165*s**4/4 - 140*s**3 + 335*s**2/2 - 60*s - 112. Determine c so that v(c) = 0.
1/4, 1, 3, 4
Let h(z) be the third derivative of z**6/840 - 3*z**5/140 - 207*z**2. Suppose h(c) = 0. What is c?
0, 9
Let g(t) be the third derivative of 4*t**7/105 - 17*t**6/30 + 37*t**5/15 - 7*t**4/6 - 10*t**3 + 2*t**2 - 16*t. Find r, given that g(r) = 0.
-1/2, 1, 3, 5
Let p(t) = -t**3 - t**2 + 3. Let f(m) = 5*m**3 - 157*m**2 - 2349*m - 2211. Let x(d) = f(d) + 8*p(d). Factor x(r).
-3*(r + 1)*(r + 27)**2
Let u(a) be the third derivative of -1/240*a**6 + 1/48*a**4 - 4*a**2 + 0*a + 1/60*a**5 - 1/6*a**3 + 0. Factor u(x).
-(x - 2)*(x - 1)*(x + 1)/2
Factor -12*b**3 - 828*b + 18*b**2 + 52*b**2 + 148*b**2 - 51*b**2 - 648 + 41*b**2.
-4*(b - 9)**2*(3*b + 2)
Let y(v) be the first derivative of -v**6/300 - 3*v**5/50 - v**4/4 - 7*v**3/15 - v**2 + 12*v + 8. Let w(i) be the second derivative of y(i). Factor w(o).
-2*(o + 1)**2*(o + 7)/5
Let r be (-8)/80*-5*22*1. Determine n, given that -88*n**4 + r*n**3 + 84*n**4 - 8*n**5 + 4*n**2 - 3*n**3 = 0.
-1, -1/2, 0, 1
Let y(d) be the third derivative of -d**5/75 - 77*d**4/30 + 316*d**3/15 - 3*d**2 - 100*d. Factor y(s).
-4*(s - 2)*(s + 79)/5
Let g(n) be the third derivative of 5*n**8/1848 - 3*n**7/308 + 2*n**6/165 - n**5/165 + n**3/3 - 9*n**2. Let o(k) be the first derivative of g(k). Factor o(s).
2*s*(s - 1)*(5*s - 2)**2/11
Let l(t) = -15*t**5 - 54*t**4 + 343*t**3 - 122*t**2 - 4. Let y(f) = f**3 + f**2 - 1. Let w(q) = -l(q) + 4*y(q). Determine i so that w(i) = 0.
-7, 0, 2/5, 3
Let y be -6*(-5)/10 - 0. Determine l, given that -2*l**2 + y*l - 4 + 11*l - 2*l**2 - 6*l**2 = 0.
2/5, 1
Let b = -151103/11 - -13737. Solve -6/11*a + 10/11*a**2 - b = 0 for a.
-2/5, 1
Factor 22/5*k - 36/5 - 2/5*k**2.
-2*(k - 9)*(k - 2)/5
Let i(q) be the first derivative of -3*q**4/32 + 5*q**3/4 - 6*q**2 + 12*q + 148. Determine b, given that i(b) = 0.
2, 4
Suppose 3*k = 0, 7*k - 5*k + 9 = 3*s. Determine q so that -6*q**s - 4*q - 4*q - 10*q**2 - 10*q**3 - 26*q**2 = 0.
-2, -1/4, 0
Let i = -63 + -132. Let m = 197 + i. Solve 5/2*l**2 - m + l - l**4 - 1/4*l**5 - 1/4*l**3 = 0.
-2, 1
Let k(w) = -3*w**3 - 25*w**2 - 84*w - 77. Let f(g) = -12*g**3 - 99*g**2 - 336*g - 309. Let u(s) = -5*f(s) + 21*k(s). Factor u(z).
-3*(z + 2)**2*(z + 6)
Find i, 