 = -8 + 6. Let b(o) = o**3 - o**2 + 1. Let s(t) = k*g(t) - 4*b(t). Let s(n) = 0. Calculate n.
-2/7, 0, 1
Let t(y) be the second derivative of -y**5/270 + y**4/27 - y**3/9 + 15*y**2/2 - 35*y. Let s(n) be the first derivative of t(n). Solve s(c) = 0 for c.
1, 3
Factor -y - 1/3*y**3 + 1/3 + y**2.
-(y - 1)**3/3
Let a(r) be the second derivative of r**8/1344 - r**6/144 + 13*r**4/12 - 7*r. Let o(u) be the third derivative of a(u). Find w, given that o(w) = 0.
-1, 0, 1
Let b(w) be the second derivative of w**4/114 - 8*w**3/19 - 52*w**2/19 - 245*w. Factor b(m).
2*(m - 26)*(m + 2)/19
Let d(h) be the first derivative of -h**3 - 48*h**2 + 99*h + 263. Determine a, given that d(a) = 0.
-33, 1
Let k(j) = -6*j**3 + 12*j**2 + 186*j + 160. Let m(x) = 2*x**3 - 4*x**2 - 62*x - 53. Let s(z) = -3*k(z) - 8*m(z). Solve s(i) = 0 for i.
-4, -1, 7
Let f(s) be the second derivative of s**7/1260 + s**6/540 - s**5/180 - s**4/36 - 8*s**3/3 - 6*s. Let a(g) be the second derivative of f(g). Factor a(n).
2*(n - 1)*(n + 1)**2/3
Factor -44/13*c + 42/13 + 2/13*c**2.
2*(c - 21)*(c - 1)/13
Let q(y) be the first derivative of -y**8/84 + y**6/10 - 2*y**5/15 - 4*y**2 + 12. Let g(f) be the second derivative of q(f). Suppose g(l) = 0. What is l?
-2, 0, 1
Let a be 16 + 2 - (-1443)/444. Find p such that -15/4*p**2 - a*p**4 + 0 - 5*p**5 - 20*p**3 + 0*p = 0.
-3, -1, -1/4, 0
Let k(x) be the third derivative of -x**5/270 + 8*x**4/27 - 20*x**3/9 - 93*x**2. What is c in k(c) = 0?
2, 30
Suppose 11*a + 57 - 57 = 0. Factor 0*g**2 + 0 + 1/3*g**3 + a*g + 1/3*g**4.
g**3*(g + 1)/3
Suppose -868 + 236 + 865*k**2 + 1390*k + 72 + 15*k**3 = 0. What is k?
-56, -2, 1/3
Factor 71*b + 39 - 61*b + 9*b**2 - 4*b**2 - 6*b**2.
-(b - 13)*(b + 3)
Let a(m) be the first derivative of -18 + 0*m + 2/9*m**3 + 0*m**2. Factor a(d).
2*d**2/3
Let t = 15625 + -15623. Solve 0 - 4/11*w**t + 4/11*w**4 + 0*w**3 + 2/11*w**5 - 2/11*w = 0 for w.
-1, 0, 1
Let j(y) = -y + 11. Let w be j(5). Let b(n) = n**3 + 12*n**2 + 9*n - 18. Let d be b(-11). Find z, given that -d*z + w + 2/3*z**2 = 0.
3
Let j(a) = -4*a**2 + 340*a - 8. Let g(f) = f**2 - 111*f + 3. Let x(l) = -8*g(l) - 3*j(l). Factor x(k).
4*k*(k - 33)
Let j be 54/351 - (-23)/(-234). Let d(h) be the first derivative of 4/9*h - 1/3*h**2 + 5 + j*h**4 + 0*h**3. Factor d(y).
2*(y - 1)**2*(y + 2)/9
Let -16/3 + 28/3*s - 23/3*s**3 + 44/3*s**2 - 5/3*s**5 - 28/3*s**4 = 0. What is s?
-4, -2, -1, 2/5, 1
Let n(t) be the first derivative of 25*t**7/56 + t**6/8 - 3*t**5/5 + t**4/4 + 26*t + 14. Let x(k) be the first derivative of n(k). Let x(q) = 0. Calculate q.
-1, 0, 2/5
Let o(p) be the first derivative of -2/9*p**3 - 10 + 0*p + 5/18*p**4 - 2/9*p**2. Suppose o(a) = 0. Calculate a.
-2/5, 0, 1
Determine j, given that 0 + 2/7*j**2 + 38/7*j = 0.
-19, 0
Let g be 4*28/96 - 1. Let d(a) be the second derivative of 0*a**2 - 3*a + 1/21*a**7 + 0 + 0*a**3 - 1/10*a**5 - g*a**4 + 1/15*a**6. Factor d(j).
2*j**2*(j - 1)*(j + 1)**2
Suppose z - 11 = 3*b, -7 = -2*z - 5*b - 18. Factor -3 - 3/2*p**3 + 3*p**z + 3/2*p.
-3*(p - 2)*(p - 1)*(p + 1)/2
Let t(m) = -2*m**2 - 41*m + 100. Let r(y) = 2*y**2 + 42*y - 100. Let n(h) = 5*r(h) + 4*t(h). Factor n(v).
2*(v - 2)*(v + 25)
Suppose u - 5 = 5*s + 7, -2*u + s = -6. Find o such that -4*o**2 - 9*o**2 + 8*o**2 + o**u = 0.
0
Suppose -3*a - 3*m = -60, -4*a - 36 = -7*a + 3*m. Let j be (a - 10)*2/4. Factor 15*r**2 + 5*r**5 + 2*r**5 + j*r + 27*r**3 + 23*r**4 - r**5 - 2*r**4.
3*r*(r + 1)**3*(2*r + 1)
Let d(w) be the second derivative of -w**6/6 + 3*w**5 + 65*w**4/12 - 76*w. Factor d(v).
-5*v**2*(v - 13)*(v + 1)
Find j such that 4 + 472*j**2 - 13*j + 3*j - 466*j**2 = 0.
2/3, 1
Let -34*o**3 + 51*o**3 - 70*o + 149 - 269 + 115*o**2 + 5*o**4 + 24*o**3 + 29*o**3 = 0. Calculate o.
-12, -2, -1, 1
Let y(s) be the first derivative of 3*s**2 - 12 + 0*s - 2/3*s**3. Solve y(z) = 0 for z.
0, 3
Let s(l) = -3*l + 9. Let f be s(3). Let d(n) be the second derivative of -1/6*n**3 + 2*n + f*n**2 - 3/16*n**5 + 0 - 1/3*n**4. Solve d(a) = 0.
-2/3, -2/5, 0
Let c(d) be the second derivative of d**5/120 - d**4/36 + d**3/36 - 7*d - 1. Factor c(w).
w*(w - 1)**2/6
Factor -24680*z + 10551 + 9604*z**4 + 147053*z**2 - 65856*z**3 + 27193*z - 196049*z + 72393 + 22291*z**2.
4*(7*z - 12)**4
Let h = 435 - 433. Let k(t) be the third derivative of -1/12*t**4 + 0 + 6*t**h + 0*t - 1/120*t**5 - 1/4*t**3. Factor k(r).
-(r + 1)*(r + 3)/2
Let w(a) be the second derivative of 0 - 18*a - 1/24*a**6 - 5/24*a**3 + 0*a**2 - 3/16*a**5 - 5/16*a**4. Solve w(p) = 0 for p.
-1, 0
Let n(l) = l + 6. Let j be n(-5). Let k(d) = -d**2 - d + 2. Let p be k(j). Factor -48 + p*s**3 - s**2 - s + 49 + s**3.
(s - 1)**2*(s + 1)
Suppose p = -5*s + 11, 24*s - 8 = 22*s - 4*p. Solve 3/2*k + k**s - 1 = 0.
-2, 1/2
Let g(d) = 27*d**3 + 66*d**2 - 123*d - 186. Let a(t) = 11*t**3 + 26*t**2 - 49*t - 74. Let f(m) = -12*a(m) + 5*g(m). Solve f(i) = 0.
-7, -1, 2
Let x(n) be the second derivative of n**7/98 - 2*n**6/35 + 9*n**5/140 + n**4/7 - 2*n**3/7 - 2*n. Solve x(w) = 0.
-1, 0, 1, 2
Let g be (-6)/(-18) + (-5)/15. Let w(f) be the third derivative of 3*f**2 + 0*f - 1/120*f**4 + 1/300*f**5 + g + 0*f**3. Factor w(t).
t*(t - 1)/5
Solve 4*p - 20*p + 5*p**4 + 106*p**2 + 20*p**3 - p**4 - 82*p**2 - 32 = 0.
-2, 1
Suppose 0 = -192*w + 219*w - 54. Find v such that -4/3*v**w + 4/3*v + 0 = 0.
0, 1
Let m = 2201 - 2197. Let r(k) be the second derivative of 1/80*k**5 + 7*k + 0*k**2 - 1/24*k**3 + 0 + 0*k**m. Factor r(v).
v*(v - 1)*(v + 1)/4
Factor 3/2*g**3 + 24 - 27/2*g**2 + 9*g.
3*(g - 8)*(g - 2)*(g + 1)/2
Suppose 4 = g - 0*g. Factor k + 6*k - 14*k + 3*k + g*k**2 + 4*k**3 - 4.
4*(k - 1)*(k + 1)**2
Let j(c) be the third derivative of c**7/2240 + c**6/160 + 9*c**5/320 - 17*c**3/6 - 7*c**2. Let d(y) be the first derivative of j(y). Solve d(v) = 0 for v.
-3, 0
Let f = -18243 - -54730/3. Determine u, given that -2/3*u + 0 - f*u**3 + u**2 = 0.
0, 1, 2
Let z(o) be the second derivative of -o**5/100 - 29*o**4/20 - 841*o**3/10 - 24389*o**2/10 + 104*o. Find i such that z(i) = 0.
-29
Let p(s) be the third derivative of -s**7/105 + s**6/6 - 6*s**5/5 + 14*s**4/3 - 32*s**3/3 + 96*s**2. Factor p(j).
-2*(j - 4)*(j - 2)**3
Let i = 24007/7 - 3435. Let f = i - -83/14. Factor -1/2 + 0*k**2 + k**3 - k + f*k**4.
(k - 1)*(k + 1)**3/2
Let z(c) be the third derivative of 0*c + 1/630*c**7 + 14*c**2 - 5/72*c**4 - 1/9*c**3 + 0 + 1/360*c**6 - 1/60*c**5. Find t, given that z(t) = 0.
-1, 2
Find p, given that 28/5 - 14/5*p**2 - 94/5*p = 0.
-7, 2/7
Let l(j) be the second derivative of -j**4/4 - 89*j**3 + 15*j - 29. Solve l(p) = 0 for p.
-178, 0
Let k(v) = -3*v**3 - 115*v**2 - 24*v + 535. Let i be k(-38). Factor 39/5*z + i*z**2 + 21/5 - 3/5*z**3.
-3*(z - 7)*(z + 1)**2/5
Let x(k) = -3761*k**5 + 11*k**4 + 1211*k**3 - 96*k + 11. Let v(l) = -1881*l**5 + 6*l**4 + 606*l**3 - 48*l + 6. Let n(s) = 11*v(s) - 6*x(s). Factor n(g).
3*g*(5*g - 2)**2*(5*g + 2)**2
Let z be (27/6 - 5)*(3 + -3). Determine g, given that 0 + 2/7*g**4 + 0*g + 2/7*g**3 + z*g**2 = 0.
-1, 0
Suppose -2*u + 25 - 28 = 3*p, -3*u - 3 = 3*p. Let m(l) be the third derivative of u*l**3 + l**2 + 0*l - 1/66*l**4 + 0 - 1/330*l**5. Let m(s) = 0. What is s?
-2, 0
Let w = 1385 - 1385. Let r(l) be the second derivative of w + 2/5*l**2 + 6*l - 1/60*l**4 + 1/10*l**3. What is d in r(d) = 0?
-1, 4
Suppose 78732 + 81*p**2 - 4374*p - 1/2*p**3 = 0. Calculate p.
54
Let g(y) be the first derivative of 4*y**3/3 + 37*y**2/3 + 4*y + 28. Factor g(z).
2*(z + 6)*(6*z + 1)/3
Solve 923 - 201 + 76*z + 4*z**2 + 3*z**2 - 5*z**2 = 0 for z.
-19
Let i(m) be the first derivative of 6 + 0*m**2 + 0*m + 3/2*m**4 - 3/5*m**5 - m**3. Factor i(t).
-3*t**2*(t - 1)**2
Let f(o) be the third derivative of -o**7/2520 - o**6/720 - o**4/6 + 5*o**3/6 - 46*o**2. Let s(j) be the second derivative of f(j). Factor s(k).
-k*(k + 1)
Let c(x) be the second derivative of -x**5/20 - 7*x**4/6 - 7*x**3/3 - 13*x**2/2 + 35*x. Let s be c(-13). Factor 6*z**4 + s + 0*z + 2/9*z**2 + 2*z**3 + 6*z**5.
2*z**2*(3*z + 1)**3/9
Suppose -4*u + 2*n = -34, -n = -5*u - 0*n + 50. Suppose -u = -21*t + 52. Factor 0*z + 2/3*z**t + 2/3*z**2 + 0.
2*z**2*(z + 1)/3
Let m be (-2)/1100*((-6579)/21 - 5). Let p = -2/275 + m. Let -p*j**2 + 4/7*j + 0 = 0. What is j?
0, 1
Let f(k) = 6*k**3 - k**2 - 5*k + 5. Let q(i) = 3*i**3 - 3*i + 3. Let b be