
0, 3
Let u(v) be the first derivative of 5*v**4/4 + 10*v**3/3 - 5*v**2/2 - 10*v + 69. Suppose u(d) = 0. Calculate d.
-2, -1, 1
Let v(z) = -z**4 + 5*z**3 - 13*z**2 - 5*z + 4. Let c(t) = 2*t**4 - 8*t**3 + 20*t**2 + 8*t - 6. Let d(f) = -5*c(f) - 8*v(f). Determine h so that d(h) = 0.
-1, 1
Let l(i) be the first derivative of 25*i**7/42 - i**6/3 - 8*i + 1. Let t(r) be the first derivative of l(r). Factor t(n).
5*n**4*(5*n - 2)
Let t(i) = 32*i - 128. Let m be t(4). Let d(l) be the second derivative of 8*l + m*l**4 + 1/10*l**5 + 0*l**3 + 0 + 0*l**2. Suppose d(y) = 0. Calculate y.
0
Let q be 1*5 - (-441)/(-105). Determine u, given that 4/5*u**2 + q*u - 8/5 = 0.
-2, 1
Let r(q) be the second derivative of q**6/90 - q**4/18 + q**2/6 - 375*q. Find o such that r(o) = 0.
-1, 1
Let -72/5*z**3 + 12/5*z**5 + 12/5 - 4/5*z**4 - 4/5*z - 72/5*z**2 = 0. Calculate z.
-1, 1/3, 3
Let f(j) be the third derivative of -7*j**5/330 + 3*j**4/44 - 2*j**3/33 + 237*j**2. Factor f(c).
-2*(c - 1)*(7*c - 2)/11
Let f(j) be the first derivative of -j**6/1800 - j**5/600 + j**4/60 - j**3 + 8. Let w(l) be the third derivative of f(l). Suppose w(t) = 0. What is t?
-2, 1
Let d(j) be the third derivative of -j**8/5040 + j**7/90 - 49*j**6/180 + 3*j**5/5 + 20*j**2. Let o(t) be the third derivative of d(t). Solve o(l) = 0 for l.
7
Suppose 0 = -7*l + 52 + 32. What is y in y**3 - 6*y**4 - 3*y**5 - 6 - y**3 + 9*y**3 + l*y**2 - 3*y**3 - 3*y = 0?
-2, -1, 1
Suppose 0 = -13*f - f + 70. Suppose 15 = -f*v - 5*n, 5*n + 14 = -2*v - 7. Suppose -l**v + 0 - 1/4*l**3 - l = 0. What is l?
-2, 0
Factor -16*f + 3*f**3 - 7*f**2 + 5*f**2 + 11*f**3 + 4*f**4 - 2*f**2 + 2*f**3.
4*f*(f - 1)*(f + 1)*(f + 4)
Suppose 23 = -v + 5*g, -4*v = -2*v - 4*g + 16. Factor 22*n**4 + 13*n**2 - 12*n**3 + n**4 - 7*n**5 - v*n - 15*n**3.
-n*(n - 1)**3*(7*n - 2)
Let o be -18*(4 - 595/147). Determine a so that 12/7 - o*a - 6/7*a**2 = 0.
-2, 1
Let a(y) be the first derivative of -4*y**3/3 + 96*y**2 - 2304*y + 302. Factor a(r).
-4*(r - 24)**2
Let v be (1/5)/(3/10). Let j = -75/2 - -39. Factor -r**2 + 0 - v*r**4 - j*r**3 - 1/6*r.
-r*(r + 1)**2*(4*r + 1)/6
Let q = 7 - 4. Let j be 0 + 0 + 3 + -1. Solve 4*y**q - 6*y**2 + 6*y - 2*y**3 + 0*y**2 - j = 0.
1
Let k(l) = -l**2 - 12*l + 2. Let c be (-172)/14 - (-20)/70. Let i be k(c). Factor -14*x**i - 32/7 - 16*x.
-2*(7*x + 4)**2/7
Let o = 67/156 - 9/26. Let q(t) be the second derivative of -1/80*t**5 + 0 - 1/6*t**3 + 8*t - o*t**4 + 0*t**2. Let q(j) = 0. Calculate j.
-2, 0
Factor 197/3*l - 5/3*l**2 + 40.
-(l - 40)*(5*l + 3)/3
Let h(s) be the second derivative of 5*s**4/12 + 11*s**3/6 + 3*s**2 - 31*s - 2. Solve h(u) = 0 for u.
-6/5, -1
Let f(z) be the second derivative of 0*z**2 - 3/20*z**5 + 0*z**3 - 7*z + 0 + 1/5*z**6 + 1/14*z**7 - 1/2*z**4. Factor f(j).
3*j**2*(j - 1)*(j + 1)*(j + 2)
Solve -5*g**3 + 38 - 145*g**2 - 3645*g + 247*g**2 + 168*g**2 - 38 = 0.
0, 27
Let j(x) = -8*x**2 + 180*x - 2695. Let k(f) = -f**2 + 1. Let h(y) = j(y) - 5*k(y). Factor h(p).
-3*(p - 30)**2
Suppose 2*p - 4*p - 2*g + 26 = 0, 5*g = 2*p + 9. Suppose -q + p = 5. Factor 0*c**q - c**5 + c**3 + c**2 - c**2 - c**2 + c**4.
-c**2*(c - 1)**2*(c + 1)
Find t such that t**2 + 0*t - 2/3*t**3 - 1/3*t**4 + 0 = 0.
-3, 0, 1
Let u(k) be the second derivative of -k**6/45 + k**5/10 + k**4/18 - k**3/3 + 4*k - 3. Find q such that u(q) = 0.
-1, 0, 1, 3
Suppose 29 = 3*k - 28. Let n = k - 17. Determine d so that 7*d**5 + 5*d**4 + 18*d**n - 5*d**3 - 23*d**2 - 2*d**5 = 0.
-1, 0, 1
Let w = -1209 - -1211. Factor -36*k**3 - 12*k**4 - 24*k + 0 - 48*k**w - 3/2*k**5.
-3*k*(k + 2)**4/2
Let k(b) be the first derivative of -b**6/2 + 186*b**5/5 - 3063*b**4/4 + 1860*b**3 - 1350*b**2 + 132. Factor k(c).
-3*c*(c - 30)**2*(c - 1)**2
Let o(s) = 28*s**2 - 3*s + 8. Let k(x) = 13*x**2 - x + 4. Let c(r) = -13*k(r) + 6*o(r). Factor c(n).
-(n + 1)*(n + 4)
Let h(q) be the first derivative of -q**6/18 - q**5/15 + 7*q**4/12 + q**3/9 - q**2 + 152. Suppose h(n) = 0. What is n?
-3, -1, 0, 1, 2
Let t(d) be the second derivative of 5*d**7/42 + 7*d**6/6 + 7*d**5/2 + 10*d**4/3 + 220*d - 2. Factor t(s).
5*s**2*(s + 1)*(s + 2)*(s + 4)
Suppose 3*k + 1178 = 5*o, -3*k - 2*o = -2*k + 378. Let h = 1936/5 + k. Factor 4/5*a + 0 + h*a**3 - 14/5*a**2.
2*a*(a - 2)*(3*a - 1)/5
Factor -144*y - 790 + 9*y**2 + 5*y**2 + 2518 - 11*y**2.
3*(y - 24)**2
Let i(g) be the first derivative of -g**4 + 2*g**2 - 4/5*g**5 + 4*g**3 - 8*g + 1. Determine o so that i(o) = 0.
-2, -1, 1
Let x(s) be the second derivative of -s**7/1120 - s**6/192 - s**5/80 - 2*s**4/3 - 11*s. Let w(p) be the third derivative of x(p). Factor w(m).
-3*(m + 1)*(3*m + 2)/4
Factor 5/2 - 5/2*w**2 + 0*w.
-5*(w - 1)*(w + 1)/2
Let a(m) be the third derivative of -1/12*m**5 - 5/24*m**4 - 16*m**2 + 1/24*m**6 + 0*m + 0 + 1/42*m**7 + 0*m**3. Let a(b) = 0. Calculate b.
-1, 0, 1
Let s(q) be the third derivative of -q**5/300 + 3*q**4/40 - 7*q**3/15 + 3*q**2 + q. Solve s(n) = 0.
2, 7
Suppose f - 4*d + 100 = 0, 5*f + 0*d = -5*d - 425. Let l = f + 91. Factor -2/3 - 2*g - 2/3*g**l - 2*g**2.
-2*(g + 1)**3/3
Factor -4/9*g**2 + 2/9*g - 2/9*g**3 + 4/9.
-2*(g - 1)*(g + 1)*(g + 2)/9
Suppose 3*x = -5*p, -17*p + 22*p - 4*x - 35 = 0. Solve 8/5*i + 0 + 343/5*i**4 + 84/5*i**2 + 294/5*i**p = 0 for i.
-2/7, 0
Let v(c) be the second derivative of c**5/20 + c**4/2 - 7*c**3/6 + 3*c**2 - 3*c. Let f be v(-7). Factor 1 - 2 - 3 + 2*s**2 - 4*s**2 + f*s.
-2*(s - 2)*(s - 1)
Let a = 372 + -370. Let o(z) be the first derivative of z**3 + 4 + 6*z + 9/2*z**a. Let o(s) = 0. Calculate s.
-2, -1
Let v(u) be the third derivative of 16/5*u**5 + 15/4*u**8 + 0*u - 64/21*u**3 + 1756/105*u**6 - 88/21*u**4 + 1732/105*u**7 + 10*u**2 + 0. Solve v(g) = 0.
-2, -2/5, -2/7, 2/9
Let w be (27/18)/(105/56). Let f(d) be the first derivative of 0*d - 9 - 3/20*d**4 + w*d**3 - 6/5*d**2. Factor f(b).
-3*b*(b - 2)**2/5
Let q be 280/(-400) - 1/((-4)/3). Let w(g) be the third derivative of -1/8*g**4 + q*g**5 + 0 + 0*g + 0*g**3 + 3*g**2. Factor w(t).
3*t*(t - 1)
Let z(u) = u**3 + 2*u**2. Let h(y) = 5*y**3 + 18*y**2 - 9*y + 4. Let o(p) = -h(p) + 6*z(p). Solve o(r) = 0.
1, 4
Let g(v) be the first derivative of 5*v**3/12 + 5*v**2/4 - 75*v/4 - 218. Determine a, given that g(a) = 0.
-5, 3
Let b = -108 + 112. Let n(w) be the second derivative of -1/165*w**6 + 0*w**3 + 0*w**2 + 0*w**b + 0 + 5*w + 1/110*w**5. What is j in n(j) = 0?
0, 1
Suppose 3*f + 26 = 3*s - f, 4*s - 5*f = 33. Let l(h) be the first derivative of 1/4*h**4 + 5 + 0*h + 4/3*h**3 - 1/2*h**s - 4/5*h**5. Let l(b) = 0. Calculate b.
-1, 0, 1/4, 1
Suppose -18*t - 5*t + 110 = 32*t. Solve -8/9*d**3 + 4/3 - 38/9*d**t - 38/9*d = 0.
-3, -2, 1/4
Let c(t) = -3*t**3 + 64*t**2 - 121*t + 64. Let s(v) = 4*v**3 - 65*v**2 + 121*v - 66. Let l(j) = -3*c(j) - 2*s(j). Factor l(k).
(k - 60)*(k - 1)**2
Let z(j) be the third derivative of -j**5/15 + 9*j**4/2 - 100*j**3/3 - 209*j**2. Factor z(b).
-4*(b - 25)*(b - 2)
Let u = -37 + 39. Factor 5 - 4*w - 4*w**2 + 5 + 2*w**u - 4.
-2*(w - 1)*(w + 3)
Find w such that 0 + 16/3*w + 1/3*w**3 - 17/3*w**2 = 0.
0, 1, 16
What is d in -96*d - 13*d**2 + 7*d**2 + 87*d + 3*d**3 = 0?
-1, 0, 3
Determine n so that -24/5*n + 2/5*n**4 - 12/5*n**3 + 8/5 + 26/5*n**2 = 0.
1, 2
Let r(c) be the third derivative of c**6/1620 - c**5/270 + 31*c**3/6 - 10*c**2. Let h(g) be the first derivative of r(g). Factor h(n).
2*n*(n - 2)/9
Let c = -40 + 183. Let s = c + -143. Suppose 1/6*x**4 + s + 1/6*x + 1/2*x**3 + 1/2*x**2 = 0. What is x?
-1, 0
Let j = 5/122 + 69/4270. Let h = j + 29/105. Factor 1/3*p**4 - 2/3*p**2 + h + 0*p**3 + 0*p.
(p - 1)**2*(p + 1)**2/3
Let j(m) be the first derivative of 14/9*m**2 - 4/27*m**3 - 8/3*m + 16. Factor j(u).
-4*(u - 6)*(u - 1)/9
Let u = -80 - -71. Let c be (8/u - -1) + 2/6. What is t in c*t - 2/3 + 2/9*t**2 = 0?
-3, 1
Suppose -12240*i = -12247*i + 21. Let 16/19*v**2 - 32/19*v + 0 - 2/19*v**i = 0. What is v?
0, 4
Factor 3/2*y**3 + 231/2*y - 24*y**2 - 147.
3*(y - 7)**2*(y - 2)/2
Suppose 5*d - 5*i = -i - 772, -3*i = 6. Let t = d + 243. Solve 6*h - 84*h**2 + t*h**2 + 1 + 2 = 0 for h.
-1
Factor -15/8*r + 3/8*r**3 - 3/4*r**2 + 9/4.
3*(r - 3)*(r - 1)*(r + 2)/8
Let a(w) = -w**2 + 9 + 2*w**2 + 6 - 5 + 8*w. Let l be a(-7). Solve -3*x + 4*x**l + 4*x**3 - 5*x**3 = 0 for x.
-1, 0, 1
Let s(l) be the first derivative of 21 - 1/10*l**5 + 0