Suppose -2*l = -0*l - 5*z - 2, 5*z - 64 = -4*l. Let t(x) = x**2 - 12*x + 11. Let r be t(l). Factor 4/11*c**2 + 2/11*c + r.
2*c*(2*c + 1)/11
Let w(y) = -y + 34. Let c be w(32). Let p(x) be the third derivative of -1/420*x**6 - 1/70*x**5 - 1/42*x**4 + 4*x**c + 0*x**3 + 0*x + 0. What is h in p(h) = 0?
-2, -1, 0
Factor 0 - 2/3*o - 5/3*o**3 - 7/3*o**2.
-o*(o + 1)*(5*o + 2)/3
Let f = -109902/17 - -6468. What is r in -18/17*r**4 + 54/17*r**3 + 0*r - f*r**2 + 0 + 2/17*r**5 = 0?
0, 3
Let k(q) be the first derivative of -3*q**4 + 6*q**2 + 3*q**3 - 12*q - 8 + 3/5*q**5. Determine b, given that k(b) = 0.
-1, 1, 2
Let h(i) be the first derivative of 0*i**2 + 0*i**5 - 7*i - 9 + 1/18*i**3 + 1/24*i**4 - 1/180*i**6. Let t(v) be the first derivative of h(v). Factor t(a).
-a*(a - 2)*(a + 1)**2/6
Let r(m) be the first derivative of -20*m**3/9 + 26*m**2 + 72*m - 353. Factor r(z).
-4*(z - 9)*(5*z + 6)/3
Suppose 5/7 - 6/7*z**2 - 4/7*z**3 + 1/7*z**4 + 4/7*z = 0. What is z?
-1, 1, 5
Let w(o) be the first derivative of -20*o - 16 - 495/2*o**4 - 110*o**2 - 785/3*o**3 - 81*o**5. Let w(m) = 0. Calculate m.
-1, -2/9
Determine x, given that -120*x**3 + 160*x**2 - 564*x + 40*x**4 + 484*x - 3*x**5 - 2*x**5 = 0.
0, 2
Factor 358/7 + 2/7*j**2 + 360/7*j.
2*(j + 1)*(j + 179)/7
Let u = -22 - -10. Let r = 15 + u. Find j such that 12*j - 8*j**2 + j**r + 4*j**2 + 5*j**3 - 17*j**2 + 12 = 0.
-1/2, 2
Factor -29*o**2 + 45*o**3 - 7*o**2 + 469*o**4 - 481*o**4 - 12*o.
-3*o*(o - 2)**2*(4*o + 1)
Let b(o) = o**4 - o. Let j(d) be the second derivative of -1/3*d**3 + 1/10*d**5 + 0*d**4 + 0 + 0*d**2 - 3*d. Let w(k) = -2*b(k) + j(k). Factor w(n).
-2*n**3*(n - 1)
Let h be -3 - (-229)/5*50/40. Let w = h + -54. Solve 1/2*d - w*d**2 + 3/4 = 0.
-1, 3
Suppose 80*h + 200 = 180*h. Determine q, given that -1/5*q**4 + 1/5*q**3 + 0*q + 1/5*q**h + 0 - 1/5*q**5 = 0.
-1, 0, 1
Suppose 3 - 7 = -2*v. Factor 352*l**2 - 172*l**2 + 2*l**5 + 8*l**4 + 10*l**3 - 176*l**v.
2*l**2*(l + 1)**2*(l + 2)
Let o be (-1 - 0) + 0 + 0. Let v be 67 - (-2 - o - 2). Factor 70*y - v*y + 3*y**2.
3*y**2
Let f(u) be the third derivative of 0*u**4 + 1/60*u**5 + 0 + 0*u + 13*u**2 + 0*u**3 - 1/120*u**6. Suppose f(v) = 0. What is v?
0, 1
Let b(s) be the second derivative of -s**7/840 - s**6/240 + s**5/240 + s**4/48 + 7*s**2 - 2*s. Let x(l) be the first derivative of b(l). Factor x(h).
-h*(h - 1)*(h + 1)*(h + 2)/4
Let 29*i**3 + 17*i**3 + 24*i**2 - 4*i**4 - 42*i**3 = 0. What is i?
-2, 0, 3
Let k(t) be the third derivative of t**9/302400 - t**7/8400 + t**6/1800 + 3*t**5/5 - 38*t**2. Let m(s) be the third derivative of k(s). Factor m(b).
(b - 1)**2*(b + 2)/5
Let o = 38 - -31. Let j be 1 - o/(-15) - 5. What is i in -3/5*i**2 + 0 + j*i = 0?
0, 1
Let w(l) be the second derivative of 3*l**5/40 - 5*l**4/4 + 21*l. Suppose w(b) = 0. What is b?
0, 10
Let u(o) be the first derivative of -3*o**4/4 + 5*o**3 + 9*o**2 - 4. Solve u(f) = 0 for f.
-1, 0, 6
Determine d so that -60*d - 23*d**2 - 66*d**3 - 3*d**4 + 45*d**3 - 31*d**2 - 24 = 0.
-2, -1
Suppose y + 8 = 5*o - 7, 25 = 5*o - 3*y. Suppose 0 = -2*x - x. Let 1/2*v**o + x*v**3 + 1/4*v - 1/4*v**5 + 0 - 1/2*v**4 = 0. Calculate v.
-1, 0, 1
Let k = 14 - 17. Let m = -2 - k. Factor 6*g**2 - 3*g**2 + m + 9*g + 3 + 2.
3*(g + 1)*(g + 2)
Let z(r) be the second derivative of -r**7/1400 + 31*r**6/1800 - 17*r**5/120 + 5*r**4/24 - 3*r**3 + r. Let v(a) be the second derivative of z(a). Factor v(p).
-(p - 5)**2*(3*p - 1)/5
Suppose -15 = -56*o + 52*o - m, 4*o = m + 25. Determine w, given that 8/5*w**3 + 2/5*w**o - 2*w + 8/5*w**4 - 4/5*w**2 - 4/5 = 0.
-2, -1, 1
Suppose 24*b = 2*x + 19*b - 20, 4*x - 2*b = 24. Let h(s) be the third derivative of -2*s**2 - 1/20*s**x + 0 - 1/4*s**4 + 0*s + 3/2*s**3. Factor h(p).
-3*(p - 1)*(p + 3)
Let x be (26/(-6) + 4/(-6))*1. Let s(f) = 4*f**2 - 9*f + 5. Let c(q) = 3*q**2 - 6*q + 3. Let d(o) = x*s(o) + 7*c(o). Factor d(u).
(u - 1)*(u + 4)
Let k = -20 - -22. Suppose 3*n - 2*g - 20 = 0, g = n + k*g. Let 2*j**2 + 1 - 8/3*j + 0*j**3 - 1/3*j**n = 0. Calculate j.
-3, 1
Let j be 4/(-7) - 151/(-7). Determine m so that -3*m**3 - 3*m**2 - m**2 + 4 - j*m**3 + 24*m = 0.
-1, -1/6, 1
Let o(j) be the first derivative of 38 - 56/3*j**6 + 8/3*j**3 - 108/5*j**5 + 3*j**4 + 0*j + 0*j**2. Determine f, given that o(f) = 0.
-1, -1/4, 0, 2/7
Let q = -1654 - -1654. Factor 1/10*x**3 + 0*x + q + 1/10*x**2.
x**2*(x + 1)/10
What is u in 3/7*u**4 + 60/7*u**2 + 30/7*u**3 - 9 - 30/7*u = 0?
-7, -3, -1, 1
Let x = 1097/90 - 169/18. Find g such that x*g - 17/5*g**2 + 4/5 + 9/10*g**3 = 0.
-2/9, 2
Let l = -7852 + 7856. Factor -10/17*r**3 - 6/17*r + 14/17*r**2 + 2/17*r**l + 0.
2*r*(r - 3)*(r - 1)**2/17
Let o(a) be the second derivative of a**5/30 + a**4/18 - 10*a**3/9 + 8*a**2/3 + 38*a. What is d in o(d) = 0?
-4, 1, 2
Suppose 0 = 4*x - 50 + 10. Find y, given that -41*y**3 + 4 + 5*y - x*y**2 + 36*y**3 + 6 = 0.
-2, -1, 1
Let z be 270/69 + 530/6095. Find i, given that -1/3*i**z + 1/3*i**2 + 2/3*i + 28/3*i**5 + 0 - 10*i**3 = 0.
-1, -1/4, 0, 2/7, 1
Let n(u) = -4*u + 2 + 0*u + 4*u + 2*u**3 - 2*u**2. Let r(f) = 10*f**3 - 9*f**2 + 11. Let m(g) = 11*n(g) - 2*r(g). What is j in m(j) = 0?
0, 2
Let h(y) be the third derivative of 14/15*y**3 + 0 - 2*y**2 - 1/300*y**6 + 2/75*y**5 - 2*y + 19/60*y**4. Factor h(r).
-2*(r - 7)*(r + 1)*(r + 2)/5
Let a(i) be the first derivative of 0*i + 11/2*i**2 + 1/180*i**6 - 1/90*i**5 + 0*i**4 + 0*i**3 - 12. Let z(v) be the second derivative of a(v). Factor z(h).
2*h**2*(h - 1)/3
Let o(b) be the first derivative of b**5/330 + b**4/6 + 11*b**3/3 + 6*b**2 - 4. Let t(j) be the second derivative of o(j). Factor t(x).
2*(x + 11)**2/11
Suppose 0 = -2*y + 3*y. Suppose y = -r - 4*r + 25. Factor -u + u**3 + r*u**2 - 5*u**2.
u*(u - 1)*(u + 1)
Let 0 - 36/5*m**3 + 24/5*m**4 - 3/5*m + 18/5*m**2 = 0. Calculate m.
0, 1/2
Let c(f) be the third derivative of 1/84*f**8 - 4/105*f**7 + 0*f + 0*f**6 + 0*f**3 - 1/6*f**4 + 5*f**2 + 0 + 2/15*f**5. Factor c(g).
4*g*(g - 1)**3*(g + 1)
Let k(m) be the first derivative of m**3/5 + 3*m**2 + 27*m/5 - 41. Factor k(c).
3*(c + 1)*(c + 9)/5
Let a = -20024/45 + 445. Let t(g) be the second derivative of 0*g**3 + a*g**6 - 1/15*g**5 + 0*g**4 + 0*g**2 + 0 + 4*g. Find l, given that t(l) = 0.
0, 2
Find c, given that -388/11*c + 490/11*c**2 + 2/11*c**5 + 112/11 + 46/11*c**4 - 262/11*c**3 = 0.
-28, 1, 2
Let a(c) be the first derivative of c**4 - 30*c**2 - 2*c - 30 + 64 + 34*c + 8*c**3. Let a(f) = 0. What is f?
-8, 1
Let m(x) be the second derivative of x**7/63 + 2*x**6/45 + x**5/30 - 92*x - 2. Determine w so that m(w) = 0.
-1, 0
Let n(q) = 57*q**2 + 126*q + 105. Let t(j) = j - 1. Let g(v) = 16*v**2 + 38*v + 28. Let f(z) = -g(z) + 2*t(z). Let a(i) = 18*f(i) + 5*n(i). Factor a(u).
-3*(u + 1)*(u + 5)
Let i = -181 - -3802/21. Let a(c) be the second derivative of -1/15*c**6 + 0 + 0*c**2 - 1/10*c**5 + 1/6*c**4 + 0*c**3 + i*c**7 - 3*c. Factor a(u).
2*u**2*(u - 1)**2*(u + 1)
Let o(b) be the first derivative of 4/5*b**5 + 32/3*b**3 + 0*b - 10 + 8*b**2 + 5*b**4. Solve o(a) = 0.
-2, -1, 0
Let l be 6/(-44)*11/(-6). Let f(b) be the third derivative of -l*b**4 + 0*b + 3*b**2 + 0*b**3 + 0 + 7/20*b**5. Factor f(h).
3*h*(7*h - 2)
Let d(n) be the third derivative of 1/1155*n**7 - 7*n**2 + 0 + 0*n - 1/132*n**4 + 1/33*n**3 - 1/165*n**5 + 1/330*n**6 - 1/1848*n**8. Let d(k) = 0. Calculate k.
-1, 1
Suppose 7*q = 10*q - 81. Find a such that 4 + 26*a - 5*a + q*a**2 - 10 = 0.
-1, 2/9
Let t(j) be the second derivative of 2/5*j**5 + 0 + 1/15*j**6 + j**2 - 44*j + 4/3*j**3 + j**4. Let t(h) = 0. Calculate h.
-1
Let u(w) be the second derivative of w**7/210 + w**6/30 - 3*w**5/50 - 48*w. Determine l, given that u(l) = 0.
-6, 0, 1
Let w = 621/13 + -1229/26. Solve -3/2*d**3 + 2*d + w*d**4 + 0*d**2 + 0 = 0.
-1, 0, 2
Suppose -3*s - 9 = -312. Let f = 407/4 - s. Solve 9/4*u**2 + 9/4*u + f*u**3 + 3/4 = 0.
-1
Let f(v) be the second derivative of -v**6/70 + 3*v**5/70 + v**4/28 - v**3/7 + v - 6. Factor f(n).
-3*n*(n - 2)*(n - 1)*(n + 1)/7
Suppose 2*h = -5*k + 16, 4*h + 1 = -3*k + 5. Determine u, given that -6*u**3 + k*u**3 + 18*u - 3*u**2 - u**3 = 0.
-3, 0, 2
Let o(k) be the third derivative of 9/8*k**4 - 9*k**2 - 3/5*k**5 + 0*k + 0*k**3 + 1/10*k**6 + 0. Determine n, given that o(n) = 0.
0, 3/2
Let m(z) = 2*z**2 + 504*z - 514. Let r(y) = y**2 + 16