- 29*d**3/3 + 102*d. Let t(c) = -c**2 - 3*c. Let n(y) = -h(y) - 6*t(y). Factor n(i).
2*i*(i - 19)*(i - 2)
Let h = -2/37237 - -37261/446844. Let q(s) be the first derivative of -31 + h*s**3 + 1/8*s**2 - 3*s. Determine j so that q(j) = 0.
-4, 3
Let p be (112/16)/((-3)/357). Let m be 110/(-18) - p/119. Find u such that -2/9*u**2 - m*u + 10/9 = 0.
-5, 1
Let k(n) = n**2 + 14*n - 67. Let v be k(-18). Let -5*h**4 + 2*h**v - h**2 + h**3 + h**5 + 2*h**2 = 0. What is h?
-1/3, 0, 1
Let f(x) be the second derivative of x**6/45 - 11*x**5/5 + 41*x**4/2 - 60*x**3 - 1753*x. Factor f(s).
2*s*(s - 60)*(s - 3)**2/3
Let u(p) be the first derivative of 6*p**5/5 + 531*p**4/4 + 262*p**3 + 261*p**2/2 - 1909. Factor u(c).
3*c*(c + 1)*(c + 87)*(2*c + 1)
Suppose 120*l + 123*l = 249*l - 12. Determine g so that 81/5*g - 18/5*g**l + 1/5*g**3 + 0 = 0.
0, 9
Let p(r) = -22*r**2 - 40*r + 48. Let i(k) = -k**3 - 22*k**2 - 46*k + 48. Let b(t) = 4*i(t) - 6*p(t). Factor b(g).
-4*(g - 12)*(g - 1)*(g + 2)
Suppose -5*l = -229 - 51. Let a = 97 - -65. Find v, given that 108*v**2 - 16 - l*v**3 - a*v**4 + 35*v + 21*v - 70*v**3 = 0.
-1, -2/3, 2/9, 2/3
Let r(k) be the second derivative of -1/20*k**4 - 215*k + 0 - 18/5*k**2 - 7/10*k**3. Suppose r(d) = 0. What is d?
-4, -3
Let o(u) be the second derivative of -u**4/24 - u**3/6 + 20*u**2 + 579*u. Factor o(t).
-(t - 8)*(t + 10)/2
Let o(t) = -t - 3. Let h be o(-4). Suppose -3*m = i - 7 - h, i - 4*m = -6. Factor 2*c**i + 10*c**2 + 19*c + 22*c - 38*c.
3*c*(4*c + 1)
Let b = 200 - 195. Factor 15*x + b*x**3 - x**3 + x - 5*x**2 - 11*x**2.
4*x*(x - 2)**2
Let v(m) be the second derivative of -m**5/130 - 419*m**4/39 - 175561*m**3/39 + 24*m - 35. Solve v(x) = 0 for x.
-419, 0
Let v(r) = -2*r**2 - 96*r + 140. Let q(x) = 2*x**2 + 97*x - 134. Let p(d) = 6*q(d) + 5*v(d). Factor p(g).
2*(g - 1)*(g + 52)
Let 187 - 133*c**2 - 6*c + 132*c**2 + c**3 - 187 = 0. What is c?
-2, 0, 3
Let v(c) = -9*c**2 + 21*c + 15. Let p(l) = 2*l**2 + l + 1. Let z(m) = -m**3 + 9*m**2 + 23*m - 115. Let n be z(10). Let q(w) = n*p(w) - v(w). Factor q(t).
3*t*(13*t - 2)
Factor 2632*c**2 - 165*c**3 + 2617*c**2 - 220*c**3 - 5313*c**2 - 5*c**5 - 4*c**5 - 582*c**4.
-c**2*(c + 64)*(3*c + 1)**2
Find n such that 1/2*n**3 - 20*n - 24 + 9/2*n**2 = 0.
-12, -1, 4
Let y(u) be the first derivative of -3*u**5/5 - 123*u**4/2 - 316*u**3 - 468*u**2 + 6224. Find s, given that y(s) = 0.
-78, -2, 0
Let p(g) be the third derivative of -5/78*g**4 + 1/780*g**6 + 8/39*g**3 + 1/390*g**5 - 43*g**2 - g + 0. Determine i so that p(i) = 0.
-4, 1, 2
Let f(o) = 5*o**3 - 35*o**2 - 110*o + 20. Let t = 382 + -352. Let a(z) = -z**2 - 3*z. Let y(p) = t*a(p) - f(p). What is c in y(c) = 0?
-2, 1, 2
Let v(g) be the first derivative of 5*g**4/4 - 25*g**3 + 125*g**2 - 2328. Let v(j) = 0. What is j?
0, 5, 10
Factor -588/5*d - 2/5*d**2 - 1168/5.
-2*(d + 2)*(d + 292)/5
Let c be 7208/5565 + ((-114)/(-126) - 1). Let -2/5*v**4 + c + 8/5*v**3 - 8/5*v - 4/5*v**2 = 0. What is v?
-1, 1, 3
Let b(o) be the third derivative of -o**6/720 - 13*o**5/360 - 5*o**4/18 - o**3 + o**2 - 855*o. Suppose b(v) = 0. What is v?
-9, -2
Let k = 63 - 151. Let a = k + 91. Factor -2*p - 8*p**3 + 22*p + 3*p**a.
-5*p*(p - 2)*(p + 2)
Let n = 15202 - 684089/45. Let f(o) be the third derivative of 32*o**2 + 1/3*o**4 - 10/9*o**3 + 0 - n*o**5 + 0*o. Factor f(a).
-4*(a - 5)*(a - 1)/3
Solve -220*q**2 + 300*q**3 - 224/3*q - 16/3 = 0.
-2/15, 1
Factor -18*g**2 + 2*g**3 - 30*g**2 - 55388*g**4 + 55389*g**4.
g**2*(g - 6)*(g + 8)
Let q(b) be the first derivative of -b**4/26 + 236*b**3/39 + 484*b**2/13 + 976*b/13 - 2411. Factor q(n).
-2*(n - 122)*(n + 2)**2/13
Let g(n) be the third derivative of 5/24*n**4 + 0*n**3 + 1/3*n**5 - 2*n - 31*n**2 + 0. Find j, given that g(j) = 0.
-1/4, 0
Let c(n) = n. Let m(q) = -q**2 + 121*q - 3969. Suppose 3*l + 18 = 5*h, -5*l + 3*l - h = -1. Let g(a) = l*m(a) - 5*c(a). Find s, given that g(s) = 0.
63
Let v = -1007917 + 1007921. Factor -3/4*u**v - 6*u + 0*u**3 + 9/4 + 9/2*u**2.
-3*(u - 1)**3*(u + 3)/4
Suppose -97 + 11 = -43*q. Let t(u) be the first derivative of 0*u**3 + 0*u**q - 7 + 1/6*u**4 + 0*u. Factor t(r).
2*r**3/3
Suppose -29*i = -173*i + 288. Let a(m) be the first derivative of 16/9*m - 23 + 10/27*m**3 + 22/9*m**i. Determine v, given that a(v) = 0.
-4, -2/5
Let d(v) be the first derivative of v**6/12 + 4*v**5/15 - 2*v**4 + 11*v**3/3 - 35*v**2/12 + v - 9606. Determine z, given that d(z) = 0.
-6, 1/3, 1
Let z(k) be the first derivative of -5*k**3 + 20 + 40*k**2 - 5/4*k**4 - 60*k. Factor z(i).
-5*(i - 2)*(i - 1)*(i + 6)
Let v(n) be the second derivative of 2*n**6/15 - 11*n**5/5 + 8*n**4 + 24*n**3 - 3*n - 81. Solve v(b) = 0.
-1, 0, 6
Let j(b) be the second derivative of -b**5/20 - 10*b**4/3 + b**3/6 + 20*b**2 - 229*b. Let j(h) = 0. What is h?
-40, -1, 1
Let l(z) = -22 + 5*z**2 - 4*z**2 + 0*z - 5*z. Let p(r) = -2*r**2 + 16*r + 68. Let q(o) = -7*l(o) - 2*p(o). Let q(x) = 0. What is x?
-2, 3
Let c(l) be the second derivative of 1/15*l**5 + 0*l**2 + 1/180*l**6 + 88*l + 0*l**3 + 0 - 1/252*l**7 - 1/6*l**4. Factor c(y).
-y**2*(y - 2)**2*(y + 3)/6
Let o(c) be the second derivative of 70*c + 12*c**2 + 3*c**3 + 0 + 1/4*c**4. Factor o(w).
3*(w + 2)*(w + 4)
Suppose -3*b + 0*b + 4*g + 4109 = 0, -4114 = -3*b + 5*g. Factor 38*m - 26*m**2 + 703 + 726 - b + 2*m**3.
2*(m - 11)*(m - 3)*(m + 1)
Suppose 2/9*i**2 - 242 - 176/9*i = 0. What is i?
-11, 99
Let u(c) be the first derivative of 138*c**2 - 2/3*c**3 - 9522*c + 121. Let u(p) = 0. Calculate p.
69
Let u(c) be the second derivative of -2*c**2 - 1/48*c**4 - 1 + 1/3*c**3 - 30*c. Factor u(z).
-(z - 4)**2/4
Let -1266629*q**2 + 1265991*q**2 + 19461*q + 82300*q + q**3 = 0. Calculate q.
0, 319
Let s(l) = -l**3 + 3*l**2 - 201*l - 203. Let c be s(-1). Let m be 2*-1 + 48/18. Factor -2/9*t**3 - m*t - 2/3*t**c - 2/9.
-2*(t + 1)**3/9
Solve 617/2*f - 380689/4 - 1/4*f**2 = 0 for f.
617
Suppose 14*y + 929 = -331. Let h be ((-54)/y)/((-1)/(3 - 5)). Let h*b**3 - 9/5*b**2 + 3/5 + 0*b = 0. Calculate b.
-1/2, 1
Suppose -6*y = -41*y + 280. Suppose -32 + 0 = -y*u. Find q such that 0 - 2/3*q**u + 2/3*q**3 + 4/3*q**2 + 0*q = 0.
-1, 0, 2
Let f(v) be the second derivative of 0 + 0*v**2 + 1/21*v**3 + 2/21*v**4 - 96*v. Suppose f(i) = 0. What is i?
-1/4, 0
Let l(x) = -2*x**3 + x**2. Suppose 2*b = -3*b + 2*t + 20, 5*t = 0. Let w(u) = 10*u**3 + 4*u**2 - 14*u - 20. Let d(z) = b*l(z) + w(z). What is c in d(c) = 0?
-5, -1, 2
Let n be 1 + 2 - 8 - 1483/(-260). Let f = n + 5/52. Find u, given that u**2 - f*u + 0 - 1/5*u**3 = 0.
0, 1, 4
Let y = -70 - -75. Suppose -7*d + y + 16 = 0. Factor -d*r**2 + 3*r**4 + 48 - 48.
3*r**2*(r - 1)*(r + 1)
Solve 24 + 10/11*s**2 - 664/11*s = 0 for s.
2/5, 66
Let r(g) be the second derivative of -g**7/630 + g**6/15 - 6*g**5/5 + 5*g**4/3 + 2*g - 2. Let m(f) be the third derivative of r(f). Factor m(o).
-4*(o - 6)**2
Let -10*k - 3*k**2 + 2*k**2 - 6*k + 63*k - 8*k = 0. What is k?
0, 39
Let t be -3 + 8 - (0 + 4 - 5). Find u, given that -20 + 11*u + 5*u - t*u**2 + 5*u**2 + 2*u**2 - 16 = 0.
-18, 2
Let w(g) be the first derivative of -2/11*g**3 - 72/11*g + 40 + 24/11*g**2. Factor w(b).
-6*(b - 6)*(b - 2)/11
Let t(c) = 2*c**2 + 43*c + 3. Let j = -16 - -19. Let x(l) = 2*l**2 + l + 1. Let h(d) = j*x(d) - t(d). Suppose h(o) = 0. Calculate o.
0, 10
Let u(r) be the second derivative of r**5/40 - 5*r**4/3 + 19*r**3/3 + 969*r. What is g in u(g) = 0?
0, 2, 38
Suppose 149*q - 1/4*q**3 - 19/4*q**2 + 315 = 0. What is q?
-35, -2, 18
Suppose 0 = -3*u - 4*i + 108, -i + 3 = -5*u + 206. Factor 2*h**2 - u - 30*h - 16*h**2 + 76.
-2*(h + 3)*(7*h - 6)
Let y = -15007 - -15011. Let p(f) be the second derivative of -1/12*f**4 + y*f - 1/2*f**2 + 1/3*f**3 + 0. Let p(g) = 0. Calculate g.
1
Determine n, given that 20*n**3 - 14*n + 14*n - 5017*n**4 - 13843*n**4 + 1874585*n**5 + 2571660*n**5 = 0.
0, 2/943
Determine r so that 33/5 - 27/5*r**2 - 294/5*r = 0.
-11, 1/9
Suppose -23*o + 19*o = -112. Let y = -26 + o. Factor -71 - 20*n**3 + 18*n + y*n + 76 - 5*n**2.
-5*(n - 1)*(n + 1)*(4*n + 1)
Suppose -64 = -6*o + 8. Suppose 10*d + 4 = o*d. Suppose 25*x - 14*x**2 - 6*x**d + 15*x**2 = 0. What is x?
0, 5
Let w(p) be the second derivative of -9*p**5/20 - 145*p**4/4 + 124*p**3 - 150*p**2 + 32*p + 4. Solve w(q) = 0 for q.
-50, 2/3, 1
Determine z so that -10/3*z**4