 0*v. Let r(b) = b**3 + 3*b**2 - 11*b - 3. Let d be r(n). Suppose -10*q**3 + 4*q + 0*q**d - 15*q**2 - 9*q = 0. Calculate q.
-1, -1/2, 0
Suppose -173 = -6*p - 11. Suppose -537 = 24*j - p*j. Factor -j*l**2 + 7*l + l + 151*l**2.
-4*l*(7*l - 2)
Let z be -2 + (-45)/6*-8. Suppose -z*d + 63*d - 5 = 0. Factor -3 - 3 + d + 8 - 3*i**4 - 6*i + 6*i**3.
-3*(i - 1)**3*(i + 1)
Let x(q) be the first derivative of 2*q**3/3 - 4*q**2 + 20*q + 218. Let r(d) = d**2 - 4*d + 9. Let i(b) = 7*r(b) - 3*x(b). Factor i(z).
(z - 3)*(z - 1)
Factor 230250*h**3 + 164*h**2 + 272 - 230310*h**3 + 85*h - 4*h**4 + 407*h.
-4*(h - 4)*(h + 1)**2*(h + 17)
Let m be (-2)/(-10)*(37 - 36). Suppose -2 = -4*h - b - b, 4*h - 7 = -b. Suppose 1/5*z**4 - 3/5*z**h - 1/5*z**2 + 0 + 2/5*z + m*z**5 = 0. Calculate z.
-2, -1, 0, 1
Let y(t) be the third derivative of t**7/840 - t**6/120 - 3*t**5/8 - 179*t**4/24 - 97*t**2. Let h(c) be the second derivative of y(c). Factor h(o).
3*(o - 5)*(o + 3)
Let s = 7127 - 7124. Let h(m) be the first derivative of -1/2*m**2 - 1/3*m**s + 0*m - 22. Find k, given that h(k) = 0.
-1, 0
Determine f so that -130*f**3 + 69090*f**4 - 2*f**5 - 54*f + 26*f**3 - 69062*f**4 + 132*f**2 = 0.
0, 1, 3, 9
Let p = 461 + -461. Suppose p = 5*t - 11 - 14. Find y such that 0*y + 0*y**2 + 2/9*y**t + 0 + 0*y**4 - 2/9*y**3 = 0.
-1, 0, 1
Let k be 4/130 - (-76962)/59085. Factor k*f + 1/3*f**2 + 4/3.
(f + 2)**2/3
Let a = 112 - 208. Let r = a - -92. Let p(l) = 9*l**2 + 29*l + 34. Let b(u) = -8*u**2 - 28*u - 33. Let t(g) = r*b(g) - 3*p(g). Determine i so that t(i) = 0.
-3, -2
Let u = 246712 + -246710. Find h, given that 0*h**3 + 3/5*h**u + 2/5*h + 0 - 1/5*h**4 = 0.
-1, 0, 2
Let h(a) = -48*a**2 - 427*a + 93. Let w(b) = 244*b**2 + 2136*b - 464. Suppose j + 4*o = 0, -4*o = -4*j + 2*j - 48. Let r(y) = j*h(y) - 3*w(y). Factor r(z).
4*(z + 12)*(9*z - 2)
Suppose 4*q - 240 = -5*k, 4*q - 144 = -3*k + 8. Let r be (-1 + 0)/((-11)/k). Factor 0*p - 2/5*p**r + 2/5*p**3 + 0 + 4/5*p**2.
-2*p**2*(p - 2)*(p + 1)/5
Find k, given that 118/3*k**2 - 2921/6*k + 529 - 5/6*k**3 = 0.
6/5, 23
Factor -874332 + 361928 - 3500*k - 918186 - 2*k**2 - 100660.
-2*(k + 875)**2
Let f(h) = h**2 + 20*h + 107. Let r be f(-9). Factor r + 17*y**2 - 15 - 6 - 7 - 15*y**2 + 18*y.
2*(y - 1)*(y + 10)
Let g(q) = 6*q**4 + 5*q**3 - 34*q**2 + 66*q - 62. Let o(x) = -7*x**4 - 4*x**3 + 32*x**2 - 64*x + 64. Let n(i) = 8*g(i) + 7*o(i). Let n(r) = 0. Calculate r.
2, 6
Let i = -15524 + 15548. Determine a so that -16/3 - 20*a**2 + 14/3*a**3 + i*a = 0.
2/7, 2
Let f(p) be the second derivative of -p**7/105 + 4*p**6/75 + 21*p**5/50 + 2*p**4/15 - 28*p**3/15 - 225*p. Determine v, given that f(v) = 0.
-2, 0, 1, 7
Let o(d) be the second derivative of d**6/60 + d**5/15 + d**4/12 + 115*d**2/2 + 46*d. Let m(g) be the first derivative of o(g). Factor m(r).
2*r*(r + 1)**2
Let 298*s - 2760*s**2 - 873*s + 2940*s**2 + 390 + 5*s**3 = 0. Calculate s.
-39, 1, 2
Let q(k) be the first derivative of 14*k - 1/12*k**3 + 0*k**2 - 1/16*k**4 - 1 - 1/80*k**5. Let i(z) be the first derivative of q(z). Factor i(c).
-c*(c + 1)*(c + 2)/4
Let a(z) be the second derivative of 2*z**6/45 + 8*z**5/15 + 23*z**4/9 + 56*z**3/9 + 8*z**2 + 768*z. Factor a(s).
4*(s + 1)*(s + 2)**2*(s + 3)/3
Suppose -9*n = -127 - 539. Let f = -53 + n. Determine r so that -1 - 3*r + 15*r**2 - f*r**2 - 3*r**3 + 1 = 0.
-1, 0
Let t = 496/13 + -1462/39. Let o(a) be the first derivative of 2*a - t*a**3 - 10 + 0*a**2. Suppose o(f) = 0. What is f?
-1, 1
Find x, given that 3/2*x**2 - 759*x + 192027/2 = 0.
253
Let u(a) be the third derivative of 7*a**2 - 120*a**3 + 23/12*a**5 - 1/42*a**7 + 1/12*a**6 - 1 + 0*a - 5*a**4. Solve u(h) = 0 for h.
-3, 4
Let l(r) = -25*r**3 + 1701*r**2 + 2255*r + 555. Let q(b) = 12*b**3 - 850*b**2 - 1128*b - 278. Let c(d) = 6*l(d) + 13*q(d). Factor c(h).
2*(h - 142)*(h + 1)*(3*h + 1)
Let w be (12/(-15))/((-36)/450). Determine a so that 2*a**2 - 6*a + 12*a + w*a + 8 + 24 = 0.
-4
Let i be 1426/(-46) + -41 + 72. Determine d, given that -1/12*d**4 + 0 + i*d + 0*d**2 + 1/12*d**3 = 0.
0, 1
Let c = 279 + -150. Suppose 41*x = -2*x + c. Determine k so that 1/2*k + 1/2*k**x + 0 + k**2 = 0.
-1, 0
Let k(x) = 8*x**2 - 17*x + 21. Let s(z) = 175*z**2 + 29*z - 201*z**2 - 14 + 21*z - 50. Let q(d) = -20*k(d) - 6*s(d). Factor q(o).
-4*(o - 9)*(o - 1)
Let g(z) be the second derivative of 0 - 7*z**4 - 17/10*z**5 - 1/15*z**6 + 260/3*z**3 + 81*z - 200*z**2. Factor g(y).
-2*(y - 2)*(y - 1)*(y + 10)**2
Let n(v) be the first derivative of 11*v**3/2 + 147*v**2/4 - 675*v - 1975. Factor n(x).
3*(x + 9)*(11*x - 50)/2
Let p(h) = -777*h - 5436. Let s be p(-7). Factor 14/3*c - 8/3*c**s + 4/3 - 10/3*c**2.
-2*(c - 1)*(c + 2)*(4*c + 1)/3
Let b = 1192 + -1132. Suppose -10 = b*s - 65*s. Factor -11/6*m**s - 2*m - 1/2*m**3 - 2/3.
-(m + 1)*(m + 2)*(3*m + 2)/6
Factor -18*r + 0 + 1/10*r**2.
r*(r - 180)/10
Suppose 32*i = -1147 + 5595. Suppose -70 = i*m - 153*m. Factor -4/3*t**3 + 0 + 2/3*t**m + 0*t**2 + 2/3*t + 0*t**4.
2*t*(t - 1)**2*(t + 1)**2/3
Let f = 1322069 + -2644133/2. Factor 125/2*l + 45/2*l**2 - f*l**3 - 165/2.
-5*(l - 11)*(l - 1)*(l + 3)/2
Let y(g) be the first derivative of -125*g + 70 - 25*g**2 - 5/3*g**3. Factor y(k).
-5*(k + 5)**2
Let c(y) be the second derivative of 2*y**6/5 - 59*y**5/10 - 7*y**4/3 + 41*y**3/3 - 10*y**2 - 430*y - 7. Let c(k) = 0. What is k?
-1, 1/3, 1/2, 10
Let l(n) = -5*n + 19. Let w be l(-16). Let g = w - 76. Factor -19*p**2 + 46*p**2 - g*p**2 - 2*p**3.
-2*p**2*(p - 2)
Suppose 526*i = 521*i. Suppose i = 16*c - 78*c + 1984. Factor -8*s**2 + 2/3*s**3 - 128/3 + c*s.
2*(s - 4)**3/3
Let f(d) be the third derivative of 0*d**4 + 0 + 0*d + 1/40*d**6 + 0*d**3 + 27*d**2 - 1/10*d**5. Factor f(v).
3*v**2*(v - 2)
Let w(l) be the first derivative of -l**8/420 + l**7/70 - l**6/30 + l**5/30 + 8*l**3 - 3*l**2/2 - 32. Let f(b) be the third derivative of w(b). Factor f(x).
-4*x*(x - 1)**3
Factor -50/3*t**2 - 5/3*t**3 - 20 + 115/3*t.
-5*(t - 1)**2*(t + 12)/3
Suppose 34/3*c**2 - 299/3*c - 1/3*c**3 + 266/3 = 0. What is c?
1, 14, 19
Let h(a) be the third derivative of -5*a**2 - 2/5*a**3 + 0 - 9*a - 88/225*a**5 - 7/12*a**4 - 16/225*a**6. Determine b, given that h(b) = 0.
-2, -3/8
Let x be (1 - -111)/(60/(-90)). Let s = x - -841/5. Find q such that 0 + 0*q**3 + 0*q - 1/5*q**2 + s*q**4 = 0.
-1, 0, 1
Let b(t) be the first derivative of t**5 + 55*t**4/4 + 115*t**3/3 - 55*t**2/2 - 120*t + 1841. Determine x, given that b(x) = 0.
-8, -3, -1, 1
Let a(g) be the first derivative of -2*g**5/5 + 11*g**4/2 - 4*g**3/3 - 92*g**2 + 240*g + 1109. Factor a(k).
-2*(k - 10)*(k - 2)**2*(k + 3)
Let -4/5*a**2 - 8/5*a + 8/5*a**3 + 4/5*a**4 + 0 = 0. What is a?
-2, -1, 0, 1
Factor 4/9*t**2 + 16*t - 148/9.
4*(t - 1)*(t + 37)/9
Let n = 2/439 + 339/21950. Let v(i) be the third derivative of -32*i**2 + 1/30*i**4 + 1/300*i**6 + 0*i**3 + 0*i + 0 - n*i**5. Determine u, given that v(u) = 0.
0, 1, 2
Determine z, given that 0 + 0*z + 6/7*z**2 + 3/7*z**3 - 3/7*z**4 = 0.
-1, 0, 2
Let n(y) be the second derivative of -y**4/6 + 358*y**3/3 + 1157*y. Factor n(g).
-2*g*(g - 358)
Let u(s) be the first derivative of 1/9*s**3 - 13*s**2 - 86 + 507*s. Factor u(k).
(k - 39)**2/3
Let d = 8557 + -8557. Let j(z) be the second derivative of -z**2 + 1/12*z**4 - 10*z + 1/6*z**3 + d. Factor j(w).
(w - 1)*(w + 2)
Let w(i) be the first derivative of -5*i**3/6 + 4465*i**2/4 + 2235*i + 2149. Factor w(y).
-5*(y - 894)*(y + 1)/2
Factor -154/13 - 2/13*f**3 - 158/13*f**2 - 310/13*f.
-2*(f + 1)**2*(f + 77)/13
Factor 380 - 1144/3*b + 4/3*b**2.
4*(b - 285)*(b - 1)/3
Let v(p) be the first derivative of -25 - 1/48*p**4 + 0*p**5 + 0*p**2 + 1/36*p**3 - 3*p + 1/360*p**6. Let z(w) be the first derivative of v(w). Factor z(j).
j*(j - 1)**2*(j + 2)/12
Let z(c) be the third derivative of c**7/630 - c**5/30 - 11*c**4/2 + 61*c**2 - 2*c. Let j(w) be the second derivative of z(w). Solve j(s) = 0 for s.
-1, 1
Let r(d) be the first derivative of -1/2520*d**6 - 1/840*d**5 + 19 - 1/3*d**3 + 0*d**4 + 0*d + 0*d**2. Let g(l) be the third derivative of r(l). Factor g(i).
-i*(i + 1)/7
Let r(s) be the second derivative of 73*s**6/5 - 429*s**5/20 - 149*s**4/4 + 143*s**3/2 + 9*s**2/2 + 613*s. Find f such that r(f) = 0.
-1, -3/146, 1
Let b = 9 + -4. Suppose -4*q - 3*h = -2*h - 18, -b*h = 5*q - 15. Find a, given tha