a + 0*l**4 - 2/45*l**5 + 0*l + 1 + 2/27*l**3. Factor u(g).
-2*g**2*(g - 1)*(g + 1)/9
Let w(z) be the third derivative of -z**5/360 - 83*z**4/72 - 6889*z**3/36 - 6*z**2 - 27*z. Let w(y) = 0. What is y?
-83
Factor 432/7*q + 1/7*q**3 - 36/7*q**2 - 1728/7.
(q - 12)**3/7
Let r(s) be the second derivative of -s**4/8 - 9*s**3/8 - 3*s**2/2 + 9*s. What is v in r(v) = 0?
-4, -1/2
Suppose 7 = -3*f - 5*n - 0, -3*f = 4*n + 8. Let r be 1 + 10 + f/2. Suppose -3*l**4 - 6*l + 30*l + r + 21*l**2 - 3*l**2 = 0. What is l?
-1, 3
Let -14149 + 1278*u - 65241 + 92*u + u**2 - 6*u**2 - 14455 = 0. Calculate u.
137
Suppose 0 = 4*a - 3*a - 2. Let g(u) = u**2 - u - 15. Let b be g(-4). Factor -13*s**a - 7*s - b*s**3 - 15*s + 4 + 18*s.
-(s + 1)*(s + 2)*(5*s - 2)
Factor 3932 - 6345*o + 182*o**2 - 11*o**3 + 91*o**2 + 2143 - 10*o**3 + 18*o**3.
-3*(o - 45)**2*(o - 1)
Let d be (-2 - (-5 + 2))/(3/5). Let c(t) be the first derivative of -5 + 10*t**2 + 20*t + d*t**3. Solve c(n) = 0.
-2
Let n(j) be the second derivative of j**6/30 + j**5/5 - j**4/4 - 5*j**3/3 + 4*j**2 - 751*j. Factor n(d).
(d - 1)**2*(d + 2)*(d + 4)
Let a(d) be the third derivative of d**8/70560 + d**7/2940 + d**6/280 - d**5/12 - d**2. Let h(c) be the third derivative of a(c). Solve h(r) = 0 for r.
-3
Determine z so that -2/7*z**2 + 26/7*z - 24/7 = 0.
1, 12
Solve -1054*h**3 + 98*h**4 + 473*h**3 + 1248*h - 2*h**5 - 1152 - 665*h**3 + 1054*h**2 = 0 for h.
-1, 1, 24
Let a(l) be the second derivative of l**7/231 - 2*l**6/55 - 12*l**5/55 - 13*l**4/33 - 3*l**3/11 + 11*l + 15. Factor a(m).
2*m*(m - 9)*(m + 1)**3/11
Let t(p) = p**5 + p**4 - p**3 + p - 5. Let b(n) = -300*n**5 - 605*n**4 - 310*n**3 - 30*n**2 - 25*n + 125. Let y(o) = -b(o) - 25*t(o). Factor y(v).
5*v**2*(v + 1)**2*(55*v + 6)
Let t = 3/17 + -118/765. Let b(h) be the third derivative of -2*h**2 + 0*h + 0 + 1/60*h**6 + 1/108*h**4 + t*h**5 + 0*h**3. Factor b(a).
2*a*(3*a + 1)**2/9
Let w = -2663/56 + 385/8. Factor w*u**3 + 10/7*u**2 + 4/7*u + 0.
2*u*(u + 2)*(2*u + 1)/7
Let y(d) be the second derivative of d**7/168 + 7*d**6/30 + 241*d**5/80 + 215*d**4/24 - 425*d**3/6 + 125*d**2 - 147*d. Factor y(p).
(p - 1)**2*(p + 10)**3/4
Solve -125/4 - 25/4*f + 1/4*f**3 + 5/4*f**2 = 0 for f.
-5, 5
Let j(c) be the second derivative of c**7/560 + c**6/36 + 9*c**5/80 + 5*c**4/24 + 5*c**3/2 - 45*c. Let t(n) be the second derivative of j(n). Factor t(b).
(b + 1)*(b + 5)*(3*b + 2)/2
Suppose -5*l + 21 = 2*c, 2*l - 4*c = -2*l. Suppose l*u = -r - 13, 3*r = 5*u + 26 + 5. Factor -5*b**2 + 2*b**2 + r*b**2 + 2 - 2*b - 3.
-(b + 1)**2
Let n(w) = 461*w + 11066. Let d be n(-24). Suppose -1/2*t - 1/8*t**d - 1/2 = 0. What is t?
-2
Suppose -t + 30 = 4*t - 5*p, -4*p - 23 = -3*t. Let k be 4/3*t*180/25. Find l, given that 1/5*l**3 + k*l - 64/5 - 12/5*l**2 = 0.
4
Let u(w) be the first derivative of 7*w**4/20 + w**3/3 - 8*w**2/5 + 4*w/5 + 75. Factor u(m).
(m - 1)*(m + 2)*(7*m - 2)/5
Let z = 1188 + -1188. Find j, given that -8/3*j + z - 2/3*j**2 = 0.
-4, 0
Let o(x) be the first derivative of x**3 - 117*x**2/2 + 222*x - 314. What is k in o(k) = 0?
2, 37
Let r(t) be the first derivative of -t**6/48 - t**5/10 + 7*t**4/8 - 4*t**3/3 + 92. Factor r(o).
-o**2*(o - 2)**2*(o + 8)/8
Let i(n) be the third derivative of -n**7/210 + n**6/60 + n**5/4 + n**4/6 - 10*n**3/3 - 21*n**2. What is u in i(u) = 0?
-2, 1, 5
Determine y, given that -8*y + 181 - 4*y**3 - 101 - 80*y**2 + 12*y = 0.
-20, -1, 1
Let v(n) be the second derivative of -n**4/6 + 7*n**3/3 - 6*n**2 + 16*n - 2. Factor v(c).
-2*(c - 6)*(c - 1)
Suppose -4*b + 4 = 2*a, 59*b + 5*a - 10 = 61*b. Let y(v) be the first derivative of 5*v**3 - 5/2*v**6 - 7*v**5 + 5*v**2 + 4 - 15/4*v**4 + b*v. Factor y(l).
-5*l*(l + 1)**3*(3*l - 2)
Suppose -9*m - 5*m - 36 = -78. Suppose -3/4 - 3/4*a**m + 3/4*a + 9/4*a**2 - 3/2*a**4 = 0. Calculate a.
-1, 1/2, 1
Let b(r) = r**3 + 3*r**2 + 5*r - 3. Let v be (-5)/(-20) + 14/8. Let q(g) = 5 + 2*g - 4*g - 6*g - 2*g**3 - 6*g**v - g. Let i(o) = -5*b(o) - 3*q(o). Factor i(c).
c*(c + 1)*(c + 2)
Let x(j) = j**3 - j**2 - j. Let z(o) = 67*o**2 - 3 + o + o**3 - 2*o**3 - 62*o**2. Let c(n) = 6*x(n) + 3*z(n). Factor c(t).
3*(t - 1)*(t + 1)*(t + 3)
Let f(m) = 2*m**3 + 15*m**2 - 15*m - 13. Let z(t) = -6*t**3 - 48*t**2 + 46*t + 38. Let v(y) = 20*f(y) + 6*z(y). Find u such that v(u) = 0.
-4, -1, 2
Let w(m) be the third derivative of m**8/28 + 76*m**7/105 + 28*m**6/5 + 96*m**5/5 + 64*m**4/3 - 2*m**2 + 39*m. Determine c, given that w(c) = 0.
-4, -2/3, 0
Let j(h) = -h**2 + h + 2. Let y(x) = 6*x**2 - 5*x - 11. Let d(u) = 5*j(u) + y(u). Let d(s) = 0. Calculate s.
-1, 1
Let j(i) be the second derivative of 3*i**5/80 + i**4/4 - 5*i**3/8 - 375*i. Factor j(k).
3*k*(k - 1)*(k + 5)/4
Let b(n) be the third derivative of 5/32*n**4 - 7/40*n**5 + 3/70*n**7 + 0 + 0*n + 6*n**2 - 1/32*n**6 + 1/4*n**3. Find i, given that b(i) = 0.
-1, -1/4, 2/3, 1
Let o(d) be the third derivative of -d**7/42 - 5*d**6/12 + 11*d**5/12 - 329*d**2. Let o(z) = 0. What is z?
-11, 0, 1
Let z(r) be the third derivative of r**5/360 - 7*r**4/144 + r**3/6 - 167*r**2 + 2. Solve z(b) = 0 for b.
1, 6
Let q(u) be the third derivative of -u**5/60 + u**4/6 + 13*u**3/6 - 9*u**2. Let n be q(6). Factor 177*s - 7 - 3*s**3 - 192*s + n - 12*s**2.
-3*(s + 1)**2*(s + 2)
Suppose 2*t = 4*q, -t + 4*q + 6 = 5*q. Suppose 3*y = t*r - 23, y = 5*r - y - 27. Find b, given that b**3 + 0 + 0*b**4 + 0*b**2 - 1/2*b**r - 1/2*b = 0.
-1, 0, 1
Suppose 0 = 3*f + j - 71, 3*f - 73 + 27 = 4*j. Factor f*d + 42 - 3*d**2 + 8*d - 36 - 54.
-3*(d - 8)*(d - 2)
Suppose 2*f - 24 = -6*s, 3*s - 9*f = -12*f + 6. Suppose 0*o**3 + 0 - 5*o**2 - 3/2*o**5 + 3/2*o + s*o**4 = 0. What is o?
-1, 0, 1/3, 1, 3
Let p(c) be the third derivative of -2/735*c**7 + 0*c**6 + 0*c**3 + 1/15*c**5 - 34*c**2 + 0 + 1/7*c**4 + 0*c. Factor p(n).
-4*n*(n - 3)*(n + 1)*(n + 2)/7
Let n(k) = 9*k**2 + 48*k - 49. Let m(d) = -2*d**2. Let h(z) = -4*m(z) - n(z). Find r such that h(r) = 0.
-49, 1
Let s(b) be the third derivative of -b**5/40 + 5*b**4/16 + 3*b**3/2 - 2*b**2 - 46. Find i such that s(i) = 0.
-1, 6
Let x(i) be the first derivative of i**4/4 + 208*i**3 + 64896*i**2 + 8998912*i + 303. Suppose x(s) = 0. What is s?
-208
Let w(c) = 28*c**2 - 140*c + 166. Let h(k) = 13*k**2 - 70*k + 81. Let f(n) = 9*h(n) - 4*w(n). Determine p so that f(p) = 0.
1, 13
Let f = -352 - -352. Let x(y) be the second derivative of 1/10*y**5 - 4*y + 1/3*y**4 + f + 0*y**2 + 1/3*y**3. Factor x(c).
2*c*(c + 1)**2
Let t(i) be the first derivative of -i**4/14 - 26*i**3/21 - 12*i**2/7 - 168. Factor t(d).
-2*d*(d + 1)*(d + 12)/7
Let r(h) be the second derivative of 0 - 5/2*h**2 - 13*h - 5/42*h**7 + 1/2*h**6 + 5/2*h**3 - 5/6*h**4 - 1/2*h**5. Find z, given that r(z) = 0.
-1, 1
Let s(y) be the first derivative of -y**4/30 - 4*y**3/9 - 23*y**2/15 - 28*y/15 + 248. Suppose s(j) = 0. Calculate j.
-7, -2, -1
Let t(s) = s**2 - 11*s - 39. Let i(k) = -1. Let h(u) = -12*i(u) - 4*t(u). Find q such that h(q) = 0.
-3, 14
Factor 0 + 44*m - 2/5*m**3 + 106/5*m**2.
-2*m*(m - 55)*(m + 2)/5
Let b(i) be the third derivative of i**6/72 - i**5/3 + 10*i**4/3 - 4*i**3/3 + 12*i**2. Let d(l) be the first derivative of b(l). What is v in d(v) = 0?
4
Let n(h) be the third derivative of 1/30*h**5 + 0*h**4 + 0*h + 0 + 0*h**3 + 1/300*h**6 - 18*h**2. Find c such that n(c) = 0.
-5, 0
Let p = -321 + 324. Let x(s) be the second derivative of 0*s**p + 0 + 0*s**2 + 3/5*s**5 + 2/3*s**4 + 7*s. Factor x(b).
4*b**2*(3*b + 2)
Let p(a) = 9*a**4 + 42*a**3 - 131*a**2 + 135*a - 55. Let i(z) = 8*z**4 + 42*z**3 - 132*z**2 + 136*z - 54. Let x(o) = -7*i(o) + 6*p(o). Factor x(f).
-2*(f - 1)**3*(f + 24)
Let k = 383/126 + -41/14. Suppose -1/9*f**5 - k*f**2 - 2/9*f + 1/3*f**3 + 1/9*f**4 + 0 = 0. What is f?
-1, 0, 1, 2
Let z(x) = -x**3 + 3*x**2 + 2*x + 7. Let w be z(3). Let o be 28/(-42)*(-6)/w. Factor 0 + 0*a - 2/13*a**5 - o*a**2 - 8/13*a**4 - 10/13*a**3.
-2*a**2*(a + 1)**2*(a + 2)/13
Factor -6*a - 13/2 + 1/2*a**2.
(a - 13)*(a + 1)/2
Let x = 103/257 - 1/1285. Factor 2*s**2 + 8/5 - 16/5*s - x*s**3.
-2*(s - 2)**2*(s - 1)/5
Let p(h) be the first derivative of 2/5*h**5 - 6 - 2/9*h**3 + 0*h + 2/3*h**4 - 2/3*h**2. Factor p(b).
2*b*(b + 1)**2*(3*b - 2)/3
Suppose 0 + 96/7*n**3 + 4/7*n**5 - 36/7*n**4 - 80/7*n**2 + 0*n = 0. Calculate n.
0, 2, 5
Let k = -3/5162 + 103261/36134