5/12, 2, 3
Factor 619 - 541*i - 233*i**2 + 75*i**2 - 77*i + 77*i**2 + 80*i**2.
-(i - 1)*(i + 619)
Let o(c) be the second derivative of -125*c - 9/40*c**5 - 1 - c**4 + 5*c**3 + 12*c**2. Determine g, given that o(g) = 0.
-4, -2/3, 2
Let i be ((-36)/225)/((-28)/140). Let y(z) be the first derivative of 4/15*z**3 - 3 - 1/10*z**4 - i*z + 1/5*z**2. Factor y(h).
-2*(h - 2)*(h - 1)*(h + 1)/5
Suppose -43*u + 4 = -42*u. Factor 5*j**u + 44*j + 4*j**4 - 36*j**2 - 16 - 2*j**3 + 6*j**3 - 5*j**4.
4*(j - 1)**3*(j + 4)
Let y(c) be the third derivative of -c**6/300 + c**5/6 - 59*c**4/30 - 48*c**3/5 - 3*c**2 + 100*c - 4. What is q in y(q) = 0?
-1, 8, 18
Let g = -7070 - -28281/4. Let o(q) be the third derivative of 0 + 1/40*q**5 - 11*q**2 - g*q**3 + 1/48*q**4 - 1/240*q**6 + 0*q. Factor o(s).
-(s - 3)*(s - 1)*(s + 1)/2
Let c(r) be the first derivative of r**4/20 + r**3/5 - 17*r**2/5 + 48*r/5 + 1960. Factor c(v).
(v - 3)*(v - 2)*(v + 8)/5
Let u(j) = -11*j**3 + j**2 + j + 1. Let x(d) = -23*d**3 - 103*d**2 + 110*d + 214. Let l(m) = -2*u(m) + x(m). Determine v so that l(v) = 0.
-106, -1, 2
Let k(v) = -v**3 - 11*v**2 - 22*v - 27. Let s be k(-9). Determine c so that 446*c - 1 - 209*c + 68*c**2 + s - 161*c = 0.
-1, -2/17
Let t(g) = 7*g**4 + 272*g**3 - 729*g**2 - 1086*g - 46. Let x(j) = 2*j**4 + 68*j**3 - 182*j**2 - 272*j - 12. Let v(r) = -6*t(r) + 23*x(r). Factor v(k).
4*k*(k - 13)*(k - 5)*(k + 1)
Let v(a) = -9*a**4 + 15*a**3 + 12*a**2 - 6. Let b(n) = 2*n**4 + 1 + 5*n**3 + 135*n**2 - 136*n**2 - 6*n**3. Let x(k) = 6*b(k) + v(k). Factor x(i).
3*i**2*(i + 1)*(i + 2)
Solve -111*p - 3/2*p**2 - 216 = 0 for p.
-72, -2
Let d(v) be the first derivative of -v**4/16 + 8*v**3/3 - 341*v**2/8 + 605*v/2 - 3529. Solve d(s) = 0.
10, 11
Let o(u) be the first derivative of -4*u**6/51 - 14*u**5/85 + u**4 - 16*u**3/51 + 798. Let o(n) = 0. What is n?
-4, 0, 1/4, 2
Let c(k) be the first derivative of -k**2 + 4 - 2/5*k**5 + 1/2*k**4 - 4*k + 2*k**3. Factor c(x).
-2*(x - 2)*(x - 1)*(x + 1)**2
Let l(r) be the second derivative of -3*r**5/80 + 71*r**4/16 - 65*r**3 + 378*r**2 + 816*r. Determine x so that l(x) = 0.
4, 63
Let y(c) = 3*c - 68. Let d be y(18). Let w be ((-1)/d)/((4 + -2)/12). Factor -w*q**2 - 3/7 - 6/7*q.
-3*(q + 1)**2/7
Let u(z) be the third derivative of -z**5/420 + 41*z**4/12 + 192*z**3/7 - 9*z**2 + 5*z - 13. Factor u(s).
-(s - 576)*(s + 2)/7
Let o(p) be the third derivative of -1/20*p**5 + 0*p + 0*p**4 + 6/35*p**7 - 1/40*p**6 + 0*p**3 + 0 + 58*p**2. Factor o(y).
3*y**2*(3*y - 1)*(4*y + 1)
Let q(m) be the second derivative of -m**4/6 + 397*m**3/3 + 398*m**2 - 452*m + 2. Factor q(c).
-2*(c - 398)*(c + 1)
Suppose -5*g = 3*q - 8, 3*g = -q - 28 + 36. Let u(v) be the third derivative of 0*v + 0*v**3 - 1/30*v**5 + 0*v**g + 6*v**2 + 0. Factor u(d).
-2*d**2
Let h = -141 + 135. Let i be -55*(-5 - (21/h - 1)). Solve -25*t**2 + 55/2*t + 30*t**4 - 5 - i*t**3 = 0 for t.
-1, 1/4, 2/3, 1
Let m(v) be the first derivative of -v**3/3 - 2*v**2 + 45*v + 52. Let o be m(5). Solve 8/7*a**2 - 4/7*a**3 + 0*a - 8/7*a**4 + 4/7*a**5 + o = 0 for a.
-1, 0, 1, 2
Let b be (-4)/66 + 272/132. Let 5216*k + 4*k**3 - 3*k**3 + 3*k**3 - 5168*k - 32*k**b = 0. Calculate k.
0, 2, 6
Let c(y) be the first derivative of y**6/21 + 12*y**5/35 + y**4/2 - 12*y**3/7 - 44*y**2/7 - 48*y/7 - 1281. Suppose c(r) = 0. What is r?
-3, -2, -1, 2
Let 2*w**5 - 66*w**3 - 89*w**2 + 62*w**4 + 27*w**2 + 51*w + 13*w = 0. What is w?
-32, -1, 0, 1
Let u(q) = -3*q**2 + 131*q + 518. Let d(x) = -2*x**2 + 11*x - 1. Let t(w) = -4*d(w) + 2*u(w). Let t(s) = 0. What is s?
-104, -5
Let f = 415/9 + -413/9. Let k(n) be the second derivative of -1/45*n**5 + 1/3*n**3 - f*n**4 + 0 - n + 1/189*n**7 + 4/135*n**6 + 0*n**2. Factor k(z).
2*z*(z - 1)**2*(z + 3)**2/9
Determine q so that -58/15*q**3 + 0*q + 0 + 56/15*q**4 + 2/15*q**2 = 0.
0, 1/28, 1
Let u(w) = -2*w + 37. Let p be u(19). Let k be (0 - (-9)/p)*6/(-6). Factor -6*v + k*v**4 + 3*v**2 + 6*v**3 - 2*v**2 - 6*v**4 - 4*v**2.
3*v*(v - 1)*(v + 1)*(v + 2)
Let x(d) be the second derivative of 1/135*d**6 + 1/45*d**5 + 0 - 1/18*d**4 - 4/9*d**2 - 8/27*d**3 - 98*d. Factor x(p).
2*(p - 2)*(p + 1)**2*(p + 2)/9
Let u(i) be the first derivative of i**7/1470 + i**6/315 + 37*i**3/3 + 52. Let q(g) be the third derivative of u(g). Suppose q(p) = 0. Calculate p.
-2, 0
Suppose 0 = 22*z + 11 - 55. Factor -14*t**2 + 13*t**z + 2 + t - 2 + 0.
-t*(t - 1)
Let o(k) be the third derivative of k**5/240 - 3*k**4/32 - k**2 - 81*k. Solve o(f) = 0.
0, 9
Factor 153/2*x**3 + 0 - 36*x**4 - 39*x**2 + 0*x - 3/2*x**5.
-3*x**2*(x - 1)**2*(x + 26)/2
Let o be 20/25*2*(-5)/4. Let i be (1 - 8) + (-23)/o. Factor -3/2*g - i*g**3 + 0 - 3/2*g**4 - 9/2*g**2.
-3*g*(g + 1)**3/2
Let z(m) = m + 6. Suppose i = 2*t - 6, i - 4*t + 4 = -6. Let r be z(i). Solve -2*q**4 - q**r + 7*q**4 - 4*q**2 = 0 for q.
-1, 0, 1
Let k(t) be the third derivative of 3*t + 1/840*t**8 + 0*t**3 - 3/40*t**4 - 3/350*t**7 + 7/600*t**6 + 0 - 93*t**2 + 3/100*t**5. Suppose k(r) = 0. Calculate r.
-1, 0, 1, 3/2, 3
Let r(k) be the first derivative of 7*k**4/18 - 22*k**3/27 - 10*k**2/9 + 16*k/9 - 2550. Factor r(m).
2*(m - 2)*(m + 1)*(7*m - 4)/9
Let f be (-16 + -8 + 2331/98)*-21. Suppose 18 - f*b**2 + 6*b - 3/2*b**3 = 0. Calculate b.
-3, -2, 2
Let q(s) be the second derivative of s**5/30 + 13*s**4/12 + 4*s**3 + 36*s**2 - 92*s. Let v(l) be the first derivative of q(l). Solve v(y) = 0.
-12, -1
Let j(x) be the second derivative of -x**9/24192 + x**7/2240 + x**6/1440 + 149*x**3/6 + 5*x. Let d(h) be the second derivative of j(h). What is n in d(n) = 0?
-1, 0, 2
Let h(g) be the third derivative of 0*g - 1/15*g**7 + 2 - 52*g**2 - 23/60*g**6 - 9/10*g**5 - 2/3*g**3 - 13/12*g**4. Let h(f) = 0. What is f?
-1, -2/7
Suppose 4*d + 12 = -z + 22, 8*d - 26 = -5*z. Suppose -13/2*q**4 - 11/2*q**3 + 0 - q**z - 2*q**5 + 0*q = 0. Calculate q.
-2, -1, -1/4, 0
Let v(h) be the first derivative of 735/4*h**4 + 349*h**3 + 168/5*h**5 + 2*h**6 + 44 + 108*h + 288*h**2. Determine l, given that v(l) = 0.
-6, -1, -1/2
Let x(l) be the first derivative of l**6/20 + 3*l**5/10 - 4*l**3 - 12*l**2 - 8*l + 24. Let f(j) be the first derivative of x(j). Factor f(q).
3*(q - 2)*(q + 2)**3/2
Let b(f) be the third derivative of -f**5/105 - 547*f**4/42 + 1096*f**3/21 - 2*f**2 + 2*f + 416. Factor b(z).
-4*(z - 1)*(z + 548)/7
Let s = -4773 + 4773. Let i(b) be the first derivative of 26 + 8*b**2 + 33*b**4 - 88/3*b**3 + s*b + 7/3*b**6 - 74/5*b**5. Suppose i(n) = 0. What is n?
0, 2/7, 1, 2
Let s(k) be the third derivative of 1/504*k**8 - 1/360*k**6 - 1/45*k**5 - 1/72*k**4 + 0 + 1/180*k**7 + 0*k + 34*k**2 + 1/36*k**3. Find r such that s(r) = 0.
-1, 1/4, 1
Let o = 18 - 35/2. Suppose -r + 5 = 0, -4*d + 3 = -5*r + 16. Factor o - 5/2*v**2 + 3/2*v**d + 1/2*v.
(v - 1)**2*(3*v + 1)/2
Let n(u) = -u**3 + 15*u**2 + 16*u + 2. Let r(j) = 3*j**2 + 4*j + 1. Let w be r(-3). Let t be n(w). Factor -5*l**t - 5*l - 5*l + 2*l + 8 + 7*l**2.
2*(l - 2)**2
Let v(b) be the second derivative of -1/60*b**4 - 118*b + 1/5*b**3 + 0 + 7/10*b**2. Let v(g) = 0. What is g?
-1, 7
Determine c, given that -1727/10*c + 133/5 - 13/10*c**2 = 0.
-133, 2/13
Let b(n) be the third derivative of n**7/1365 - n**6/130 - 17*n**5/130 + 61*n**4/39 - 84*n**3/13 - 2*n**2 + 3*n + 12. Let b(u) = 0. Calculate u.
-7, 2, 9
Let x(g) be the first derivative of -1 + 0*g**3 + 42*g + 1/30*g**6 + 1/6*g**4 + 0*g**2 - 3/20*g**5. Let c(q) be the first derivative of x(q). Solve c(k) = 0.
0, 1, 2
Let j(v) = -v**3 + 177*v**2 + 2233*v - 418. Let s be j(-12). Solve 324/13*i - 738/13*i**s - 10/13*i**4 + 0 - 176/13*i**3 = 0 for i.
-9, 0, 2/5
Let i = -32 + 45. Let w(o) = -4 - 21 - 10 - 8 + i*o - o**2. Let y(v) = -4*v + 14. Let m(r) = -4*w(r) - 14*y(r). Factor m(u).
4*(u - 2)*(u + 3)
Suppose -621 = 23*m - 736. Let f(i) be the third derivative of 0*i**3 + 0 + 1/540*i**6 - 17*i**2 + 1/135*i**m + 0*i**4 + 0*i. Factor f(t).
2*t**2*(t + 2)/9
Solve -3235*m + 2415 + 883*m**2 - 58*m**2 + m**3 - 6*m**3 = 0.
1, 3, 161
Factor 24*i + 22 + 15/2*i**2 + 1/2*i**3.
(i + 2)**2*(i + 11)/2
Suppose -89 = 3*y - 4*y. Suppose 101*r**2 - 180*r**2 + y*r**2 - 178*r - 36 = 0. What is r?
-1/5, 18
Determine t so that -10/3*t**4 + 0 - 686/3*t**2 + 68*t**3 + 164*t = 0.
0, 1, 3, 82/5
Suppose 4*x = -3*a + 2*x + 24, 7 = a + x. Suppose o + 5 = 2*g, -3*g + a