Let o(n) = -n**3 - 12*n**2 - 8*n + 3. Let a(g) = 28*m(g) + 4*o(g). Factor a(j).
-4*(j + 1)*(j + 2)**2
Let c(u) be the third derivative of -u**8/2520 + u**7/1575 + u**6/180 + u**5/150 + 82*u**2. Let c(q) = 0. What is q?
-1, 0, 3
Let o(u) be the second derivative of 2*u**5/45 - u**4/36 + 3*u**2 - 8*u. Let b(k) be the first derivative of o(k). Suppose b(n) = 0. What is n?
0, 1/4
Let i(f) be the third derivative of -13/600*f**5 - 1/150*f**6 + 0*f**3 + 2*f**2 - 1/2100*f**7 - 1/40*f**4 + 0 + 2*f. Factor i(x).
-x*(x + 1)**2*(x + 6)/10
Let k(g) be the second derivative of 9/5*g**5 + 29/14*g**4 + 20*g + 12/7*g**2 - 76/21*g**3 - 7/15*g**6 + 0. Determine z so that k(z) = 0.
-1, 2/7, 3
Let m = 30 - 28. Factor 420 - 420 - 4*l**3 - 4*l**m.
-4*l**2*(l + 1)
Find v such that -16/5 + 17/5*v**2 - 1/5*v**4 + 6/5*v - 6/5*v**3 = 0.
-8, -1, 1, 2
Let x(c) be the first derivative of c**4/16 + 11*c**3/6 + 21*c**2/8 - 124. Factor x(g).
g*(g + 1)*(g + 21)/4
Factor 19/7*n - 60/7 - 1/7*n**2.
-(n - 15)*(n - 4)/7
Let n(h) be the second derivative of 2*h**7/147 - 2*h**6/105 - 3*h**5/35 + h**4/21 + 4*h**3/21 - 13*h - 1. Determine y so that n(y) = 0.
-1, 0, 1, 2
Suppose -5*f - 14 = 3*l, -176 = -5*f + 4*l - 134. Solve -2/7*x**f + 36/7*x - 162/7 = 0 for x.
9
Determine m so that -16*m - 21*m**3 - 45*m + 5 + 13 - 26*m + 69*m**2 + 21*m**2 = 0.
2/7, 1, 3
Let q(k) = -k**2 - k - 2. Let c(g) = -2*g**3 + 46*g**2 - 80*g + 44. Let n(t) = -c(t) - 2*q(t). Solve n(i) = 0 for i.
1, 20
Let a be (-120)/(-25) + -8 + 4. Let c(o) = o**2 - 2*o - 11. Let v be c(5). Solve v*n**2 + a + 6/5*n**3 + 18/5*n = 0.
-2, -1, -1/3
Let t = -2/459 - -37183/918. Find p such that 72*p - 24 + 21/4*p**3 + t*p**2 = 0.
-4, 2/7
Let g(u) be the first derivative of 7*u**4/3 - 92*u**3/3 + 68*u**2 + 64*u/3 + 112. Suppose g(j) = 0. Calculate j.
-1/7, 2, 8
Let o(b) = -b - 56. Let x be o(0). Let k be (-343)/x - 6 - 18/(-112). Suppose -k*c**2 - 32/7 + 16/7*c = 0. Calculate c.
4
Let t(a) be the third derivative of a**11/332640 + a**10/75600 + a**9/60480 + 3*a**5/10 + 6*a**2. Let o(x) be the third derivative of t(x). Factor o(n).
n**3*(n + 1)**2
Let s be (28 + -2)*((-91)/14 + 5). Let v be ((-2)/(-10))/((-13)/s). Suppose 0 - v*x**3 + 0*x + 0*x**2 = 0. Calculate x.
0
Let l(j) = 22*j**2 + 6*j + 20. Let a be l(-3). Let n = -198 + a. Factor -b - 1/4 - b**n.
-(2*b + 1)**2/4
Let s(c) = -23*c**4 - 93*c**3 - 70*c**2 + 8*c. Let d(g) = -45*g**4 - 186*g**3 - 139*g**2 + 16*g. Let y(b) = 4*d(b) - 7*s(b). Factor y(j).
-j*(j + 1)*(j + 4)*(19*j - 2)
Let c = -70 + 78. Suppose 2*t + 3*v = -6, -c*t + 8 = -10*t - 4*v. Factor -3/4*z**3 + 0 + t*z + 1/4*z**2 - z**4.
-z**2*(z + 1)*(4*z - 1)/4
Let o be (-3520)/960 - 8/(-2). Determine p so that -1/3 + p - p**2 + o*p**3 = 0.
1
Solve -1/3*g**2 - 13 + 16/3*g = 0.
3, 13
Let c(w) = 2*w**2 - 8*w + 1. Let n be c(5). Factor -8*m**2 - 12 - n*m - 3*m - 14*m.
-4*(m + 3)*(2*m + 1)
Let i be -14*(-13 + (-534)/(-42)). Let 10/3*c**2 + 4/3*c + 0 + 14/3*c**5 - 6*c**3 - 10/3*c**i = 0. What is c?
-1, -2/7, 0, 1
Let u be (100/(-8) - -11)/(-18). Let g(f) be the first derivative of 0*f - 14 + 1/2*f**2 - u*f**3. Factor g(v).
-v*(v - 4)/4
Let l(j) be the second derivative of j**7/24 - j**6/6 - j**5/6 - 5*j**3/6 + 9*j. Let z(k) be the second derivative of l(k). Factor z(q).
5*q*(q - 2)*(7*q + 2)
Let g(i) be the first derivative of 13*i**3/12 - i**2/2 - 9*i/4 - 198. Solve g(l) = 0.
-9/13, 1
Determine d, given that 5*d - 8/3*d**4 + 0 + 8/3*d**2 - 14/3*d**3 - 1/3*d**5 = 0.
-5, -3, -1, 0, 1
Let y(k) = 2*k**2 - 5. Let r(z) = 2*z + 6. Let h be r(4). Let j(d) = 10*d**2 - 26. Let g = -10 + 7. Let a(w) = g*j(w) + h*y(w). Solve a(n) = 0.
-2, 2
Solve 3*d**3 + d**3 + 14*d**2 + 31*d**2 + 6*d**2 + 36*d - 11*d**2 = 0.
-9, -1, 0
Factor 0 - 2/7*d**2 - 8/7*d.
-2*d*(d + 4)/7
Let c(z) be the first derivative of 2/39*z**3 - 1/26*z**4 - 2/13*z - 4 + 1/13*z**2. Determine l, given that c(l) = 0.
-1, 1
Let i(y) = -5*y**3 - 50*y**2 + 5*y + 53. Let o be i(-10). Factor 0*k**o - 2/9*k - 4/9*k**2 + 0 + 2/9*k**5 + 4/9*k**4.
2*k*(k - 1)*(k + 1)**3/9
Let u(d) be the third derivative of -d**8/672 + 23*d**7/420 - 91*d**6/240 - 169*d**5/40 + 2*d**2 + 4*d. Find c such that u(c) = 0.
-3, 0, 13
Factor 1/2*w**2 + 0 - 6*w.
w*(w - 12)/2
Suppose 8*v - 36 = -v. Let b(r) be the second derivative of r + 0 - 1/15*r**v - 2/5*r**3 + 8/5*r**2. Factor b(m).
-4*(m - 1)*(m + 4)/5
Suppose 31 = -3*w - 4*c, -5*w = -5*c + 13 - 8. Let j be (w - -7) + 6 - 15/3. Find h such that -3/2*h**j + 3/2*h - 3/2 + 3/2*h**2 = 0.
-1, 1
What is n in 258 + 5*n**2 - 329 + 52*n - 6*n**2 - 605 = 0?
26
Let j(d) be the second derivative of -d**4/108 + 31*d**3/18 - 46*d**2/9 - 395*d. Suppose j(k) = 0. What is k?
1, 92
Solve -39 + 7*v + 3 - 136*v**2 - v + 138*v**2 = 0.
-6, 3
Let g be (-12)/(4/(-1)) - (-1700)/(-522). Let o = -1/29 - g. Factor 0*f**4 - 2/9*f + 0*f**2 + 0 + 4/9*f**3 - o*f**5.
-2*f*(f - 1)**2*(f + 1)**2/9
Let t(q) be the second derivative of 3/40*q**5 + 0 - 1/3*q**3 - 1/84*q**7 + 0*q**2 + 12*q + 1/30*q**6 - 1/6*q**4. Let t(z) = 0. What is z?
-1, 0, 2
Suppose -4*w - 17 = -5*c + 5, 0 = 4*w + 5*c - 38. Determine r, given that 0 - 4/3*r**w - 4/3*r = 0.
-1, 0
Suppose -4*t + 8 = 4*y, -8 = -4*t - 632*y + 627*y. Factor -1/2*o**t + 0*o**3 + 0*o + 1/2*o**4 + 0.
o**2*(o - 1)*(o + 1)/2
Suppose 1/11*v**5 - 40/11*v - 21/11*v**3 - 47/11*v**2 - 12/11 - 1/11*v**4 = 0. What is v?
-2, -1, 6
Let -61*a - 3*a**5 - 3*a**4 - 3 + 58*a + 28*a**2 - 22*a**2 + 6*a**3 = 0. What is a?
-1, 1
Let j(x) be the first derivative of x**3/9 + 2*x**2 - 13*x/3 - 33. Suppose j(a) = 0. What is a?
-13, 1
Let g(s) be the first derivative of -s**5/5 + s**3 - s**2 + 104. Factor g(k).
-k*(k - 1)**2*(k + 2)
Let p(g) be the second derivative of 1/8*g**4 - 1/3*g**3 - 1/60*g**5 + 0 - 3*g + g**2. Let m(f) be the first derivative of p(f). What is n in m(n) = 0?
1, 2
Let w(o) = -76*o - 72*o**2 - 62*o - 6*o + 8*o**3. Let s(x) = 3*x**3 - 24*x**2 - 48*x. Let r(k) = 17*s(k) - 6*w(k). Solve r(v) = 0 for v.
-4, 0
Let j(r) be the first derivative of -r**3 + 51*r**2/2 + 114*r + 398. Solve j(u) = 0 for u.
-2, 19
Let c = -32 - -34. Determine u so that 4*u**c - 5 + 9 + 7827*u + 8 - 7843*u = 0.
1, 3
Suppose -4*w + 3 = -13. Suppose -5 + 37 = 4*i. Determine d so that i*d**2 - 7*d**3 - d**w - 3*d**2 - 2*d + 4*d**3 + d**5 = 0.
-2, 0, 1
Let c = -18887/4 + 4626. Let k = -95 - c. Find t, given that 3/4*t**3 + 0 + 3/4*t**4 - 3/4*t - k*t**2 = 0.
-1, 0, 1
Let i(x) be the first derivative of 3 + 1/2*x**3 + 21/16*x**4 - 21/8*x**2 - 3/2*x. Factor i(t).
3*(t - 1)*(t + 1)*(7*t + 2)/4
Let g(v) be the third derivative of 12*v**2 + 2/21*v**4 + 8/21*v**3 - 1/105*v**5 + 0*v - 1/210*v**6 + 0. Factor g(f).
-4*(f - 2)*(f + 1)*(f + 2)/7
Let v(z) be the third derivative of -z**8/151200 + z**7/7560 - z**6/1350 - 7*z**5/30 - 30*z**2. Let w(i) be the third derivative of v(i). Factor w(c).
-2*(c - 4)*(c - 1)/15
Let -38/3*h**2 + 4 - 22*h**3 + 40/3*h**5 + 26/3*h + 26/3*h**4 = 0. Calculate h.
-1, -2/5, 3/4, 1
Let m be (-490)/(-84)*3080/98. What is j in 910/3*j**2 + 80/3 + 245/6*j**3 - m*j = 0?
-8, 2/7
Let x be ((-205)/4485)/(3/(-90)). Let y = x + -28/23. What is u in 2/13*u**2 - 2/13*u**4 + 0 - y*u + 2/13*u**3 = 0?
-1, 0, 1
Let m(u) be the second derivative of -5*u**7/21 - 32*u**6/15 - 77*u**5/10 - 43*u**4/3 - 44*u**3/3 - 8*u**2 + u - 67. Determine w so that m(w) = 0.
-2, -1, -2/5
Let y(b) = 6*b + 104. Let x be y(-17). What is f in -1/7*f**x + 4/7*f - 3/7 = 0?
1, 3
Let l(h) be the second derivative of 2*h**7/21 + 2*h**6 + 72*h**5/5 + 36*h**4 - 120*h. Let l(t) = 0. What is t?
-6, -3, 0
Let p(u) = 2*u**5 - 4*u**4 + 8*u**3 - 2*u. Let i be 69/12 + 3/(-4). Let g(f) = -4*f**3 + f**i + f**3 - f**4 + 4*f**3. Let k(d) = 4*g(d) - p(d). Factor k(y).
2*y*(y - 1)**2*(y + 1)**2
Let q(b) be the third derivative of -b**5/480 - 7*b**4/64 - 5*b**3/12 - b**2 - 50. Solve q(n) = 0.
-20, -1
Let i(z) = -10*z + 42. Let c be i(4). Suppose 35*b**3 - 9*b**2 - 11*b - 38*b**3 + c*b - 3 = 0. What is b?
-1
Find h such that 0 - 2/13*h**5 + 2/13*h**2 + 6/13*h**3 - 4/13*h - 2/13*h**4 = 0.
-2, -1, 0, 1
Let o(s) = 3*s**2 + 3*s - 6. Let l(v) = 4*v**2 + 4*v - 9. Let d(k) = -2*l(k) + 3*o(k). Factor d(x).
x*(x + 1)
Solve -1/5*h + 4/5*h**4 - 2*h**2 + 6/5 + 0*h**3 + 1/5*h**5 = 0.
-3, -2, -1, 1
Let u(g) be the first derivative of -g*