**9/12096 + y**7/3360 - 11*y**3/3 + 2*y**2 - 68. Let m(o) be the first derivative of r(o). Let m(n) = 0. What is n?
-1, 0, 1
Determine k, given that -2/3*k**2 + 34/3*k - 20 = 0.
2, 15
Let u be (-4)/5 - (-56)/(-5). Let f(n) = 19*n + 230. Let l be f(u). Factor 15/4*o + 9/2 + 3/4*o**l.
3*(o + 2)*(o + 3)/4
Let h be 63 + 6440/(-115) - (-14)/4. Suppose 12*i + 0 + h*i**3 + 21*i**2 + 3/2*i**4 = 0. Calculate i.
-4, -2, -1, 0
Let s be (-10)/4*(-36)/(-45). Let b(o) = -o - 1. Let u(g) = -3*g**2 + 9*g + 12. Let n be (-15)/10 + ((-43)/2 - -1). Let l(p) = n*b(p) + s*u(p). Factor l(i).
2*(i + 1)*(3*i - 1)
Suppose 3*h - 12 = 0, -3*o = -17*h + 18*h - 10. Factor -18*k**2 - 4*k**o + 14 - 65 - 2*k**3 + 0*k**2 + 33 - 38*k.
-2*(k + 1)**2*(k + 9)
Factor -3/2 - 3/2*b**2 - 3*b.
-3*(b + 1)**2/2
Let d = 883429 - 883426. Factor -3/5*m**d - 72/5*m - 27/5*m**2 - 12.
-3*(m + 2)**2*(m + 5)/5
Let a = -55496 + 55540. Suppose -6*k**3 + a*k**2 - 152/3*k + 16 = 0. Calculate k.
2/3, 6
Let m = -14 + 16. Let d be (m/(-7))/(12/(-168)). Factor 13*j**d - 14*j**3 + 2*j**2 - 6*j**2 - 2*j**4 + 7*j**4.
2*j**2*(j - 1)*(9*j + 2)
Let z(x) = 9*x**3 - 299*x**2 - 637*x + 911. Let v(d) = 8*d**3 - 298*d**2 - 634*d + 912. Let u(y) = 4*v(y) - 3*z(y). Let u(l) = 0. What is l?
-3, 1, 61
Let m(d) be the first derivative of -d**6/420 - d**5/42 + d**4/14 - 57*d**2/2 - d - 263. Let p(g) be the second derivative of m(g). Factor p(j).
-2*j*(j - 1)*(j + 6)/7
Let r(p) be the third derivative of -70*p**2 - 1/480*p**6 + 1/6*p**3 + 0 + 1/24*p**4 - 1/240*p**5 + 0*p. Suppose r(k) = 0. Calculate k.
-2, -1, 2
Factor h**5 - 4*h**2 - 469*h + 4*h**4 + 465*h + 3*h**3 + 0*h**5.
h*(h - 1)*(h + 1)*(h + 2)**2
Let g(m) be the second derivative of m**4/8 + 75*m**3/4 - 729*m**2/2 + 7789*m. Factor g(z).
3*(z - 6)*(z + 81)/2
Let w be 9/(27/(-12)) + -5 + (-2436)/(-270). Let d(v) be the third derivative of 1/6*v**4 + 0 + 0*v**3 + w*v**5 + 27*v**2 + 0*v. Find a such that d(a) = 0.
-3, 0
Suppose -36*w - 96*w = 132 - 528. Let z(r) be the second derivative of 1/48*r**4 + 5/8*r**2 + 1/4*r**w + 0 + 27*r. Factor z(l).
(l + 1)*(l + 5)/4
Let a(y) = -y. Let u(f) = -f**2 + 4*f - 1. Let s(x) = 5*a(x) + u(x). Let v(j) = 65*j + 65*j - 167*j + 53*j - 5. Let l(o) = -4*s(o) - v(o). Factor l(p).
(2*p - 3)**2
Let w(f) be the first derivative of -f**6/6 - f**5/4 + 5*f**4 + 70*f**3/3 + 40*f**2 + 40*f - 55. Let k(x) be the first derivative of w(x). Factor k(m).
-5*(m - 4)*(m + 1)*(m + 2)**2
Let r(b) = -b - 5. Let y be r(-5). Let d = y - -7. Factor 4*q**2 + 8*q - 5*q - d*q.
4*q*(q - 1)
Let a(d) = d**3 - 7*d**2 + 11*d + 7. Let t be a(4). Let o(m) be the first derivative of -1/3*m**t + 5*m**2 - 25*m + 14. Let o(l) = 0. What is l?
5
Suppose -93*v + 28*v = -780. Let m(i) be the first derivative of -v*i**2 - 36*i - 1/4*i**4 + 11/3*i**3 + 4. Find q such that m(q) = 0.
-1, 6
Factor -17*j**2 + 35*j - 1/3*j**3 - 53/3.
-(j - 1)**2*(j + 53)/3
Let y(i) = i**2 - 174*i + 3217. Let q be y(21). Let b(f) be the first derivative of 7/2*f**2 + 1/20*f**q + 49/5*f - 13/15*f**3 + 30. Factor b(k).
(k - 7)**2*(k + 1)/5
Let 694/3*m - 1/6*m**2 - 240818/3 = 0. What is m?
694
Let w = 1317 + -1311. Let g(m) be the first derivative of -10/3*m**w - 8/5*m**5 + 8/3*m**3 + 0*m + 5*m**4 + 4 + 0*m**2. Suppose g(z) = 0. What is z?
-1, -2/5, 0, 1
Let v be (14 - 13056/900)/(52/(-102)). Let o = v + -21/25. Factor 6/13*w + 10/13*w**2 + o*w**3 + 0 - 2/13*w**4.
-2*w*(w - 3)*(w + 1)**2/13
Let a(j) be the second derivative of 1/210*j**6 - 19*j - 1/21*j**3 + 0*j**5 + 0*j**2 - 1/28*j**4 + 0. Determine r so that a(r) = 0.
-1, 0, 2
Factor -5337*l**3 - 3*l**4 + 165*l**2 + 5289*l**3 - 36*l - 78*l.
-3*l*(l - 2)*(l - 1)*(l + 19)
Let x(r) be the first derivative of -3/7*r**2 - 2/21*r**3 - 4/7*r + 9. Solve x(l) = 0 for l.
-2, -1
Solve -33/5*j**4 - 9408/5*j - 12348/5 - 1/5*j**5 - 2863/5*j**2 - 87*j**3 = 0 for j.
-7, -6
Let c(t) be the first derivative of 51/10*t**5 - 17/2*t**3 + 3/2*t**2 - 268 - 15/2*t**6 + 0*t + 21/2*t**4. Find l such that c(l) = 0.
-1, 0, 1/6, 2/5, 1
Let n(b) be the third derivative of -b**7/1050 + b**6/100 - b**5/100 - b**4/12 - 2*b**2 - 557. Suppose n(l) = 0. Calculate l.
-1, 0, 2, 5
Suppose -27/2 - 381/2*q**2 - 204*q = 0. What is q?
-1, -9/127
Suppose 3*i - d = -2*i + 15, 2*i + 4*d = 6. Factor -5*t**3 + 4*t**3 - 96*t**2 - 12 + 44*t - 11*t**i + 76*t**2.
-4*(t - 1)*(t + 3)*(3*t - 1)
Let h(z) be the third derivative of -1/8*z**5 + 0*z - 9*z**2 + 1/72*z**6 - 5/6*z**4 + 0 - 5/2*z**3. Let k(o) be the first derivative of h(o). Factor k(j).
5*(j - 4)*(j + 1)
Let o be 477/26 - ((-1364)/(-260) + -4 - (-483)/(-345)). Suppose -17/2 + 26*r + r**3 - o*r**2 = 0. What is r?
1/2, 1, 17
Let f(p) = -p**2. Let h(l) = -17*l**2 + 15*l - 1. Let u(c) = -3*f(c) + h(c). Let z be u(1). Let 16/5 - 12/5*x**2 + z*x - 4/5*x**3 = 0. What is x?
-2, 1
Let a(k) be the first derivative of -3*k**5/20 - 5*k**4/4 + 16*k**3 - 54*k**2 - 239*k + 129. Let d(u) be the first derivative of a(u). Factor d(m).
-3*(m - 2)**2*(m + 9)
Let p(o) be the first derivative of -3*o**5/5 - 30*o**4 - 498*o**3 - 3240*o**2 - 5103*o + 3901. Suppose p(t) = 0. What is t?
-21, -9, -1
Let b be 19 - ((-40)/(-50))/((-2)/(-5)). Let k(j) = -2*j**3 + 31*j**2 + 52*j - 17. Let h be k(b). Let 0*i + h - 1/5*i**2 = 0. Calculate i.
0
Let o(h) be the first derivative of 4*h**5/15 + 10*h**4/3 - 44*h**3/9 + 1095. Factor o(x).
4*x**2*(x - 1)*(x + 11)/3
Let j(h) = h**2 - 5*h + 56. Let t be j(7). Factor -w**4 - 75*w**2 + t*w**2 + 2*w**4 + 4*w**4.
5*w**2*(w - 1)*(w + 1)
Suppose -4*i + 2*i = -3*z + 8, 5*i - 5 = -5*z. Suppose -k = z*k - 3*h - 18, -3*k = -4*h - 22. Factor k*y + 2*y**2 - 7*y - 3*y**2.
-y*(y + 5)
Let q be ((-14)/(-28))/(5/60). Suppose -16*s = -q*s + s. Factor s + 2/15*t**2 - 2/15*t.
2*t*(t - 1)/15
Let d = 17 - 14. Suppose -m + 6*m + 4*s - 30 = 0, 7 = -4*m + d*s. Let -11*c + 0*c**3 + 3*c**m - 5*c**4 + 16*c - 5*c**3 + 2*c**2 = 0. What is c?
-1, 0, 1
Let s be (28/(-12) + 3)/((-4)/(-30)). Suppose -6*t = -19 - s. Determine y, given that 2*y - 13*y - 4 - t*y**2 + y = 0.
-2, -1/2
Suppose 0 = 4*b - 6*b - 22*b + 120. Let t(o) be the third derivative of -11/12*o**b + 8*o**2 - 125/6*o**3 - 175/24*o**4 + 0 + 0*o - 1/24*o**6. Solve t(a) = 0.
-5, -1
Find s such that -5112*s**3 + 10212*s**3 - 5104*s**3 + 4*s**5 = 0.
-1, 0, 1
Let s(w) be the first derivative of -w**4/10 - 168*w**3/5 - 497*w**2/5 + 300*w - 5016. Factor s(o).
-2*(o - 1)*(o + 3)*(o + 250)/5
Let t(m) be the third derivative of -m**6/120 - m**5/8 - 3*m**4/4 + 37*m**3/3 - 2*m**2 - 9*m. Let u(a) be the first derivative of t(a). Solve u(b) = 0 for b.
-3, -2
Let b(m) be the first derivative of -7*m**3 - 3/32*m**4 + 0*m + 0*m**2 + 2 - 1/80*m**5 - 1/1440*m**6. Let i(y) be the third derivative of b(y). Factor i(t).
-(t + 3)**2/4
Let a(y) = 4*y**3 + 28*y**2 + 16*y + 52. Suppose -4*b + 16 = 12. Let t(z) = -2*z + 1. Let s(v) = b*a(v) - 20*t(v). What is c in s(c) = 0?
-4, -2, -1
Suppose -5*k - x + 12 - 7 = 0, -15 = 3*x. Suppose 19*m = 15*m + 8. What is r in 71 + 2*r**k - 59 + 10*r + 0*r**m = 0?
-3, -2
Let l be 52/(-6)*9/(-6). Let x be (-468)/(-48) - (-20)/16. Let -p + 4 + l*p**2 - 4*p**3 - x*p - p**2 = 0. Calculate p.
1
Let u(w) be the second derivative of -w + 8*w**3 + 1/9*w**4 - 9 - 74/3*w**2. Suppose u(z) = 0. What is z?
-37, 1
Let x(n) = -5*n - 1. Let m(y) = -2*y**3 - 177*y**2 - 97*y + 86. Let o(a) = m(a) - 2*x(a). Factor o(j).
-(j + 1)*(j + 88)*(2*j - 1)
Let s(g) be the first derivative of -5*g**4/4 - 12*g**3 + 83*g**2/2 + 18*g - 3561. Factor s(t).
-(t - 2)*(t + 9)*(5*t + 1)
Let z(x) be the second derivative of -x**5/10 + 25*x**4/6 - 167*x**3/3 + 143*x**2 + 184*x + 3. Factor z(g).
-2*(g - 13)*(g - 11)*(g - 1)
Let j(k) = k**2 - 39*k + 297. Let b be j(29). Let z(i) be the first derivative of -5/6*i**2 - 2/3*i + b + 11/9*i**3 - 1/3*i**4. Suppose z(q) = 0. What is q?
-1/4, 1, 2
Let a = -5023 + 5023. Let t(i) be the first derivative of 1/30*i**4 + 4/15*i**2 + a*i - 20 + 2/9*i**3. Factor t(x).
2*x*(x + 1)*(x + 4)/15
Let k = -262697 + 262702. Find a such that 36/7*a**4 - 1168/7*a**2 + 2/7*a**k + 24/7*a**3 - 2304/7 + 3072/7*a = 0.
-12, 2
Let z = -155860 + 155864. Factor -2/5*d**3 + 0 + 0*d - 2/5*d**z + 4/5*d**2.
-2*d**2*(d - 1)*(d + 2)/5
Let t(s) be the third derivative of 0*s**3 + 0 + 64*s**2 + 11/96*s**6 + 1/168*s**7 + 