
Let m be -6 - -3*1841/147. Let u = m + -2203/70. Factor -u*w**2 + 0 + 1/10*w.
-w*(w - 1)/10
Let m(s) be the second derivative of -s**5/45 + s**4/6 + 12*s**2 + 93*s. Let c(n) be the first derivative of m(n). Suppose c(j) = 0. What is j?
0, 3
Let l(r) = 11*r**4 + 68*r**3 + 23*r**2 - 21*r. Let a(h) = h**4 + 6*h**3 + h**2 + h. Let f(v) = 9*a(v) - l(v). Find b, given that f(b) = 0.
-5, -3, 0, 1
Let k = -2146488 + 6439465/3. Let h = -140/3 - -47. Find y, given that h*y - k*y**2 + 2/3 = 0.
-1, 2
Let z(r) be the first derivative of -3/4*r**4 - 27/5*r**3 + 9/25*r**5 - 48/5*r**2 + 1/10*r**6 - 36/5*r + 17. Determine j so that z(j) = 0.
-2, -1, 3
Let t(d) = -5*d**3 + 45*d**2 - 108*d + 18. Let m(s) = -9*s**3 + 91*s**2 - 222*s + 30. Let n(q) = -6*m(q) + 10*t(q). Find f, given that n(f) = 0.
0, 3, 21
Let s(v) be the third derivative of -v**8/112 + 12*v**7/35 - 33*v**6/20 + 16*v**5/5 - 21*v**4/8 - 95*v**2 + 2*v - 1. Suppose s(k) = 0. What is k?
0, 1, 21
Let o(s) = -4*s**4 + 6*s**3 - 193*s**2 - 882*s + 15. Let r(x) = -3*x**4 + 4*x**3 - 195*x**2 - 882*x + 12. Let p(u) = 4*o(u) - 5*r(u). Factor p(l).
-l*(l - 18)*(l + 7)**2
Let d = -12911/27 - -12983/27. Determine w, given that -2/3*w**4 - 2*w**3 + d*w**2 + 0*w + 0 = 0.
-4, 0, 1
Factor 327*n + 3/2*n**2 + 651/2.
3*(n + 1)*(n + 217)/2
Let n(h) be the second derivative of -4 + 3/2*h**2 + 5/12*h**4 + 1/20*h**5 - 7*h + 7/6*h**3. Factor n(j).
(j + 1)**2*(j + 3)
Find n such that 0 - 13646*n**2 + 0 + 511*n + 13647*n**2 = 0.
-511, 0
Let q(h) = 19*h**3 - 341*h**2 - 703*h + 11. Let o(v) = -5*v**3 + 85*v**2 + 175*v - 3. Let c(k) = 11*o(k) + 3*q(k). Factor c(t).
2*t*(t - 46)*(t + 2)
Determine w, given that 2/9*w**5 + 4*w**3 + 20/9*w**4 - 80/9*w**2 - 38/9*w + 20/3 = 0.
-6, -5, -1, 1
Let u(o) be the third derivative of o**6/40 - 579*o**5/20 + 111747*o**4/8 - 7189057*o**3/2 - 948*o**2. Find j, given that u(j) = 0.
193
Let y = -1890 - -1895. Suppose 3 = -2*c + 3*s, -31 = -y*c - 4*s - 4. Determine q, given that -792/13*q**2 + 3456/13 - 2/13*q**4 - 2592/13*q - 70/13*q**c = 0.
-12, 1
Let u = -645/154 - -16777/770. Factor -28/5*j**2 + u*j - 16 + 2/5*j**3.
2*(j - 10)*(j - 2)**2/5
Let h be (-85785)/(-131670) - (-2 - (-22)/12). Factor -104/11*a**2 + h*a**4 + 448/11*a + 784/11 - 48/11*a**3.
(a + 2)**2*(3*a - 14)**2/11
Factor -1224 + 3084*m - 1478*m - 1468*m - 3*m**2.
-3*(m - 34)*(m - 12)
Factor 12/13 + 206/13*k + 100/13*k**2.
2*(k + 2)*(50*k + 3)/13
Suppose -3*o = 5*q + 140, -o - 105 = -3*q + 7*q. Let l = -21 - q. Solve 10*j**3 - 5*j**4 + 20*j**2 - 64*j - l + 54*j - 11 = 0.
-1, 1, 3
Let f(p) be the first derivative of 2*p**3/27 + 104*p**2/3 + 5408*p + 508. Factor f(n).
2*(n + 156)**2/9
Let c(f) be the third derivative of f**5/140 + 24*f**4/7 + 81*f**3/2 + 2*f**2 + 362*f + 4. Factor c(b).
3*(b + 3)*(b + 189)/7
Let q be 15 + 6*(-1 + (-9 - -8)). Find m such that -13/6*m**2 - m**q - 1/6*m**4 - 2/3 - 2*m = 0.
-2, -1
Determine c, given that -11*c**4 - 5*c**4 - 12*c**4 - 60*c**3 + 178*c**2 + 101*c**2 + 168 + 31*c**4 - 390*c = 0.
1, 4, 14
Let p(x) be the third derivative of x**7/210 + 11*x**6/120 - 2*x**5 + 9*x**4/2 - 2*x**2 + 37*x - 18. Let p(w) = 0. Calculate w.
-18, 0, 1, 6
Let o(n) be the third derivative of 0 - 1/6*n**4 + 1/105*n**7 + 0*n**3 - 1/40*n**6 - 7*n - 2/15*n**5 - 5*n**2 + 1/336*n**8. Find z such that o(z) = 0.
-2, -1, 0, 2
Let c = -2 + 4. Let m be ((-6177)/(-12))/((-6)/(-24)). Solve -2065 + c*a - a**2 + m + 5*a = 0 for a.
1, 6
Suppose -8*p + 10*p = 2*r, 1423*r - 1420*r = 0. Let 0*y - 3/4*y**3 - y**2 + 1/4*y**4 + p = 0. What is y?
-1, 0, 4
Let y(r) = 4*r**3 - 36*r**2 - 176*r - 192. Let d(j) = -4*j**3 + 35*j**2 + 176*j + 192. Let x(u) = 4*d(u) + 3*y(u). Solve x(i) = 0.
-2, 12
Let t(a) be the third derivative of a**6/540 - a**5/36 - 11*a**3/6 - 11*a**2. Let z(d) be the first derivative of t(d). Factor z(w).
2*w*(w - 5)/3
Suppose 112*c - 37 - 428 = -17. Let p(f) be the first derivative of -1/22*f**c + 16/11*f + 2/33*f**3 + 10/11*f**2 - 40. Solve p(m) = 0 for m.
-2, -1, 4
Let a = 3559 + -3557. Let f(y) be the first derivative of 1/10*y + 2/15*y**3 + 14 + 1/5*y**a. Factor f(k).
(2*k + 1)**2/10
Let y(x) be the second derivative of x**7/147 + 16*x**6/105 + 41*x**5/70 + 13*x**4/21 - 3*x + 117. Let y(p) = 0. What is p?
-13, -2, -1, 0
Let b(y) be the second derivative of 19*y**5/4 - 30*y**4 + 50*y**3 + 40*y**2 + 1154*y. Factor b(q).
5*(q - 2)**2*(19*q + 4)
Let u(i) = -13*i**5 - 619*i**4 - 796*i**3 + 4*i + 8. Let c(a) = 38*a**5 + 1856*a**4 + 2390*a**3 - 11*a - 22. Let g(m) = -4*c(m) - 11*u(m). Factor g(w).
-3*w**3*(w + 67)*(3*w + 4)
Let k(j) = -51*j**2 - 411*j + 420. Let c(m) = -145*m**2 - 1233*m + 1259. Let r(f) = -6*c(f) + 17*k(f). Suppose r(t) = 0. What is t?
-138, 1
Let i be (28/((-2352)/36))/(4/(-266)) - (-1 - -10). Determine b so that 15/2*b**2 + 3*b**5 + 27/2*b**4 - 9/2*b - 3 + i*b**3 = 0.
-2, -1, 1/2
Solve -13/2 + 1/2*k**2 + 6*k = 0 for k.
-13, 1
Let b(r) be the first derivative of -r**4/26 + 40*r**3/39 - 133*r**2/13 + 588*r/13 + 871. Factor b(a).
-2*(a - 7)**2*(a - 6)/13
Let -10*a**5 + 45*a**2 + 17305*a**4 + 17278*a**4 - 34628*a**4 - 25*a + 35*a**3 = 0. Calculate a.
-5, -1, 0, 1/2, 1
Suppose -1746*v + 528 = -1749*v. Let b be 19/44 - (-44)/v. Factor 2/11*a**2 - b*a**3 + 2/11*a - 2/11.
-2*(a - 1)**2*(a + 1)/11
Let q be -1 - (-1 + 0)*4. Let w be (324/(-60) + 6)*5. Factor -3*a**2 + 3 - a + 6*a - w*a**q + 7*a + 9.
-3*(a - 2)*(a + 1)*(a + 2)
Let v(h) = h**2 - 4*h + 6. Let z = -31 + 34. Let r be v(z). Factor 4 + 12*j**2 + 7*j**3 + r*j**3 + 2 - 7*j**3 + 15*j.
3*(j + 1)**2*(j + 2)
Let o be (960/112)/10*(3 - 603/243). Solve o*a**3 + 8/9*a**2 + 0 - 4/3*a = 0 for a.
-3, 0, 1
Let j(k) = -2*k + 17. Let f be j(6). Suppose 2*w = -7*r + 3*r, -f*r = -5*w. Factor 1/5*m**2 + 2/5*m + w.
m*(m + 2)/5
Let z = -354 - -452. Suppose -100*b**4 - 14*b**3 - 15*b**2 + z*b**4 - 18*b - 15*b**2 = 0. Calculate b.
-3, -1, 0
Let p = -1014034 - -5070954/5. Factor -4/5*r**4 + 0 - p*r - 896/5*r**2 - 116/5*r**3.
-4*r*(r + 1)*(r + 14)**2/5
Let t(x) be the third derivative of 0*x + 89*x**2 - 3/4*x**3 + 11/96*x**4 - 1/240*x**5 + 0. Factor t(m).
-(m - 9)*(m - 2)/4
Let f be (104/(-10) - 12)/(2/(-10)). Factor f*b**2 - 18*b**4 + 38*b**2 + 96*b + 42*b**2 + 78*b**3 + 27*b**4.
3*b*(b + 4)**2*(3*b + 2)
Let h = 1336/16075 + -2/643. Let b(v) be the first derivative of 27 + 1/5*v**4 - 2/5*v**2 + 0*v**3 - h*v**5 + 2/5*v. Factor b(r).
-2*(r - 1)**3*(r + 1)/5
Let f(g) = -84*g**2 + 15*g. Let u(z) be the second derivative of 7*z**4/4 - 2*z**3/3 - 23*z + 1. Let t(d) = -6*f(d) - 22*u(d). Factor t(k).
2*k*(21*k - 1)
Let p = 413 + -431. Let d be (p/(-35))/(351/585). Solve 15/7*v + 6/7 + d*v**2 = 0 for v.
-2, -1/2
Suppose -42 - 178/5*y + 34/5*y**2 + 2/5*y**3 = 0. Calculate y.
-21, -1, 5
Let q be (-136)/(-34)*((-15)/(-20) + 0). Let r(c) be the first derivative of 2/3*c**2 + 0*c - 2/3*c**q + 25. Factor r(l).
-2*l*(3*l - 2)/3
Let o(c) = c**2 + 6*c + 2. Let q be o(-6). Suppose -q*v + 20 = 8*v. Factor 4*x**3 - 9*x**3 - 10*x**v + 2*x - 6*x - x.
-5*x*(x + 1)**2
Let t(b) be the first derivative of -12/11*b**2 - 5/33*b**3 - 43 - 16/11*b. Factor t(r).
-(r + 4)*(5*r + 4)/11
Let p(v) be the first derivative of 119 - 4/5*v**3 - 1/15*v**6 - 13/10*v**4 - 16/25*v**5 + 0*v + 0*v**2. Factor p(u).
-2*u**2*(u + 1)**2*(u + 6)/5
Let h(g) be the second derivative of 3*g**5/70 + 3*g**4/28 - g**3/7 + 23*g + 29. Factor h(f).
3*f*(f + 2)*(2*f - 1)/7
Factor -1/6*z**3 + 16/3*z**2 + 179/6*z + 37.
-(z - 37)*(z + 2)*(z + 3)/6
Let c(w) = 9*w**2 + 16 + 19*w - 17*w**2 + 4*w. Let f(i) = 2*i**2 - i. Let m(t) = -c(t) - 5*f(t). Determine z, given that m(z) = 0.
-8, -1
Let h(z) be the second derivative of -5*z**7/42 - 7*z**6/3 - 63*z**5/4 - 265*z**4/6 - 140*z**3/3 + 1183*z. Let h(i) = 0. What is i?
-7, -4, -2, -1, 0
Let s(j) = 17*j**2 - 816*j - 1676. Let g(y) = 65*y**2 - 3265*y - 6700. Let c(h) = 4*g(h) - 15*s(h). What is o in c(o) = 0?
-2, 166
Let g(v) = -v**3 - 6*v**2 - 16*v - 52. Let w be g(-5). Solve 40*r**3 - 26 - 64 + 2*r**4 + 0*r**w + 100*r**2 + 18 - 40*r - 30 = 0 for r.
-17, -3, -1, 1
Let d = 38693/63 + -4211/9. Factor 2/7*a**3 + 48/7*a**2 + d + 384/7*a.
2*(a + 8)**3/7
Suppose -1750/3 + 50/3*h**2 - 1/3*h**5 - 1975/3*h - 28/3*h**4 + 248/3*h**3 = 0. What is h?
-35, -2, -1, 5
Let h(z) = 18*z**3 + 3746*z**2 + 422*z + 1253. Let