0. Determine s, given that g(s) = 0.
-298, -2
Factor -32*g**2 + 4/5*g**3 + 320 + 1436/5*g.
4*(g - 25)*(g - 16)*(g + 1)/5
Let c(r) be the first derivative of -16*r**2 - 2*r**4 + 16*r**3 + 2/3*r**6 - 124 - 12/5*r**5 + 0*r. Suppose c(k) = 0. What is k?
-2, 0, 1, 2
Let g(t) = 7*t**2 - 57*t + 726. Let a be (-24)/84 - 38/14. Let n(h) = 12*h**2 - 113*h + 1453. Let k(l) = a*n(l) + 5*g(l). Suppose k(i) = 0. What is i?
27
Suppose 46*g = 48*g - 20. Suppose -2*b + g = 3*b. Factor 6*m - 9*m**4 - 4*m**3 + 5*m - 7*m**5 + 14*m**b - 7*m**4 + 2 + 0*m**2.
-(m - 1)*(m + 1)**3*(7*m + 2)
Let n(r) be the third derivative of r**9/3024 + r**8/240 - r**7/840 - 7*r**6/360 + 17*r**3/6 + 131*r**2. Let o(p) be the first derivative of n(p). Factor o(h).
h**2*(h - 1)*(h + 1)*(h + 7)
Let x(l) = 40*l**2 + 163*l + 158. Let n(y) = 23*y**2 + 82*y + 79. Let w(j) = 7*n(j) - 4*x(j). Factor w(u).
(u - 79)*(u + 1)
Suppose 0 = -0*n + 4*n - 44. Suppose -5*q + n = g, -g - 4*g = 2*q - 32. Factor -t**5 - t**2 - 2*t + 9*t**3 - g*t**3 + 0*t**3 + t**4.
-t*(t - 2)*(t - 1)*(t + 1)**2
Let m(t) be the third derivative of 1/27*t**3 + 0 + 1/135*t**5 - 22*t - 1/36*t**4 + 1/270*t**6 + 1/1512*t**8 - 1/315*t**7 - 3*t**2. Let m(b) = 0. Calculate b.
-1, 1
Let m(l) be the third derivative of 0 + 1/8*l**3 + 2*l**2 + 3/160*l**5 - 5/64*l**4 - 1/560*l**7 + 1/320*l**6 - 90*l. Factor m(d).
-3*(d - 1)**3*(d + 2)/8
Let h be (-83612)/(-9) + 4/(-18) - 0. Suppose 0*o = 3*n - 2*o - 5587, 5*n + o = h. Determine t so that 1859*t + 33*t**3 + 12*t**4 - 9*t**2 - n*t = 0.
-3, 0, 1/4
Let d be 3/(-8) - 19/((-3116)/615). Determine t, given that 45/8*t + 3/8*t**3 + d + 21/8*t**2 = 0.
-3, -1
Let o = -4425 + 4441. Let t(z) be the second derivative of 0 - o*z - 3/2*z**2 + 1/2*z**3 - 1/16*z**4. Factor t(n).
-3*(n - 2)**2/4
Suppose -24 + 49/2*n - 1/2*n**2 = 0. Calculate n.
1, 48
Suppose -49 = 8*k + 31. Let h = k - -13. Solve 3 + 5*i**h - 6*i**2 - 11*i**3 + 3*i**5 + 3*i**4 - 44*i + 47*i = 0.
-1, 1
Let j(p) be the first derivative of -p**6/6 - 4*p**5/5 + 12*p**4 - 110*p**3/3 + 97*p**2/2 - 30*p - 14825. Factor j(r).
-(r - 3)*(r - 1)**3*(r + 10)
Let z(c) be the second derivative of -28/3*c**3 + 14/5*c**5 + 98*c**2 - 12*c - 16*c**4 - 2/15*c**6 + 0. Factor z(f).
-4*(f - 7)**2*(f - 1)*(f + 1)
Suppose 7*s - 20 = 17*s. Let k(c) = -29*c + 1. Let z be k(s). Solve -5 - 62*i**2 + 10*i - z*i**2 + 116*i**2 = 0.
1
Let x = 135398 + -541587/4. Let n = 20 - 79/4. Factor 1/2*y**2 - x*y**3 + 0 + 0*y - n*y**5 + y**4.
-y**2*(y - 2)*(y - 1)**2/4
Let g(j) = 2*j**2 - 8*j + 6. Suppose -3*u = -0*u - 18. Let v be g(u). Factor -8*t + 2*t - 5*t**2 + 11*t + v.
-5*(t - 3)*(t + 2)
Let d(u) = -13*u - 88. Let o be d(-7). Factor -3*y**2 + 48/5*y + 1/5*y**o + 64/5.
(y - 8)**2*(y + 1)/5
Suppose 12 = -c - 4*c + t, -5*c - 4*t - 2 = 0. Let w be (165/30)/((-1)/c). Factor -w*a**2 - 10*a**2 - 15*a**2 + 35*a**2 - 4 - 5*a.
-(a + 1)*(a + 4)
Let o be 14*21/2793 + (-279)/(-57). Let c(a) be the first derivative of 27/5*a**o + 75/4*a**4 + 9/2*a**2 + 21*a**3 - 6*a - 36. Let c(z) = 0. Calculate z.
-1, 2/9
Let b = -157726 - -157728. Factor -1568/5 - 2/5*m**b + 112/5*m.
-2*(m - 28)**2/5
Suppose 5*x - b = 11, -5*x - 2*b + 7 = -4*b. Let k**3 - x*k**3 + 7*k**2 - 6*k**2 + 7*k**2 = 0. What is k?
0, 4
Let k(x) be the third derivative of 5/6*x**4 + 0*x + 0 - 27*x**2 + 1/15*x**5 - 4*x**3. Factor k(t).
4*(t - 1)*(t + 6)
Determine b, given that 20*b**2 - 8*b + 8*b**5 - 16 + 12*b**5 - 8*b**4 - 18*b**5 + 2*b**3 = 0.
-1, 2
Suppose 0 = 61*m - 57*m - 3*u - 10, -3*m + 4 = -4*u. Let i(l) be the first derivative of -m + 1/3*l**3 + 0*l**2 + 0*l. Solve i(q) = 0 for q.
0
Let t be ((5016/(-220))/(-19))/2. What is n in 12/5*n**2 + t*n**3 + 0 + 9/5*n = 0?
-3, -1, 0
Let s(n) be the third derivative of 9800/3*n**4 + 26/15*n**6 + 0*n - 42875/3*n**3 - 42*n**2 + 0 + 1/105*n**7 + 119*n**5. Find k, given that s(k) = 0.
-35, 1
Let n be 39 - (-25 + (-5700)/(-90)). Factor 4/3*b + n*b**2 + 0.
2*b*(b + 2)/3
Let c(d) be the second derivative of d**6/1800 - d**4/30 + d**3/3 + 7*d**2 - 2*d + 3. Let u(n) be the second derivative of c(n). Find z, given that u(z) = 0.
-2, 2
Let a be 36/(-30)*(-25)/10. Suppose -i**2 - 47*i**3 + i**4 + 45*i**a + i**2 = 0. What is i?
0, 2
Let c(p) be the first derivative of -1/20*p**4 - 52 + 10*p - 9/2*p**2 + 4/5*p**3. Factor c(d).
-(d - 5)**2*(d - 2)/5
Let a(w) be the first derivative of w**4/22 - 36*w**2/11 + 1568. Find j such that a(j) = 0.
-6, 0, 6
Let f(l) be the third derivative of 0*l + 22*l**2 - 1/56*l**6 - 1/784*l**8 + 2/245*l**7 + 0*l**4 + 0*l**3 + 1/70*l**5 + 0. Let f(j) = 0. Calculate j.
0, 1, 2
Suppose -14 = 4*t + 2*v - 28, -4*t = -5*v + 7. Solve 2*u**2 - 5 + 3*u**4 + 17 + 9*u**3 - 5*u - 13*u**t - 4*u**2 - 4*u = 0 for u.
-4, -1, 1
Let t(v) = -6*v**4 + 14*v**3 - 64*v**2 + 149*v - 108. Let s(b) = -b**4 + b**2 + b. Let q(z) = 15*s(z) - 3*t(z). Find l, given that q(l) = 0.
2, 3, 6
Let g(x) = x**2 + x - 4. Let y(l) = -12*l**2 - 96*l + 140. Let m(r) = -16*g(r) - y(r). Determine z so that m(z) = 0.
1, 19
Factor 1/10*w**3 + 544/5*w - 578/5 + 67/10*w**2.
(w - 1)*(w + 34)**2/10
Let l(h) be the first derivative of h**9/1512 - h**8/840 - h**7/420 + h**6/180 - 31*h**3 - 96. Let o(c) be the third derivative of l(c). Factor o(b).
2*b**2*(b - 1)**2*(b + 1)
Let v be (4/(-14))/(((-22)/55)/(5957/230)). Find w, given that -8 + 6*w**3 + 21*w - v*w**2 - 1/2*w**4 = 0.
1, 2, 8
Suppose -11*y - 51 - 345 = 0. Let p = y + 38. Determine t so that -8*t + 6*t**3 + 0*t**5 - p*t**3 + 11*t**5 + 12*t**2 - 7*t**5 - 12*t**4 = 0.
-1, 0, 1, 2
Let i(u) = 3*u**3 - 3*u**2 - 6*u. Let x be ((-15)/(-6))/(2/20). Let w = x + -32. Let c(f) = 3*f**3 - 4*f**2 - 6*f. Let v(o) = w*i(o) + 6*c(o). Factor v(p).
-3*p*(p - 1)*(p + 2)
Let x(v) = -8*v**4 - 37*v**3 + 639*v**2 + 1342*v + 699. Let i(n) = n**4 + 2*n**3 + n - 3. Let c(k) = -5*i(k) - x(k). Factor c(b).
3*(b - 12)*(b + 1)**2*(b + 19)
Let l = 21 + -159. Let b be l/(-14) - 1/(-7). Solve -187*i + 4 + b*i**2 + 187*i - 2*i**4 - 12 = 0 for i.
-2, -1, 1, 2
Let h be 5/(3 - 43/14). Let k = 0 - h. Factor 0 + 0 - 5 + 60*g**2 + 10*g + k*g**3 + 25*g**4 + 0.
5*(g + 1)**3*(5*g - 1)
Factor -458*h**4 + 240*h**4 - 9*h - 57*h**2 - 99*h**3 + 191*h**4.
-3*h*(h + 3)*(3*h + 1)**2
Let v be (-41 - 8*8/(-2)) + 46/4 + -2. Factor g**2 + 0 - v*g**3 + 0*g.
-g**2*(g - 2)/2
Suppose -4*h + 14 = -11*t + 6*t, t - 20 = -3*h. Factor 7*b**3 - h*b**4 + 9*b**3 + 8*b**4.
2*b**3*(b + 8)
Let u(q) = -4*q**3 + 12*q**2 + 15*q - 28. Let x(s) = -3*s**3 + 11*s**2 + 14*s - 26. Let d(n) = 2*u(n) - 3*x(n). Let o be d(10). Factor -10 - 2/5*k**o - 4*k.
-2*(k + 5)**2/5
Let o(a) be the second derivative of a**4/108 - 1187*a**3/54 + 593*a**2/9 + 5*a - 858. Factor o(l).
(l - 1186)*(l - 1)/9
Let c(f) = 296*f + 17180. Let w be c(-58). Let w*p**2 + 16/11 - 94/11*p + 18/11*p**3 = 0. What is p?
-8, 1/3
Factor 10*d**3 + 68*d**4 + 3*d**5 + 2*d**3 - 126*d**2 - 10*d**4 + 9*d - 28*d**4 + 72*d.
3*d*(d - 1)**2*(d + 3)*(d + 9)
Suppose -6*q - 352 + 100 = 0. Let n = 48 + q. Suppose -5*f**3 - 6*f**4 - n*f**3 + f**4 - 5*f**2 + f**3 = 0. What is f?
-1, 0
Suppose 3/5*s**4 + 5370732/5 + 612831/5*s**2 + 3604572/5*s + 2694/5*s**3 = 0. Calculate s.
-446, -3
Suppose -322*i + 1558 + 6986 = -55*i. Let x(t) be the first derivative of 48*t**2 + 7/4*t**4 - i*t - 38 + 18*t**3. Factor x(r).
(r + 4)**2*(7*r - 2)
Let j(n) = 90*n**3 - 156*n**2 + 328*n. Let s(h) = -56*h**3 + 104*h**2 - 219*h. Let r(k) = -5*j(k) - 8*s(k). What is d in r(d) = 0?
-28, 0, 2
Let q(z) = 8*z**2 + 6*z - 55. Let b be q(12). Let g = b - 8181/7. Factor 1/7*x - g + 1/7*x**2.
(x - 1)*(x + 2)/7
Let h(q) be the second derivative of q**4/84 - 173*q**3/42 - 87*q**2/7 + q + 296. Factor h(k).
(k - 174)*(k + 1)/7
Let 42*f**2 + 473*f**3 + 10*f**2 + 240 - 305*f - 468*f**3 + 8*f**2 = 0. Calculate f.
-16, 1, 3
Let a(k) = -9*k + 34. Let c(v) = 17*v - 67. Let x(z) = 5*a(z) + 3*c(z). Let b be x(14). Factor -b*d**2 + 26*d**2 - 3*d + 26*d**2.
-d*(d + 3)
Let n = -119 + 121. Factor -79 + 111 + 5*q**n - 52 + 15*q.
5*(q - 1)*(q + 4)
Let 18 + 1/2*t**4 + 63/2*t**2 + 85/2*t + 15/2*t**3 = 0. Calculate t.
-9, -4, -1
Suppose 238 = 2*b + 2*o - 1224, 2*b - 5*o = 1476. Factor -b*g**2 + 703*g**2 + 0*g**3 + 5*g**5 - 5*g**3 + 30*g**4.
5*g**2*(g - 1)*(g + 1)*(g + 6)
Suppose 41*i = 4*i + 9*i. Factor -4/5*q**3 + 8/5*q**2 + i - 4/5*q