**2
Suppose 49271*o**2 - 132612*o + 9360*o**2 + 6902*o**2 + 378*o**3 + 66564 + 136*o**3 - o**4 + 2*o**4 = 0. Calculate o.
-258, 1
Let c(o) be the third derivative of o**6/1140 + o**5/114 - 13*o**4/228 + 7*o**3/57 + 3580*o**2. Factor c(s).
2*(s - 1)**2*(s + 7)/19
Determine w so that 6*w**2 - 412 - 1001*w + 587*w + 3*w**2 - 19*w**2 + 8*w**2 = 0.
-206, -1
Suppose 0 = x + 3*v + 1, 554*v + 1 = -2*x + 549*v. Factor 26/3*i**x - 2/3*i**4 + 20/3*i + 4/3*i**3 + 0.
-2*i*(i - 5)*(i + 1)*(i + 2)/3
Let f(v) = v + 10. Let x = 392 - 399. Let p be f(x). Factor 0 + 1/4*w + 3/4*w**2 + 1/4*w**4 + 3/4*w**p.
w*(w + 1)**3/4
Let g(t) be the third derivative of 0 + 0*t**3 - 1/150*t**5 - 1/60*t**4 + 0*t - 21*t**2. Factor g(a).
-2*a*(a + 1)/5
Let h(l) = -21*l**2 + 3273*l. Let g(t) = 48*t**2 - 6546*t. Let k(u) = -3*g(u) - 7*h(u). Factor k(p).
3*p*(p - 1091)
Determine q so that 520200 - 806*q**2 - 2040*q + 1620*q**2 - 812*q**2 = 0.
510
Let q(z) = -31*z**4 - 615*z**3 + 782*z**2 - 148*z + 68. Let x(u) = 309*u**4 + 6150*u**3 - 7821*u**2 + 1479*u - 663. Let k(t) = 39*q(t) + 4*x(t). Factor k(g).
3*g*(g - 1)*(g + 24)*(9*g - 2)
Let v(p) be the third derivative of -p**2 + 11/8*p**4 + 0*p**3 + 0*p + 52 - 1/20*p**5. Find l such that v(l) = 0.
0, 11
Let u(k) be the first derivative of -2*k**3/27 + 28*k**2/9 - 2019. Factor u(b).
-2*b*(b - 28)/9
Factor -90*h**4 - 315*h - 23153 - 480*h**2 - 103*h**3 + 23075 + 5*h**5 - 8*h**5 - 227*h**3.
-3*(h + 1)**4*(h + 26)
Let h(f) be the third derivative of -f**6/180 - 17*f**5/10 - 867*f**4/4 + 46*f**3/3 + 4*f**2 + 12*f. Let v(t) be the first derivative of h(t). Factor v(q).
-2*(q + 51)**2
Suppose -304/3*j**2 - 33*j**3 + 1/3*j**4 - 68*j + 0 = 0. Calculate j.
-2, -1, 0, 102
Let y(j) be the first derivative of -3*j**6/23 + 14*j**5/23 - j**4/2 - 26*j**3/23 + 32*j**2/23 + 8*j/23 - 1184. Solve y(q) = 0 for q.
-1, -1/9, 1, 2
Let n(r) be the first derivative of 3*r**4/16 - 18*r**3 + 198*r**2 - 768*r + 5738. Factor n(l).
3*(l - 64)*(l - 4)**2/4
Let f(x) = 2*x - 38. Let a be f(20). Suppose 0 = -3*h - a + 20. Suppose -10*g**2 + h*g**2 - 2*g + 6*g**2 = 0. What is g?
0, 1
Let d be (44/12 - 3) + (-86)/(-6). Factor -d*x**3 - 17*x**2 + 22*x**2 + 7*x**2 + 3*x**4.
3*x**2*(x - 4)*(x - 1)
Let c(k) be the first derivative of 2*k**3/9 + 1043*k**2/3 - 696*k - 1813. Find u such that c(u) = 0.
-1044, 1
Factor 28619 - 18730*x - 740*x**2 + 77413 + 16*x**3 - 20*x**3 - 14358*x.
-4*(x - 3)*(x + 94)**2
What is f in -231 + 66*f**4 + 5*f**5 + 125*f - 76*f**4 + 68 + 260*f**2 - 130*f**3 - 87 = 0?
-5, -1, 1, 2, 5
Suppose 5*a + 106 = -3*u + 2*u, -584 = 5*u - 2*a. Let g = u - -119. Solve 5/6*m**g - 5/6*m - 7/6*m**4 - 1/3 + 3/2*m**2 = 0 for m.
-1, -2/7, 1
Let y = 438096 - 438094. Determine k so that -1/5*k**y - k + 0 = 0.
-5, 0
Let o be ((-1)/(-8) - (-153)/(-72)) + -15. Let b(d) = -d**2 + 3. Let a(h) = -3*h**2 + 10. Let l(k) = o*b(k) + 6*a(k). Let l(v) = 0. Calculate v.
-3, 3
Let k be ((-10560)/(-225))/22 - (-6)/(-45). Solve -2*a + 15/4 + 1/4*a**k = 0.
3, 5
Let t = 52663/28104 + 4/3513. Let o(a) be the third derivative of 0*a + 7/12*a**5 + 29*a**2 + t*a**4 + 5/3*a**3 + 0. Factor o(y).
5*(y + 1)*(7*y + 2)
Suppose 2146 = -3*q + 2206. Let w be 2 - 4 - (-120)/q. Factor -1/4*z**5 + 0*z - 3/4*z**w + 0 - 1/2*z**3 + 0*z**2.
-z**3*(z + 1)*(z + 2)/4
Let g(h) be the second derivative of -h**4/16 - 29*h**3/8 + 36*h**2 - 3287*h. Factor g(a).
-3*(a - 3)*(a + 32)/4
Let g be (-3)/((-4469)/82 + 53). Find k such that 2/7*k**3 - 12/7*k**g + 0 + 0*k + 2/7*k**5 + 8/7*k**4 = 0.
-3, -2, 0, 1
Let o be (33/(-22))/((-25)/((-200)/(-6))). What is w in o*w**2 + 6/5*w + 2/5*w**3 - 18/5 = 0?
-3, 1
Let o = 1/5231 + 15691/10462. Let v be -3*(-1)/4 + 0. Factor 0*n**2 + 0 - o*n**3 + v*n + 3/4*n**5 + 0*n**4.
3*n*(n - 1)**2*(n + 1)**2/4
Let k(c) be the third derivative of -60*c**2 + 0 - 3*c - 1/1575*c**7 - 1/180*c**6 - 7/450*c**5 + 0*c**3 - 1/60*c**4. Find v, given that k(v) = 0.
-3, -1, 0
Let k(x) be the second derivative of x**8/3920 - x**6/210 - 49*x**3/6 - 39*x. Let n(i) be the second derivative of k(i). Suppose n(s) = 0. Calculate s.
-2, 0, 2
Let 20/7*f**4 - 1116/7*f**2 - 856/7*f - 432/7*f**3 - 192/7 = 0. Calculate f.
-1, -2/5, 24
Suppose 1076 = -3*g + 2*h + 1088, -2*h - 12 = -4*g. Factor g*s + 0 + 0*s**2 - 3/5*s**3.
-3*s**3/5
Suppose -25 - 30 = -5*z. Let o(m) = -2*m**3 + z*m**2 - m**3 - 42*m - m**3 + 22 + 19*m**2. Let a(c) = -c**2 - c - 1. Let y(w) = 2*a(w) + o(w). Factor y(g).
-4*(g - 5)*(g - 1)**2
Suppose 0 = -30*m + 38*m - 32. Factor 97 - 802*o + m*o**2 + 730*o + 227.
4*(o - 9)**2
Suppose 5*y = 34 + 11. Suppose y*m = 344 + 187. Factor 0*t**3 + 6*t**3 + 56*t - m*t - 3*t**5.
-3*t*(t - 1)**2*(t + 1)**2
Factor 11*a**2 - 14/3*a**3 + 4/3*a - 44/3 + 1/3*a**4.
(a - 11)*(a - 2)**2*(a + 1)/3
Let h(z) be the second derivative of -1/6*z**4 - 39 - 2916*z**2 - 36*z**3 + 3*z. Determine y so that h(y) = 0.
-54
Let u(o) = -7*o**3 - 166*o**2 - 425*o + 646. Let z(v) = 64*v**3 + 1496*v**2 + 3824*v - 5832. Let r(x) = -28*u(x) - 3*z(x). Determine h, given that r(h) = 0.
-37, -4, 1
Let n = -3383/27 + 3407/27. Suppose 4/9 + n*j**2 + 2*j = 0. What is j?
-2, -1/4
Let 4*j**2 + 78*j + 85*j - 4*j**4 - 16*j**3 - 147*j = 0. Calculate j.
-4, -1, 0, 1
Let o(r) = -r**3 - 9*r**2 + 11*r + 10. Let c be o(-10). Let x be ((-888)/648 + 1)/(25/(-15)). Factor c + 2/9*p - x*p**2.
-2*p*(p - 1)/9
Let o(h) be the second derivative of h**7/504 - h**6/64 + h**5/48 - h**4/2 - h - 20. Let z(n) be the third derivative of o(n). Find q, given that z(q) = 0.
1/4, 2
Suppose -12*k = -10*k, 5*z = 2*k. Let u(x) be the third derivative of 16*x**2 - 1/540*x**6 + z + 0*x**3 + 0*x - 1/54*x**5 - 1/36*x**4 + 1/945*x**7. Factor u(s).
2*s*(s - 3)*(s + 1)**2/9
Let a(x) be the first derivative of -x**5/240 - x**4/4 + 57*x**2/2 + 164. Let n(b) be the second derivative of a(b). Factor n(v).
-v*(v + 24)/4
Let l = -22888/220185 + 2/8155. Let o = l + 10/27. Solve -2/15 - o*i - 2/15*i**2 = 0 for i.
-1
Let a(j) be the first derivative of j**4/8 - 17*j**3/12 + 31*j**2/8 + 5*j + 100. Factor a(n).
(n - 5)*(n - 4)*(2*n + 1)/4
Let k(z) be the second derivative of z**6/360 - 7*z**5/45 + z**4/2 - 19*z**3/2 - z**2 - 31*z. Let t(l) be the second derivative of k(l). Factor t(s).
(s - 18)*(3*s - 2)/3
Let p be (4*1/(-8))/(23/(-1380)). Let f(m) be the first derivative of p + 196/3*m + 4/9*m**3 + 28/3*m**2. Find x such that f(x) = 0.
-7
Let -2/5*i**4 - 26/5*i**3 - 52/5 + 6/5*i**2 + 74/5*i = 0. What is i?
-13, -2, 1
Let b(m) be the first derivative of 121 - 64/9*m**2 - 272/9*m + 4/27*m**3. Find v, given that b(v) = 0.
-2, 34
Suppose -f + 38 = g + 2, 2*f + 3*g - 69 = 0. Suppose -144*j + 131*j = -f. Factor -1/5*p**j + 0*p**2 - 2/5 + 3/5*p.
-(p - 1)**2*(p + 2)/5
Factor -73*p**2 - 33123/5*p + 33489/5 - 1/5*p**3.
-(p - 1)*(p + 183)**2/5
Let c = -325 - -337. Let s be c/153*(-81)/(-2). Factor 44/17*z**3 - 76/17*z**2 + s*z - 6/17*z**4 - 14/17 - 2/17*z**5.
-2*(z - 1)**4*(z + 7)/17
Let r(a) be the first derivative of a**5 - 201 + 15/4*a**4 - 40*a - 30*a**2 - 10/3*a**3. Let r(c) = 0. What is c?
-2, -1, 2
Let b(c) = 6*c**4 + 34*c**3 + 24*c**2 - 4*c. Let a(k) = -13*k**4 - 69*k**3 - 46*k**2 + 10*k. Let g(r) = -2*a(r) - 5*b(r). Factor g(j).
-4*j**2*(j + 1)*(j + 7)
Let m(t) = -t**2 + 11*t + 9. Let n be m(12). Let h(y) = -y**3 - 3*y**2 - y. Let c be h(n). Determine f so that -7*f**3 + 2*f**c + 7*f**3 - 2*f**2 = 0.
0, 1
Let o(b) be the second derivative of -b**6/30 + 15*b**5/4 + 77*b**4/12 - 25*b**3/2 - 38*b**2 - b - 575. Determine h, given that o(h) = 0.
-1, 1, 76
Let f(w) be the third derivative of -21*w**3 + 31/6*w**4 + 0*w - 266*w**2 + 1/30*w**5 + 0. Determine a, given that f(a) = 0.
-63, 1
Let i be (-564)/15228*6/(-1). Solve 8/3*p - i*p**2 - 22/9 = 0 for p.
1, 11
Let h(t) = t**3 - 5*t**2 + 53*t - 467. Let k be h(7). Let w = -22 + 162/7. Suppose 2/7*d**3 - 4/7*d**k - 2*d - w = 0. Calculate d.
-1, 4
Factor y**4 + 8*y**3 - 16*y**2 + 5*y - 32*y**3 + 27*y + 3*y**4 + 4*y**5.
4*y*(y - 2)*(y - 1)*(y + 2)**2
Let t be (6 - 16 - -5)*474/(-10). Let v = 237 - t. Let 0 + 0*b**3 + v*b - 2/3*b**5 + 0*b**2 - 2/3*b**4 = 0. What is b?
-1, 0
Let a(g) be the first derivative of -g**6/15 - 236*g**5/25 - 3481*g**4/10 + 3260. Factor a(w).
-2*w**3*(w + 59)**2/5
Let 562*g + 1272 + 73*g**3 - 126*g**2 + 2*g**4 - 206*g - 500*g**2 + 198*g