
Factor 0 - 51*s + 19/2*s**2 - 1/6*s**3.
-s*(s - 51)*(s - 6)/6
Let m(g) be the second derivative of 0*g**2 - 1/168*g**7 + 0*g**3 + 1/24*g**4 - 1/60*g**6 + 1/80*g**5 + 4 + 11*g. Suppose m(t) = 0. Calculate t.
-2, -1, 0, 1
Let a = 53960 + -53957. Factor 3/2*z**4 - 648 + 108*z**2 - 24*z**a + 0*z.
3*(z - 6)**3*(z + 2)/2
Let k(m) = m**3 - 8*m**2 + 10*m - 17. Let u be k(7). Let i(x) = x + 3. Let d be i(6). Factor 18*h**3 - 3*h**5 - 160*h**u - d - 63*h - 30*h**2 - 18 + 169*h**4.
-3*(h - 3)**2*(h + 1)**3
Suppose -930*b**3 + 240258*b**2 + 243675 - 455*b**3 + 3*b**4 + 411558*b - 319*b**3 + 74082*b = 0. What is b?
-1, 285
Suppose 384*g + 2*g**2 - 16*g**2 + 14*g**2 - 2*g**2 = 0. Calculate g.
0, 192
Let t be (-6479)/(-11935) - 2/(-28)*-2. Let r(a) be the first derivative of 2/5*a**2 + 0*a + t*a**4 + 2/25*a**5 + 2/3*a**3 - 15. What is o in r(o) = 0?
-2, -1, 0
Let z = 34 + -32. Suppose 2*q = -z*q + 100. Suppose 3*h**3 - 16*h**3 + 20 + 8*h**3 + q*h**2 - 40*h = 0. What is h?
1, 2
Let z(y) be the first derivative of -1/14*y**4 + 5 + 0*y - 1/7*y**2 + 4/21*y**3. What is g in z(g) = 0?
0, 1
Suppose 0 = -3*v - 14 + 26. Suppose 4*l - 16 = -2*i, -l = v*i + i - 13. Factor 0*u + 3/8*u**4 + 0 - 3/8*u**3 + 0*u**i.
3*u**3*(u - 1)/8
Let q(m) be the second derivative of -m**5/90 + 11*m**4/54 + 14*m**3/3 - 19*m + 8. Let q(t) = 0. What is t?
-7, 0, 18
Determine l, given that 215/4*l**2 - 5/4*l**4 + 375/2*l + 0*l**3 + 180 = 0.
-3, -2, 8
What is g in 384/5*g**3 + 0 - 1/5*g**4 - 7449*g**2 + 72962/5*g = 0?
0, 2, 191
Let w = -32171 + 225201/7. Let 4/7 + w*v**2 - 8/7*v = 0. Calculate v.
1
Let b be (63 - (-15444)/(-243))*3/(-5). Factor -b*c**2 - c - 2/3.
-(c + 1)*(c + 2)/3
Let u(c) be the third derivative of 0 - 37/72*c**4 + 137*c**2 + 0*c + 1/360*c**5 + 1369/36*c**3. Factor u(p).
(p - 37)**2/6
Let o(a) be the first derivative of -48*a**2 + 2*a**5 + 128/3*a**3 - 46/3*a**4 + 128 + 32/3*a. Factor o(i).
2*(i - 2)**3*(15*i - 2)/3
Let z be (-4)/28 - (114/(-14) + -1). Suppose 4*q - z*q = 0. Determine h so that 37*h + 283 + q*h**2 - 91 + 11*h + 3*h**2 = 0.
-8
Factor 0 + 12*c**3 - 1092/5*c**2 + 5408/5*c - 1/5*c**4.
-c*(c - 26)**2*(c - 8)/5
Let g be ((57 - 72)*2)/((-3)/((-6)/(-16))). Let 1/4*n**2 - 7/2*n - g = 0. Calculate n.
-1, 15
Let t(a) be the third derivative of -a**5/240 + 223*a**4/48 - 49729*a**3/24 - 37*a**2 + 4*a. Factor t(m).
-(m - 223)**2/4
Let s = -44 - -48. Suppose s*x = 14 - 6. Factor -2 + 0*z**3 - 22*z + 1 + 3*z**3 + z**x + 19*z.
(z - 1)*(z + 1)*(3*z + 1)
Let x(w) be the third derivative of 29/525*w**7 - 9*w**2 - 673/150*w**5 - 163/300*w**6 - 256/15*w**3 - 184/15*w**4 - 1/840*w**8 + 0 - 6*w. Factor x(q).
-2*(q - 16)**2*(q + 1)**3/5
Let s(c) be the third derivative of c**9/30240 - c**8/10080 + 37*c**5/30 + 22*c**2. Let z(a) be the third derivative of s(a). Determine g, given that z(g) = 0.
0, 1
Let g = 37638 + -112874/3. Solve 84*m**2 + g*m**3 - 686/3 + 2/3*m**4 + 392/3*m = 0.
-7, 1
Let s(c) be the second derivative of c**4/36 - 317*c**3/18 - 319*c**2/3 + 2*c - 3092. Factor s(h).
(h - 319)*(h + 2)/3
Suppose 2*m - 3*d = 11 + 12, -3*m = -5*d - 37. Factor 2*n**3 - 8*n**2 - 8*n + 8*n**2 - m*n**2 + 16.
2*(n - 2)**2*(n + 2)
Find x, given that -1716*x**2 + 1/2*x**3 + 1963104*x - 748596992 = 0.
1144
Let o(c) = -3*c**4 - 19*c**3 + 7*c**2 + 59*c - 54. Let p(u) = 2*u**4 + 10*u**3 - 3*u**2 - 29*u + 26. Let n(l) = -3*o(l) - 5*p(l). Factor n(v).
-(v - 4)**2*(v - 1)*(v + 2)
Let f(v) be the second derivative of v**5/15 - 778*v**4/3 + 1210568*v**3/3 - 941821904*v**2/3 + 1751*v + 3. Solve f(t) = 0 for t.
778
Let q(l) be the second derivative of 7*l - 67/9*l**3 + 2*l**2 - 3 + 64/27*l**4 - 7/30*l**5. Let q(a) = 0. What is a?
2/21, 3
Let t(c) = -5*c**2 - 52*c + 24. Let a(o) = o**2 + 10*o - 5. Suppose 2*g - 6*g + 12 = 0, 5*g + 95 = 5*v. Let k(j) = v*a(j) + 4*t(j). Solve k(b) = 0 for b.
-7, 1
Suppose -173 = 10*z - 213. Factor -3*w**3 + 11862 + z*w**3 - w**2 + w - 2*w - 11861.
(w - 1)**2*(w + 1)
Let t be (-2)/(-24)*0/(-145). Let j(l) be the second derivative of 10*l + 0*l**2 + 1/27*l**4 + t*l**3 + 7/270*l**6 + 4/45*l**5 + 0. Factor j(h).
h**2*(h + 2)*(7*h + 2)/9
Let z(x) be the second derivative of -x**7/1120 + x**6/80 + 7*x**5/160 - 91*x**3/3 + 55*x - 2. Let r(q) be the second derivative of z(q). Solve r(b) = 0 for b.
-1, 0, 7
Suppose 522 = 585*t - 579*t. Suppose -84*h = -t*h. Determine a, given that -9/2*a**2 + h + 3/4*a**3 + 6*a = 0.
0, 2, 4
Let u be (30 - 8) + -4 + 5. Suppose -27*a = u*a - 200. Factor -4/5*p**2 - 8/5*p**3 + 0*p**a + 2/5*p**5 + 4/5 + 6/5*p.
2*(p - 2)*(p - 1)*(p + 1)**3/5
Factor 0 + 0*o + 2/3*o**5 + 32/3*o**2 + 136/3*o**3 + 65/6*o**4.
o**2*(o + 8)**2*(4*o + 1)/6
Let v be -4 + 18 - 13224/945. Let x(b) be the third derivative of -2/9*b**4 + 0*b + v*b**7 - 1/15*b**5 + 8/9*b**3 + 9*b**2 + 1/45*b**6 + 0. Factor x(l).
4*(l - 1)**2*(l + 2)**2/3
Let q = 1334/13 - 21019/208. Let m(d) be the third derivative of 0 - 2*d**2 + 0*d - 1/160*d**5 - 5/32*d**4 - q*d**3. Factor m(x).
-3*(x + 5)**2/8
Let g(r) be the second derivative of 4*r**6/15 + r**5/2 - r**4/3 - r**3 - 71*r + 5. Determine a, given that g(a) = 0.
-1, 0, 3/4
Determine g, given that -4/3*g**5 + 44/3*g**4 + 380/3*g - 40*g**3 + 100 - 88/3*g**2 = 0.
-1, 3, 5
Let t = 8933 + -5993. What is d in -140*d + 8*d**2 - 1960 - 4*d**2 + t + d**2 = 0?
14
Let t(i) = -3*i**2 - 22*i + 1. Let a be t(-8). Let d be 1 + 3 + (-16 - a). Factor 1/3*l**4 - 4/3 - 4/3*l**d + l**2 + 4/3*l.
(l - 2)**2*(l - 1)*(l + 1)/3
Let b(o) be the first derivative of -1/14*o**4 + 224 + 16/7*o + 2/21*o**3 + 10/7*o**2. Factor b(k).
-2*(k - 4)*(k + 1)*(k + 2)/7
Solve -10/7*n**4 - 164/7*n**3 + 1240/7*n**2 - 1488/7*n + 2/7*n**5 - 2880/7 = 0 for n.
-10, -1, 4, 6
Let i(m) = 3*m**2 + 153*m - 7. Let h(y) = -2*y**2 + y + 7. Let u(x) = -5*h(x) - 5*i(x). Factor u(j).
-5*j*(j + 154)
Let s(x) be the first derivative of x**4/10 - 148*x**3/5 + 12321*x**2/5 + 480. Factor s(n).
2*n*(n - 111)**2/5
Let y(i) be the third derivative of -i**7/420 + i**6/240 + 149*i**5/120 - 143*i**4/16 + 12343*i**2. Factor y(l).
-l*(l - 11)*(l - 3)*(l + 13)/2
Let b(l) be the first derivative of 6/17*l - 5/17*l**4 - 6/85*l**5 + 153 + 0*l**3 + 10/17*l**2. Find j such that b(j) = 0.
-3, -1, -1/3, 1
Suppose 19*k - 35*k = 81*k + 456*k. Factor -648/7*g - 468/7*g**2 + k - 4/7*g**4 - 80/7*g**3.
-4*g*(g + 2)*(g + 9)**2/7
Let p(u) be the first derivative of -u**4/18 - 2*u**3/9 + 34*u**2/9 - 32*u/3 - 781. Suppose p(h) = 0. Calculate h.
-8, 2, 3
Find q, given that -82*q - 104/5 + 24/5*q**2 = 0.
-1/4, 52/3
Let c(x) be the third derivative of x**6/780 - x**5/130 - x**4/39 + 4*x**3/13 - 14*x**2 + 3*x + 3. Let c(u) = 0. What is u?
-2, 2, 3
Let k(j) be the second derivative of -2*j**6/75 + 3*j**5/50 + 17*j**4/30 - 9*j**3/5 + 9*j**2/5 + 194*j - 9. Determine n, given that k(n) = 0.
-3, 1/2, 1, 3
Let k(i) be the third derivative of i**8/756 - i**7/315 - i**6/60 + 4*i**5/135 + i**4/9 - 324*i**2 + 7. Find o, given that k(o) = 0.
-3/2, -1, 0, 2
Let d(f) be the third derivative of 2/3*f**3 + f**2 + 0*f - 16 + 29/270*f**5 + 1/945*f**7 - 1/60*f**6 - 13/36*f**4. Factor d(w).
2*(w - 3)**2*(w - 2)*(w - 1)/9
Let p(k) be the first derivative of k**6/30 - 7*k**5/20 - k**4/12 + 7*k**3/6 + 149*k - 156. Let q(u) be the first derivative of p(u). Factor q(w).
w*(w - 7)*(w - 1)*(w + 1)
Let l(s) be the first derivative of -5*s**4/2 - 109*s**3/3 - 45*s**2 + 2011. Solve l(w) = 0.
-10, -9/10, 0
Let g(w) be the second derivative of w**7/273 - 206*w**6/195 - 83*w**5/26 - 8*w**4/3 + 2*w - 282. Let g(q) = 0. Calculate q.
-1, 0, 208
Let u(a) be the first derivative of -5*a**3/3 - 135*a**2 - 1000*a - 1555. Factor u(y).
-5*(y + 4)*(y + 50)
Let j = 28162/84495 + 1/28165. Determine r so that 729*r - 6561 - 27*r**2 + j*r**3 = 0.
27
Suppose -5*a + 48 = -2*h, 93*h = 5*a + 92*h - 29. Factor 11/2 - 1/4*n**a + 9/4*n.
-(n - 11)*(n + 2)/4
Suppose 25 - 46 - 47 = -34*n. Let i(k) be the second derivative of 0*k**n + 0 + 0*k**3 + 0*k**4 - 23*k - 3/20*k**5 + 1/5*k**6 - 1/14*k**7. Factor i(g).
-3*g**3*(g - 1)**2
Let q(k) be the third derivative of 0 - 1/112*k**8 - 2/35*k**7 - 1/10*k**6 + k**3 + 61*k**2 + 1/10*k**5 + 0*k + 5/8*k**4. Let q(w) = 0. Calculate w.
-2, -1, 1
Let z(u) be the second derivative of -3 + 24*u + 1/30*u**4 + 1/75*u**6 + 1/25*u**5 + 0*u**2 + 0*u**3. Facto