
Let d(g) be the second derivative of -g**5/120 - 85*g**4/72 + 173*g**3/36 - 29*g**2/4 - 357*g. Determine t, given that d(t) = 0.
-87, 1
Let j = 36439/2 + -18219. Factor -j*h**2 - 6 - 4*h.
-(h + 2)*(h + 6)/2
Factor -4*u**4 + 154*u**2 + 40*u**3 + 119*u**3 + 251*u**2 - 23*u**3 - 117*u**2.
-4*u**2*(u - 36)*(u + 2)
Let a be 6 - (332/(-312) + 7). Let k = 49/156 - a. Determine n, given that -n + n**3 + k*n**4 + 3/4*n**2 - 1 = 0.
-2, -1, 1
Let z be (12/(-2))/(-6 - -4). Suppose z*v = -5*n + 7705, 2*n - n + 7675 = 3*v. Find f such that v - 2560 + 20*f + 5*f**2 = 0.
-4, 0
Let z(m) be the first derivative of 22*m**3/3 + 133*m**2/4 + 3*m/2 - 9183. Factor z(c).
(c + 3)*(44*c + 1)/2
Determine d so that -1/3*d**3 + 410/3 + 10*d**2 + 147*d = 0.
-10, -1, 41
Factor 9*c**2 + 145*c**2 - 81*c**2 - 134*c - 74*c**2 - 1680.
-(c + 14)*(c + 120)
Let m(x) be the first derivative of 11*x**4/4 + 31*x**3/6 - x**2 + 18*x - 50. Let b(c) be the first derivative of m(c). Factor b(h).
(h + 1)*(33*h - 2)
Let p(y) = -12*y**4 - 22*y**3 - 14*y**2 + 8. Let j(n) = -37*n**4 - 66*n**3 - 40*n**2 + 22. Let t(r) = -8*j(r) + 22*p(r). Factor t(m).
4*m**2*(m + 1)*(8*m + 3)
Let s be 419/(-210) + (8/(-10))/(6/(-15)). Let x(l) be the third derivative of -s*l**6 + 0 + 16*l**2 + 0*l + 0*l**3 - 1/21*l**4 - 1/35*l**5. Factor x(p).
-4*p*(p + 1)*(p + 2)/7
Suppose 6*a - 9*a + 12 = 0. Suppose -5*d = -15, -6*h + 2*d = -a*h + 6. Determine p, given that 1/3*p**2 + h + 0*p = 0.
0
Let w = 47071/15 - 3138. Let m(u) be the second derivative of 1/6*u**4 + 1/42*u**7 + 0*u**2 - 1/6*u**3 + 0 + 0*u**5 - 7*u - w*u**6. Factor m(o).
o*(o - 1)**3*(o + 1)
Let g(p) = -19*p**2 - 225*p + 6495. Let f(v) = -45*v**2 - 449*v + 12989. Let w(q) = -3*f(q) + 7*g(q). Solve w(o) = 0 for o.
57
Find b such that -30*b + 34*b + 20*b**3 + 15*b**2 - 60 + 16*b**3 - 37*b**3 = 0.
-2, 2, 15
Let d = -79454/29 - -397357/145. Find v such that d*v**5 + 0 + 3/5*v**2 - 3/5*v**4 - 21/5*v**3 + 18/5*v = 0.
-2, -1, 0, 1, 3
Let r(i) = 13*i**3 + 58*i**2 - 11*i + 3. Suppose -15 = 86*k - 85*k. Let z(o) = 2*o**3 + o**2 - o + 1. Let j(n) = k*z(n) + 5*r(n). Factor j(l).
5*l*(l + 8)*(7*l - 1)
Suppose -44 = -5*r + 71. Let m = r - 18. Determine f, given that -f**4 + f**m + f**2 - 5*f + 6*f - 3*f**3 + f = 0.
-1, 0, 1, 2
Let c = 2618 - 2613. Let v(p) be the second derivative of -1/120*p**c - 8/9*p**3 + 7/3*p**2 + 0 + 41*p + 11/72*p**4. Factor v(l).
-(l - 7)*(l - 2)**2/6
Let t(r) be the second derivative of 0*r**3 + 3*r - 20 + 0*r**5 + 0*r**2 + 1/15*r**6 - 2/3*r**4. Determine q, given that t(q) = 0.
-2, 0, 2
Determine m, given that -2/5*m**2 - 1902/5*m + 0 = 0.
-951, 0
Let l(c) = -c**2 - 210*c + 3861. Let b be l(17). Let y be 1/(-3) - (-68)/60. Factor -4*r + 5 + y*r**b.
(2*r - 5)**2/5
Let q(m) be the third derivative of m**8/1008 - 2*m**7/315 - 7*m**6/8 - 99*m**5/10 - 1280*m**2. Factor q(a).
a**2*(a - 22)*(a + 9)**2/3
Let x = 69 + 69. Factor -124*z**2 + 280*z**2 + 15*z**4 - x*z**2 + 51*z**3.
3*z**2*(z + 3)*(5*z + 2)
Let c be 1 + 0 + (-16)/(-16). Factor 85*m - 15 - 27 - 4*m**c + 39*m - 78.
-4*(m - 30)*(m - 1)
Let w(d) be the first derivative of 29/2*d**2 - 9 + 2/9*d**4 + 4/45*d**5 + 0*d**3 + 0*d - 1/30*d**6. Let k(n) be the second derivative of w(n). Factor k(i).
-4*i*(i - 2)*(3*i + 2)/3
Let t(q) = -1449*q**2 + 1459*q + 8. Let a(u) = -2900*u**2 + 2922*u + 17. Let x(l) = 6*a(l) - 13*t(l). Determine i so that x(i) = 0.
-2/1437, 1
Let o(w) be the first derivative of 3*w**4/10 + 68*w**3/5 - 843*w**2/5 + 1476*w/5 - 4246. Suppose o(v) = 0. What is v?
-41, 1, 6
Let q(d) = d**2 + 11*d - 16. Let b be q(-12). Let i be (6/b)/(16/(-32)). Factor o**5 + o**2 - 2*o**4 - 152*o**i + o**4 + 151*o**3.
o**2*(o - 1)**2*(o + 1)
Let g(a) be the second derivative of 3*a**5/160 - 13*a**4/32 - 7*a**3/8 - 31*a + 19. Factor g(i).
3*i*(i - 14)*(i + 1)/8
Let k be (17 - -8)*4/8. Let n(o) be the second derivative of 0 + 5/3*o**3 - o - 1/12*o**4 - k*o**2. Solve n(s) = 0.
5
Suppose 5*r - 4*s = 52, 2*r - 2*s - 20 = -0*s. Suppose 0 = -0*x - 3*x + r. Find l such that 2*l**2 + 3*l + x - 8*l + 2*l**2 - 3*l**2 = 0.
1, 4
Let l be (18/(-216))/(5/4 - 895/537). Factor -l*h**2 - h - 6/5.
-(h + 2)*(h + 3)/5
Suppose 0 = 36*m - 39*m - 5*c - 19, 2*m + 3*c = -11. Let u(q) be the first derivative of 0*q + 2/27*q**3 + 8 - 2/9*q**m. Factor u(l).
2*l*(l - 2)/9
Determine u, given that -3*u**2 + 753 - 862 + 2476*u + 7*u**2 + 2591 + 2454 = 0.
-617, -2
Suppose 528 = -l - 3. Let z = 536 + l. Factor 2/9*f**z - 2/9*f + 0 - 4/9*f**4 + 0*f**3 + 4/9*f**2.
2*f*(f - 1)**3*(f + 1)/9
Let d(n) be the third derivative of 1/540*n**5 - 20/27*n**3 - 13/72*n**4 - 3*n + 0 + 10*n**2. Factor d(u).
(u - 40)*(u + 1)/9
Let i = 1893 + -1853. Suppose 3*g + 2*g - 280 = 0. Factor 0 - i*f - 242*f**3 + 8 + 330*f**2 - g*f.
-2*(f - 1)*(11*f - 2)**2
Let m(a) = -a + 3. Let g(s) = 5*s - 51. Let t(w) = 2*g(w) + 4*m(w). Let x be t(15). Factor 4/3*y**3 + 0 - 4/3*y**5 - 2*y**4 + x*y + 0*y**2.
-2*y**3*(y + 2)*(2*y - 1)/3
Let n(v) = 13*v + 110. Let i be n(-8). Let h be 12/(1/(3 + -2)). Let -16*f**2 + h*f**4 + i*f**4 + 0*f**4 - 8*f - 4*f**3 + 10*f**3 = 0. Calculate f.
-2/3, 0, 1
Let o = -1865 - -1865. Let m(z) be the second derivative of -1/8*z**3 + 3/160*z**5 + 0 - 1/32*z**4 + 20*z + o*z**2. Factor m(s).
3*s*(s - 2)*(s + 1)/8
Suppose 2*d - 50 = 16. Suppose -3*k + d = -5*l - 0*l, 5*l + 49 = 4*k. Factor -186*o - k + 206*o + 1 - 5*o**2.
-5*(o - 3)*(o - 1)
Let w = -389 + 391. Factor -42 + 6*x**w + 7*x**2 + 2*x**2 - 8*x - 13*x**2.
2*(x - 7)*(x + 3)
Suppose -22*p = 39 - 127. Factor 5*j**2 + 116*j**p - 111*j**4 + 14*j**3 - 4*j**3.
5*j**2*(j + 1)**2
Solve -39/2*q**2 + 3/4*q**3 - 255/4*q - 87/2 = 0.
-2, -1, 29
Let a be (-30)/105 + (-715)/(-91) - 5. Factor -3648/7*m + 1152/7 + a*m**4 + 3176/7*m**2 - 456/7*m**3.
2*(m - 12)**2*(3*m - 2)**2/7
Factor 4/3*g**3 + 1/9*g**4 + 29/9*g**2 + 0 + 2*g.
g*(g + 1)*(g + 2)*(g + 9)/9
Let v(s) be the first derivative of -1/32*s**4 - 1/24*s**3 + 1/48*s**6 - 37 + 1/40*s**5 + 0*s + 0*s**2. Suppose v(m) = 0. Calculate m.
-1, 0, 1
Let x be 1425/150*8/38. Let a(i) be the second derivative of -13*i + 1/4*i**5 + 5*i**x + 25/6*i**3 + 0 + 5/3*i**4. Factor a(r).
5*(r + 1)**2*(r + 2)
Let q(n) be the second derivative of n**7/14 - 23*n**6/10 + 519*n**5/20 - 481*n**4/4 + 165*n**3 + 1000*n. Let q(m) = 0. What is m?
0, 1, 5, 6, 11
Suppose -1640 = -74*n + 66*n. Solve -101*t + n*t**2 - 210*t**2 - 14*t - 110 = 0.
-22, -1
Let v = 5360 - 26796/5. Let s(l) be the first derivative of -21 + l**4 + v*l**5 - 2*l**2 - 4*l**3 + 8*l. Find t such that s(t) = 0.
-2, -1, 1
Let q(a) be the third derivative of -1/2*a**4 + 4/3*a**3 - 2 - 2/105*a**7 + 1/10*a**6 - 1/15*a**5 + 0*a - 65*a**2. Factor q(u).
-4*(u - 2)*(u - 1)**2*(u + 1)
Let r(l) be the first derivative of l**5/2 - 45*l**4/8 + 35*l**3/6 + 45*l**2/4 - 20*l - 3648. Suppose r(m) = 0. What is m?
-1, 1, 8
Let s = 272 - 267. Suppose -s*x**3 - 5*x**2 - 3*x**2 + 3*x**2 = 0. What is x?
-1, 0
Let q = 21581 - 21572. Let k(r) be the second derivative of -q*r - 5/12*r**4 + 20*r**2 - 5/3*r**3 + 0. Factor k(n).
-5*(n - 2)*(n + 4)
Let x be (-5 - (-4 + 1)) + 4. Factor 72 - 16*o**2 - 10*o - x*o + 570*o**3 - 566*o**3.
4*(o - 3)**2*(o + 2)
Let b be 3/(0 - 1 - (-7 + 5)). Suppose -2*d**3 + b*d**4 + 5*d**3 - 2*d**4 - d**3 = 0. Calculate d.
-2, 0
Suppose -62*k = -84*k + 44. Determine z, given that -6080*z + 316*z**2 + 5776 + 499*z**2 - 507*z**k - 4*z**3 = 0.
1, 38
Let o = -66798 - -66800. What is w in 11/4*w + w**o - 1/4*w**3 + 3/2 = 0?
-1, 6
Suppose 2*g + 2*s - 26 = 0, g - 5*s = -2*g + 55. Find m, given that 11*m + g*m - 18*m - 2*m**3 = 0.
-2, 0, 2
Let t(b) = -74*b**3 - 85*b**2 - 351*b + 440. Let f(g) = -118*g**3 - 128*g**2 - 526*g + 660. Let d(m) = 5*f(m) - 8*t(m). Suppose d(n) = 0. What is n?
-11, -10, 1
Let k(g) be the third derivative of g**5/240 + 49*g**4/12 + 4802*g**3/3 + 131*g**2 + 3*g. Determine r so that k(r) = 0.
-196
Suppose 776504 - 53864 = 12*z. Determine p so that -z*p + 701*p**4 + 24380*p - 11520*p**3 - 93651*p**2 - 1106*p**4 - 3920 + 9211*p**2 = 0.
-14, -2/9
Let a(h) = h**3 - 12*h**2 - 27*h - 12. Let q be a(14). Let -86*z**2 + 88*z + 44*z**2 + 78*z**q - 4*z**3 = 0. Calculate z.
-2, 0, 11
Let z be ((-4656)/3880)/(3 - 6). Let a be ((-2)/2 - -1)/1. Determine n so that 0*n - 2/5*n**2 + z*n**3 + a = 0.
0, 1
Factor -178