
Let p(b) be the third derivative of -5*b**2 + 3*b - 1/12*b**4 - 1/15*b**6 + 8/105*b**7 - 1/3*b**5 + 0 + 2/3*b**3 + 5/168*b**8. Suppose p(h) = 0. What is h?
-1, 2/5, 1
Let y = -16779/5 - -3356. Let b(v) be the second derivative of 2/3*v**3 + 14*v + 0 - y*v**5 + 2*v**2 - 1/3*v**4. Factor b(m).
-4*(m - 1)*(m + 1)**2
Suppose 4*u = 59*l - 56*l + 22, u + 6 = -5*l. Let t(n) be the second derivative of -20*n**2 - 1/30*n**u + 29*n - 4/3*n**3 + 0. Factor t(p).
-2*(p + 10)**2/5
Factor -72/11*j**3 - 2/11*j**4 - 578/11 - 716/11*j**2 - 1224/11*j.
-2*(j + 1)**2*(j + 17)**2/11
Let x(v) = -5*v**2 + 34*v - 239. Let b(p) = 13*p**2 - 100*p + 719. Let z(f) = -3*b(f) - 8*x(f). Factor z(g).
(g - 7)*(g + 35)
Let n(i) = 2*i + 24. Let w be n(-8). Factor -3*f + w*f - 3*f - 6*f + 4*f**2.
4*f*(f - 1)
Let x be (4*1)/(-20 + 22) - (-8 - -6). Let o(h) be the second derivative of 0*h**2 + 11*h + 0*h**3 + 1/24*h**x + 0 + 3/80*h**5. Let o(d) = 0. What is d?
-2/3, 0
Let d be 9/(-300 - 15)*16/(-3). Let l(c) be the second derivative of 0 - 2/5*c**2 - 13/6*c**4 + 19/15*c**3 + 2*c**5 + d*c**7 - 2*c - 68/75*c**6. Solve l(h) = 0.
1/4, 1/2, 1, 2
Let c be (1 + 9/(-12))*(-12)/(-1). Suppose k + c*d - 31 = 0, -8 = -4*d + 2*d. Suppose -k*i - 35*i - 5*i**2 + 24*i - 245 - 40*i = 0. Calculate i.
-7
Let k(x) be the first derivative of -1/3*x**3 - 1089*x - 95 + 33*x**2. Suppose k(l) = 0. What is l?
33
Let v(u) be the first derivative of 9*u**6 + 456*u**5/5 - 16*u**4/3 - 5408*u**3/9 - 1168*u**2/3 - 256*u/3 - 622. Let v(w) = 0. Calculate w.
-8, -2, -2/9, 2
Let a(x) be the third derivative of 0*x**4 + 4/945*x**7 - 1/3024*x**8 - 5/54*x**5 + 0 + 0*x**3 + 0*x - 67*x**2 - 1/216*x**6. Determine o, given that a(o) = 0.
-2, 0, 5
Let g(f) = -24*f**2 - 551*f - 502. Let c be g(-22). Find h such that 0 - 21*h - 87/2*h**2 - 3/2*h**c - 24*h**3 = 0.
-14, -1, 0
Let z(p) be the first derivative of -1024*p**5/45 - 13216*p**4/3 + 6640*p**3 - 3741*p**2 + 936*p + 680. Factor z(l).
-2*(l + 156)*(8*l - 3)**3/9
Let f(z) = -4*z**3 - 2*z**2 - 3*z - 2. Let q be f(-1). Find y, given that -40 - 32*y + 74*y**3 + 2*y**2 - 72*y**q - 4*y**2 = 0.
-2, 5
Let c = -22 + 16. Let f be (9 - 6)*((-14)/c - -2). Find q, given that f - 5 + 0 + q**2 - 3 - 6*q = 0.
1, 5
Let w = -5 - -4. Let u(n) = 8*n**3 - 15*n**2 - 3*n. Let r(g) = g**3 - g. Let x(d) = -6*d - 57. Let p be x(-10). Let s(h) = p*r(h) + w*u(h). Factor s(t).
-5*t**2*(t - 3)
Factor -5*z**4 - 163*z**3 + 5*z**4 + 18*z**3 - 4*z**4 - 912*z + 368 - 23*z**3 + 716*z**2.
-4*(z - 2)*(z - 1)**2*(z + 46)
Let h(i) be the third derivative of i**7/210 + 29*i**6/120 - 283*i**5/60 + 475*i**4/24 - 37*i**3 + 1073*i**2. Factor h(j).
(j - 6)*(j - 1)**2*(j + 37)
Suppose 1 = 2*s + 3*i, 1311*s - 8 = 1309*s + 4*i. Let o(y) be the second derivative of -5/9*y**3 - 1/72*y**4 + 0 + 11*y - 25/3*y**s. Factor o(t).
-(t + 10)**2/6
Let l be (-4)/(-22) - ((-490)/572 + 1). Let n = 107/78 - l. Solve -n + 4*s + 2*s**3 - 1/3*s**4 - 13/3*s**2 = 0.
1, 2
Let t be (-6)/10 + 10/(-25) - -3. Suppose 5*u - 4*r - 149 = 0, -2*u + u + t*r = -31. Factor 2*n**2 - u*n - 2*n**3 + 2*n + 5*n**3 + 15 + 7*n**2.
3*(n - 1)**2*(n + 5)
Let q(h) be the first derivative of 0*h + 2*h**2 + 29 + 2/9*h**3 - 1/6*h**4. Factor q(y).
-2*y*(y - 3)*(y + 2)/3
Let f = 1433 - 1431. Suppose d - f = -2*q, -3*d - 24 + 6 = -2*q. Factor 9/5 + 3/5*x + 1/5*x**q - x**2.
(x - 3)**2*(x + 1)/5
Let u be (-5 - 416/(-48)) + 5. What is a in -2/3*a**2 - 8 + u*a = 0?
1, 12
Let h(y) be the second derivative of y**6/90 + 13*y**5/60 + 10*y**4/9 + 73*y + 6. Find g such that h(g) = 0.
-8, -5, 0
Let o(n) be the third derivative of n**5/210 - 58*n**4/21 + 650*n**2. Factor o(p).
2*p*(p - 232)/7
Suppose 3639 + 158*j**2 - 750 - 1325*j - 574*j - 4*j**2 + 149*j**2 + 3*j**3 = 0. What is j?
-107, 3
Let y(t) = -t**3 + 34*t**2 - 199*t - 3. Let d(r) = -3*r**3 + 104*r**2 - 589*r - 8. Let u(z) = -3*d(z) + 8*y(z). Determine q, given that u(q) = 0.
0, 5, 35
Let v = 299357 + -299354. Suppose 10/3*n - 5/3*n**2 + 0 + 5/3*n**4 + 5/3*n**5 - 5*n**v = 0. What is n?
-2, -1, 0, 1
Let f = -180221 - -180221. Factor 0*z**3 - 2/3*z**4 + 0 + 0*z**2 + f*z - 2/9*z**5.
-2*z**4*(z + 3)/9
Let f(i) be the first derivative of -8*i**5/15 - 43*i**4/3 + 116*i**3/3 + 844*i**2/3 + 736*i/3 - 301. Determine q, given that f(q) = 0.
-23, -2, -1/2, 4
Factor 272*j**2 - 24 - 26*j**3 + 313*j**2 - 555*j**2 + 152*j.
-2*(j - 3)*(j + 2)*(13*j - 2)
Suppose -2*i**2 + 0 - 214*i + 321/2*i**3 + 1/2*i**5 + 55*i**4 = 0. Calculate i.
-107, -2, 0, 1
Let a = -690946 + 4845600/7. Determine i so that a + 268/7*i + 2/7*i**2 = 0.
-67
Let b(c) be the first derivative of -c**4 + 28*c**3 - 76*c**2 - 1661. Factor b(s).
-4*s*(s - 19)*(s - 2)
Factor -140*g**4 + 495*g - 740*g**2 + 490*g**3 - 124 + 20*g**4 + 786*g**5 - 787*g**5.
-(g - 1)**4*(g + 124)
Determine o, given that 96*o - 2/9*o**2 - 10368 = 0.
216
Suppose -8*v + 11*v + 37 = 2*u, 2*v = -6. Let p(h) be the first derivative of u + 0*h**2 - 8/5*h + 2/15*h**3. Determine y so that p(y) = 0.
-2, 2
Let k(f) = 875*f**2 - 1985*f + 580. Let x(d) = -438*d**2 + 991*d - 296. Let h(y) = -3*k(y) - 5*x(y). Determine t, given that h(t) = 0.
26/87, 2
Let h(l) be the third derivative of -l**7/945 + 19*l**6/135 - 197*l**5/45 + 53*l**4 - 171*l**3 + 2865*l**2. Let h(f) = 0. What is f?
1, 9, 57
Factor -575*d**2 - 245*d**4 + 10*d**5 + 879*d**3 - 5*d**5 + 276*d**3 - 340*d**4.
5*d**2*(d - 115)*(d - 1)**2
Let g = -44 - -44. Suppose -o = -g*o - 4. Solve 13*n + 5*n**3 + 25*n**2 + 7*n - n**2 - 15*n**o + 16*n**2 = 0 for n.
-1, -2/3, 0, 2
Solve -198*h**2 + h**3 - 8581 - 1996*h + 34*h**2 + 5474 + 31331 + 8380*h = 0 for h.
-4, 84
Let s(r) be the second derivative of -1/60*r**4 + 4/5*r**3 + 5/2*r**2 + 0 + 71*r. Suppose s(v) = 0. Calculate v.
-1, 25
Solve 436/11*d**2 + 2/11*d**4 + 960/11*d + 576/11 + 54/11*d**3 = 0 for d.
-12, -2, -1
Let t(w) be the third derivative of -w**5/100 - 947*w**4/20 - 896809*w**3/10 + 27*w**2 - 52*w. Factor t(r).
-3*(r + 947)**2/5
Let z(l) = -7*l**3 + 110*l**2 - 446*l + 468. Let w(d) = 9*d**3 - 111*d**2 + 444*d - 468. Let t(a) = -5*w(a) - 6*z(a). Find n, given that t(n) = 0.
-39, 2
Let v = -266 + 510. Factor 129*x**3 - v*x**3 - 540 - 75*x**2 + 360*x + 120*x**3.
5*(x - 6)**2*(x - 3)
Factor -12*c**4 - 20402000*c**2 - 14*c**4 + 98*c**4 - 20200*c**3 - 77*c**4.
-5*c**2*(c + 2020)**2
Let z = -270/509 + 1828/1527. Find b such that -z + 0*b + 2/3*b**2 = 0.
-1, 1
Let m(q) be the second derivative of -19*q**6/15 - 29*q**5/10 - 5*q**4/3 + 3007*q. Solve m(f) = 0.
-1, -10/19, 0
Let z(k) = -3*k + 38. Let b be z(12). Suppose 247*o**b + 237*o**2 - 22*o - 482*o**2 = 0. What is o?
0, 11
Suppose -22272*z + 27832/5*z**3 + 51952/5*z**2 + 2/5*z**5 - 215296/5 + 468/5*z**4 = 0. What is z?
-116, -2, 2
Let x(d) be the first derivative of 5*d**9/3024 - d**8/84 + 5*d**7/168 - d**6/36 - d**3 - 15*d**2/2 - 41. Let k(l) be the third derivative of x(l). Factor k(g).
5*g**2*(g - 2)*(g - 1)**2
Let j(z) be the first derivative of 94 - 32/11*z - 24/11*z**2 + 10/11*z**3 - 1/11*z**4. Solve j(l) = 0 for l.
-1/2, 4
Suppose -10*m + 13*m = 99. Suppose 11*w - m = 55. Suppose 6*d - w*d - 3*d**2 - 12 - 10*d = 0. Calculate d.
-2
Let a(y) be the first derivative of -y**6/1620 - y**5/90 + 4*y**4/27 - y**3 + 9*y**2/2 - 35. Let z(b) be the third derivative of a(b). Solve z(d) = 0.
-8, 2
Let c(d) = 2*d**3 - 5*d**2 - 3*d + 2. Let q be c(3). Factor 14*r**q + 11*r**2 + 37*r + 27*r - 74*r.
5*r*(5*r - 2)
Let j(s) be the third derivative of -1/840*s**7 + 0*s + 59*s**2 + 1/1344*s**8 + 0*s**3 + 0*s**4 + 0*s**5 - 1/240*s**6 + 0. Factor j(f).
f**3*(f - 2)*(f + 1)/4
Let i(g) be the first derivative of -2*g**3/9 + 42*g**2 - 250*g/3 - 1838. Factor i(q).
-2*(q - 125)*(q - 1)/3
Let r(s) = s**2 + 10*s - 93. Let a be r(-16). Let g be a + (-34)/28 - 12/42. Let 0 + g*z**5 - 3/2*z**3 - z**2 + 0*z + z**4 = 0. Calculate z.
-1, -2/3, 0, 1
Determine b so that 16/3*b - 2/3*b**2 + 0 = 0.
0, 8
Let r(l) be the third derivative of -l**3 - 69*l**2 - 7/8*l**4 - 1/70*l**7 - 1/8*l**6 + 0*l + 0 - 9/20*l**5. Factor r(g).
-3*(g + 1)**3*(g + 2)
Let q = 152265 - 761289/5. Find d, given that -24/5*d**2 + q*d - 16/5 + 4/5*d**3 = 0.
1, 4
Solve 4*a**4 - 23*a**2 + 148*a**3 + 12*a + 4*a - 36*a**3 - 193*a**2 + 288 - 52*a**3 = 0.
-18, -1, 2
Let q(h) be the second derivative of 3*h**5/20 - 21*h*