4032 - 23*m**8/2240 - 3*m**7/80 + 13*m**3 - 103*m**2. Let d(x) be the first derivative of t(x). Factor d(p).
-3*p**3*(p + 2)*(p + 21)/4
Let f(r) be the second derivative of r**5/20 - 343*r**4/3 - 1373*r**3/6 - 3661*r. Find k such that f(k) = 0.
-1, 0, 1373
Let i(b) be the third derivative of 0 - 23/120*b**4 + 11/15*b**3 + 157*b**2 + 0*b + 1/300*b**5. Factor i(t).
(t - 22)*(t - 1)/5
Factor -101 + 336*g - 34 + 29 - 2*g**2 - 23 - 205.
-2*(g - 167)*(g - 1)
Let h = -4393660/19 - -231246. Suppose -2/19*t**2 + 54/19*t - 2/19*t**4 - h*t**3 - 36/19 = 0. Calculate t.
-6, -3, 1
Let m(n) be the third derivative of -n**6/480 + 31*n**5/120 - 61*n**4/96 - 1522*n**2. Factor m(z).
-z*(z - 61)*(z - 1)/4
Let f(d) = -2*d**2 - 3*d + 4. Let x be f(0). Factor 8*i**3 + 40*i - 30*i**2 - 53*i**3 - 5*i**x + 16*i + 24*i.
-5*i*(i - 1)*(i + 2)*(i + 8)
Let d(o) = -6*o**3 + 36*o**2 - 126*o - 2. Let k(c) = 14*c**3 - 72*c**2 + 250*c + 5. Let a(v) = 10*d(v) + 4*k(v). Factor a(q).
-4*q*(q - 13)*(q - 5)
Suppose 39*y + 4*y**3 + 40*y**2 - 146 + 300 + 53*y - 98 = 0. What is y?
-7, -2, -1
Factor 952/9 + 862/9*j + 2/9*j**3 - 88/9*j**2.
2*(j - 28)*(j - 17)*(j + 1)/9
Suppose -23*w + 2593 = 270. Let t = w + -101. Factor -k**2 + 0 + t*k - 1/3*k**3.
-k**2*(k + 3)/3
Let j(g) = -g**4 + g**3 + g + 3. Let q(s) = 212*s**3 - 1152*s**2 - 4*s - 12. Let w(b) = -4*j(b) - q(b). Find m such that w(m) = 0.
0, 6, 48
Let o(l) be the second derivative of l**6/15 - l**5/5 - l**4/2 + 2626*l - 2. Suppose o(s) = 0. What is s?
-1, 0, 3
Let n = 930052/7 + -132864. Determine l so that 8/7*l**2 + 8/7 + 16/7*l**3 + n*l**5 - 20/7*l - 16/7*l**4 = 0.
-1, 1, 2
Let w = -2/615703 + 3078523/2462812. Let -20*x - w*x**2 - 80 = 0. What is x?
-8
Let p(i) be the third derivative of -152*i**2 + 0 + 529/2*i**4 - 23/10*i**5 + 0*i + 1/120*i**6 - 48668/3*i**3. Factor p(b).
(b - 46)**3
Let n(r) be the second derivative of -49/5*r**2 - 88*r + 1/30*r**4 + 16/5*r**3 + 0. Factor n(c).
2*(c - 1)*(c + 49)/5
Let u(g) be the first derivative of 2*g**3/9 - 6*g + 1264. Let u(j) = 0. Calculate j.
-3, 3
Let w(t) be the second derivative of t**6/15 + 29*t**5/5 + 323*t**4/6 + 578*t**3/3 + 312*t**2 + 154*t - 2. Find s, given that w(s) = 0.
-52, -3, -2, -1
Let u(x) be the first derivative of x**5/20 + 3*x**4/2 + 12*x**3 - 176. Let u(o) = 0. What is o?
-12, 0
Let j(n) be the second derivative of -n**4/18 + 14*n**3/9 + 1531*n. Find x such that j(x) = 0.
0, 14
Suppose 0 = -5*z - r + 208, 3*z - 118 = -4*r - 0*r. Let l be ((-8)/12)/((-14)/z). Let 0*d**4 + 12/7*d**3 + 0 + 8/7*d**l - 4/7*d**5 + 0*d = 0. Calculate d.
-1, 0, 2
Let t = 664653/5 - 7309703/55. Let -t*w + 2/11*w**2 + 10952/11 = 0. What is w?
74
Let t(v) be the second derivative of v**9/3024 - v**8/672 - v**7/72 - v**6/36 - 10*v**4 - 109*v. Let n(d) be the third derivative of t(d). Factor n(u).
5*u*(u - 4)*(u + 1)**2
Let i be (24/42*(-35)/30)/(295/(-354)). Factor 0*m + 0 + 0*m**2 - i*m**4 - 4/5*m**3.
-4*m**3*(m + 1)/5
Let w = -788 - -1034. Find t, given that w*t**3 + 0 - 174*t**3 - 18 + 2*t**4 + 69*t - 102*t**2 + 3*t**5 - 26*t**4 = 0.
1, 2, 3
Let w(l) be the first derivative of -6*l**2 - 18 + 0*l + 0*l**4 + 2/21*l**3 - 1/420*l**5. Let p(b) be the second derivative of w(b). What is h in p(h) = 0?
-2, 2
Let y(h) be the second derivative of -h**6/15 - 8*h**5/5 - 40*h**4/3 - 128*h**3/3 + 9*h - 108. Find f such that y(f) = 0.
-8, -4, 0
Suppose -12 = 26*o - 22*o. Let g(b) = -b**2 - 5*b - 4. Let y be g(o). Determine v, given that 10*v - 3*v - 10*v**y + 2*v**3 + 4*v + v = 0.
0, 2, 3
Factor 5*w**4 - 168*w**2 - 327*w**3 + 221*w**2 + 817*w**2 - 110*w**2 - 252*w.
w*(w - 63)*(w - 2)*(5*w - 2)
Let w = 19/461 - -223951/2305. Determine y, given that -w*y + 0 + 48/5*y**3 - 27*y**2 - 3/5*y**4 = 0.
-2, 0, 9
Suppose 4*k**2 - 736268 - 64*k + 736268 = 0. What is k?
0, 16
Factor 3*a**5 - 8*a**4 - 7*a**3 + 384*a**2 - 768 - 5*a**3 - 13*a**4 - 12*a**3 - 384*a.
3*(a - 4)**3*(a + 1)*(a + 4)
Let p(k) be the second derivative of -k**6/72 + 5*k**5/24 - 2*k**3 + 2*k**2 - 162*k. Let g(h) be the second derivative of p(h). Factor g(b).
-5*b*(b - 5)
Let w(a) be the first derivative of -4/15*a**5 - 4/3*a**2 - 2/9*a**6 + 4/9*a**3 + a**4 + 47 + 0*a. Suppose w(k) = 0. What is k?
-2, -1, 0, 1
Factor -164/3*z - 1/6*z**2 - 13448/3.
-(z + 164)**2/6
Let v be (36/8)/((-12)/(-24)) - 7. Solve 0 - 3/2*j + 3*j**v = 0.
0, 1/2
Factor 139129/2 + 1/2*p**2 - 373*p.
(p - 373)**2/2
What is t in 29/7*t**3 - 222/7*t**2 + 56 + 20*t - 1/7*t**4 = 0?
-1, 2, 14
Let k(n) be the second derivative of n**5/70 + 16*n**4/21 - 4*n**3/21 - 128*n**2/7 + 1703*n. Factor k(r).
2*(r - 2)*(r + 2)*(r + 32)/7
Let v be 27/(-54)*(-11 - -1). Suppose -97*r + 160*r**4 - 7*r**5 + 3*r**v - 593*r - 1432*r**3 - 3360*r**2 - 263*r - 811*r = 0. What is r?
-1, 0, 21
Let z be 10/(-680) - 31/(-868)*7. Let m = 15 + -11. Factor 4/17*u + 0 + 2/17*u**m - 2/17*u**2 - z*u**3.
2*u*(u - 2)*(u - 1)*(u + 1)/17
Let -560*x - 2/3*x**3 - 302/9*x**2 - 3096 = 0. What is x?
-18, -43/3
Let v(i) be the first derivative of -2*i**5/5 + 15*i**4 - 112*i**3 - 1280*i**2 + 12288*i - 3139. Solve v(k) = 0 for k.
-6, 4, 16
Suppose -375 = -5*a + 5*y - 35, 0 = 5*a - 3*y - 332. Factor -16 + 24*z - 20 - 16*z**3 + 3*z**4 + 14*z**2 - 20 - 17 + a.
(z - 3)**2*(z + 1)*(3*z - 1)
Factor 3*v**3 + 21/4*v**2 + 189/4 - 381/2*v.
3*(v - 7)*(v + 9)*(4*v - 1)/4
Suppose 0 = -236*t + 221*t + 2235. Suppose -p - 2*x = -38, 4*p = -5*x + 289 - t. Determine c so that p*c**3 - 84*c**2 - 48/5 + 264/5*c = 0.
2/5, 2
Let p(i) be the third derivative of 29*i**6/420 + 19*i**5/35 - 89*i**4/21 + 8*i**3/7 - 4520*i**2. Factor p(k).
2*(k - 2)*(k + 6)*(29*k - 2)/7
Let c(p) be the second derivative of -p**6/45 + 4*p**5/15 + 155*p**4/18 + 50*p**3 - 370*p - 5. Solve c(l) = 0.
-5, 0, 18
Suppose 17*m + 1605 = -7320. Let a be ((-25)/(m/28))/((-4)/(-14)). Factor -2/9*q**3 - a*q - 4 - 16/9*q**2.
-2*(q + 2)*(q + 3)**2/9
Let w = 4393/7749 - -5/1107. Let o(k) be the first derivative of w*k + 22 - 5/14*k**2 + 1/21*k**3. Solve o(m) = 0.
1, 4
Let q(c) be the third derivative of -c**6/120 + 14*c**5/15 - 279*c**4/8 + 243*c**3 - c**2 + 7427*c. Find m such that q(m) = 0.
2, 27
Suppose -2*r - 35*m + 33*m = -1672, -2*m - 1660 = -2*r. Let n be (-16)/(-10) - r/(-595). Factor 2000/13 + 60/13*d**2 - 2/13*d**n - 600/13*d.
-2*(d - 10)**3/13
Let a(m) be the first derivative of 1/8*m**4 - 144 + 31/6*m**3 + 33/2*m - 65/4*m**2. Suppose a(y) = 0. What is y?
-33, 1
Solve -702/7 + 15/7*x + 3/7*x**2 = 0 for x.
-18, 13
Let p be 143/66 + 3/(-12)*5. Let t(z) be the first derivative of 2/9*z**3 - p*z**2 - 22 + z. Factor t(m).
(m - 2)*(4*m - 3)/6
Let v(u) = -u**2 - 262*u - 9932. Let g be v(-46). Factor 0*p - 2/7*p**2 + 0 - 1/7*p**g + 3/7*p**3.
-p**2*(p - 2)*(p - 1)/7
Let b(s) be the third derivative of s**6/60 + 8*s**5/5 - 17*s**4/4 - 98*s**3/3 + 676*s**2. Factor b(i).
2*(i - 2)*(i + 1)*(i + 49)
Let u(i) = -155*i + 185. Let p be u(3). Let s be (-1568)/p - (-5 + 1). Let 0 + 0*c + s*c**2 + 24/5*c**3 + 3/5*c**4 = 0. What is c?
-4, 0
Let g(l) = 4*l + 4. Let p be g(-2). Let c be (p + 11 + -9)*2/(-16). Find x, given that 1/4*x**2 + 1/2*x + c = 0.
-1
Let c(u) be the first derivative of -u**6/9 + 4*u**5/3 - 11*u**4/3 - 16*u**3/3 + 21*u**2 + 36*u - 4827. Find z, given that c(z) = 0.
-1, 3, 6
Factor -249*p**3 + 2*p**2 - 91 + 89 + 557*p - 308*p.
-(p - 1)*(p + 1)*(249*p - 2)
Factor 1/4*j**2 + 91/2 - 93/4*j.
(j - 91)*(j - 2)/4
Let -120*n - 39/2*n**3 + 367/4*n**2 + 49 - 5/4*n**4 = 0. Calculate n.
-98/5, 1, 2
Let l = 106 - 101. Suppose -8*t + l*t = -21. Factor 16*u - 20*u**2 + t*u + 16*u**2 + 17*u - 36.
-4*(u - 9)*(u - 1)
Let y(q) be the second derivative of q**4/28 + 4*q**3/7 - 192*q**2/7 - 271*q. Determine b so that y(b) = 0.
-16, 8
Let r be (-2100)/(-500) - (2 - (-18)/(-10)). Let k(q) be the second derivative of -3/5*q**2 + 0 - 3/10*q**3 - 1/20*q**r - q. Let k(i) = 0. Calculate i.
-2, -1
Let h = -483959/24 - -20165. Let l(m) be the second derivative of 0*m**2 - 1/84*m**7 + h*m**4 + 21*m + 1/40*m**5 + 0*m**3 + 0 - 1/60*m**6. Factor l(p).
-p**2*(p - 1)*(p + 1)**2/2
Let s be (-8)/(-8) + (2 - 3). Let o = -191 + 959/5. Factor s*g**2 - 4/5*g**3 + 0 + o*g**4 + 0*g.
4*g**3*(g - 1)/5
Let n(p) be the third derivative of 5*p**8/336 - p**7/7 - p**6/12 + p**5 + 5*p**4/24 - 5*p**3 - 277*p**2. Let n(i) = 0. What i