 o(u) be the first derivative of -1/7*u**3 - 41 + 3/14*u**2 + 0*u. Factor o(z).
-3*z*(z - 1)/7
Let j(n) be the first derivative of n**7/840 + n**6/12 + 5*n**5/2 + 125*n**4/3 - 23*n**3 - 72. Let z(g) be the third derivative of j(g). Factor z(m).
(m + 10)**3
Let s(n) be the third derivative of 0*n - 4*n**3 + 1/15*n**5 - 15*n**2 - 1/6*n**4 + 0. Find p, given that s(p) = 0.
-2, 3
Let p = 8 + 1. Suppose 0 = 2*i - p*i + 21. Suppose -4*f + i*f - 9*f - 100*f**4 + 25*f**2 + 85*f**3 = 0. Calculate f.
-2/5, 0, 1/4, 1
Suppose 11*p = 14*p - 9. Suppose p*k - 12 = -m - 5, -5*m - 13 = -k. Factor 2 - 4*s**2 + k*s**2 + 4*s + s**2 + 2*s**2.
2*(s + 1)**2
Let v(j) = -4*j**4 + 601*j**3 + 1228*j**2 + 630*j. Let a(x) = -x**4 + 201*x**3 + 409*x**2 + 209*x. Let s(g) = -14*a(g) + 4*v(g). Factor s(w).
-2*w*(w + 1)**2*(w + 203)
Let t = 1316 + -1312. Suppose 2 = 4*p + 3*f, -p + 115*f = 118*f + t. Factor -1/3*g + 1/6*g**p + 2/3*g**3 + 0 - 1/2*g**4.
-g*(g - 1)**2*(3*g + 2)/6
Let k(i) be the first derivative of -27*i**4/4 - 46*i**3 - 99*i**2/2 + 216*i - 3794. Factor k(t).
-3*(t + 3)**2*(9*t - 8)
Let i(g) be the third derivative of -2*g**7/315 - 4*g**6/15 - 23*g**5/45 + 2386*g**2. Factor i(k).
-4*k**2*(k + 1)*(k + 23)/3
Factor -147456/5 - 1/5*u**2 - 768/5*u.
-(u + 384)**2/5
Let n = 84912/5 + -16980. Let o(g) be the first derivative of n*g**5 + 32 + 4*g**3 - 1/2*g**6 + 0*g - 3/2*g**2 - 9/2*g**4. Factor o(b).
-3*b*(b - 1)**4
Let t(x) = 4*x + 216. Let b be t(-48). Let c(w) = -w**2 + 25*w - 18. Let n be c(b). Factor 1/3*o**2 + n*o + 27.
(o + 9)**2/3
Let p(h) be the first derivative of h**7/56 - 17*h**6/120 + 3*h**5/40 + 9*h**4/8 - 37*h**3 - 2. Let d(k) be the third derivative of p(k). Factor d(g).
3*(g - 3)*(g - 1)*(5*g + 3)
Let f be 46/4 + ((-594)/(-12))/(-33). Let w(g) = g**2 - 19*g + 92. Let u be w(f). Factor -13/5*n - 7/5*n**3 - 3/5 - 17/5*n**u.
-(n + 1)**2*(7*n + 3)/5
Let w(q) = -q**3 + 23*q**2 + 26*q - 40. Let t be w(24). Suppose -2*u = -14 + t. Factor -u*z**2 + 0*z - 14*z**2 + 5*z - 3*z**2.
-5*z*(4*z - 1)
Suppose 4*p = 2*p + 6, -5*n = 3*p - 19. Factor c**3 - 10*c**2 - 6*c + 17*c**2 - 12*c**n.
c*(c - 6)*(c + 1)
Suppose 3*s + 5 = -2*s + 5*i, -2*s - 3*i = -13. Suppose v - 4*w - 6 = 0, -s*v - 3*w = 2*w + 1. Factor -72*c + 75*c + c**v - c**2 - 3*c**2.
-3*c*(c - 1)
Let b(m) be the second derivative of m**6/135 - m**5/45 - 8*m**4/27 + 2*m**3/27 + 5*m**2/3 + 2499*m. Find i, given that b(i) = 0.
-3, -1, 1, 5
Factor -262 + 4*i**3 - 6*i + 315 + 172*i**2 + 2*i - 225.
4*(i - 1)*(i + 1)*(i + 43)
Let j be (9 + (-1050)/112)/((-27)/(-914)). Let x = -94/9 - j. Factor -3/4*w**2 - x - 15/4*w + 3/4*w**3.
3*(w - 3)*(w + 1)**2/4
Let y(b) be the first derivative of -136 + 17/3*b**2 + 0*b + 2/9*b**3. Factor y(r).
2*r*(r + 17)/3
Let u(z) be the second derivative of z**5/120 + 61*z**4/72 + 5*z**3/3 - 623*z + 1. Find v such that u(v) = 0.
-60, -1, 0
Let n(p) be the third derivative of 2*p**7/315 + 287*p**6/90 + 19*p**5/3 - 287*p**4/18 - 572*p**3/9 - 1084*p**2. Find o such that n(o) = 0.
-286, -1, 1
Let r(t) be the second derivative of t**6/165 - 19*t**5/110 + 4*t**4/3 - 33*t + 64. Factor r(h).
2*h**2*(h - 11)*(h - 8)/11
Let s(f) be the third derivative of f**5/300 + 41*f**4/15 - 16*f**2 - 23. Factor s(l).
l*(l + 328)/5
Suppose 55*t - 34*t = 40*t. Let h(s) be the third derivative of 4/105*s**7 + 0*s**3 + t - 1/4*s**6 + 33*s**2 + 0*s + 1/3*s**4 + 2/5*s**5. Factor h(w).
2*w*(w - 2)**2*(4*w + 1)
Solve -1/8*j**2 + 55/4 - 1/8*j = 0 for j.
-11, 10
Let r(k) be the third derivative of k**6/24 - 22*k**5/3 - 1000*k**4/3 - 16640*k**3/3 - 501*k**2 - 6*k - 2. Solve r(o) = 0 for o.
-8, 104
Let n be 2 - (6/(-14))/((-54)/(-378)). Let s(a) be the first derivative of 0*a + 10 - 5*a**3 - 5/4*a**4 - n*a**2. Factor s(u).
-5*u*(u + 1)*(u + 2)
Let x(p) be the second derivative of -3*p**5/100 + 41*p**4/20 + 37*p**3/2 - 135*p**2/2 + 3402*p. Solve x(v) = 0 for v.
-5, 1, 45
Solve 7*c**5 - 5*c**5 + 43*c**4 + 3*c**4 + 437*c + 12*c**4 - 332*c**2 - 174 + 21*c - 12*c**3 = 0 for c.
-29, -3, 1
Let j(o) be the first derivative of 0*o + 11/32*o**4 - 3/4*o**3 + 14 - 3/80*o**5 + 1/2*o**2. Let l(z) be the second derivative of j(z). Factor l(m).
-3*(m - 3)*(3*m - 2)/4
Suppose -836 + 188 = -6*i. Factor 252*t**2 - 410*t + 8*t**4 - 26*t**3 - 50*t**3 + 86*t + i.
4*(t - 3)**3*(2*t - 1)
Let b = 9366/8525 - 6/775. Let r be 105/627 - 234/(-2223). Solve r*w - 6/11*w**4 - 10/11*w**2 + b*w**3 + 0 + 1/11*w**5 = 0.
0, 1, 3
Let v be (6/(-10) - 57822/230)/1. Let u be (v/168)/((-7)/(-10) - 1). Find y, given that -3*y**2 - u*y + 25/3 - 1/3*y**3 = 0.
-5, 1
Solve -2450*y**2 + 283*y + 8*y**4 - 283*y - 10*y**4 + 140*y**3 = 0.
0, 35
Suppose -4*w - 10 = b, -5*w = -1175*b + 1173*b + 32. Factor -b*k**2 - 45*k - 1/5*k**3 + 0.
-k*(k + 15)**2/5
Factor -16/5*v + 2/5*v**3 + 0 + 14/5*v**2.
2*v*(v - 1)*(v + 8)/5
Let u(o) = 16*o**2 + 256*o + 244. Let w(l) = -13*l**2 - 254*l - 244. Let r(s) = -3*u(s) - 4*w(s). Suppose r(j) = 0. Calculate j.
-61, -1
Suppose 2*d - 3*d + 29 = 3*l, -5*l + d = -59. Let p be (-14)/(-6) - ((-66)/(-18))/l. Factor 0 - 1/3*c**p - 1/3*c.
-c*(c + 1)/3
Let r = -214 + 219. Factor -9*m - r*m - 3*m + 5*m**2 + 5*m**3 - 45 - 28*m.
5*(m - 3)*(m + 1)*(m + 3)
Let f = 483582 - 483582. Let 0*z + 8/3*z**2 - 32/3*z**4 + f - 4*z**3 - 4*z**5 = 0. Calculate z.
-2, -1, 0, 1/3
Solve -16*j - 168/5 + 2/5*j**2 = 0.
-2, 42
Let j be 5337/(-297) + (-90)/(-15) - -12. Let s(d) be the third derivative of 3*d**2 + 0*d - j*d**4 + 1/330*d**5 + 4/33*d**3 + 0. Solve s(a) = 0.
2
Let u(i) = 15*i**2 + 220*i + 855. Let s(y) = 8*y**2 + 113*y + 429. Let d(a) = -5*s(a) + 3*u(a). Factor d(z).
5*(z + 7)*(z + 12)
Let d = 386048 - 386045. Determine y so that -d - 23/3*y**3 - 4/3*y**4 - 43/3*y**2 - 11*y = 0.
-3, -1, -3/4
Let a(i) be the third derivative of 3*i**7/1120 + 13*i**6/240 + i**5/10 + 26*i**3/3 + 7*i**2 + 1. Let z(k) be the first derivative of a(k). Factor z(f).
3*f*(f + 8)*(3*f + 2)/4
What is t in -5/4*t + 1 + 1/4*t**2 = 0?
1, 4
Let v be (-4)/(-10) - (-32)/20. Let m = -4050 + 4050. Factor 24/5*b + m + 18/5*b**3 + 3/5*b**4 + 36/5*b**v.
3*b*(b + 2)**3/5
Let z(g) be the second derivative of g**4/90 - 7*g**3/15 + 22*g**2/3 + 905*g. Find m such that z(m) = 0.
10, 11
Factor 694/7*z**2 - 44/7*z**3 + 1575 - 660*z + 1/7*z**4.
(z - 15)**2*(z - 7)**2/7
Let t(h) be the third derivative of h**7/1365 - 7*h**6/130 + 157*h**5/390 - 16*h**4/13 + 76*h**3/39 - 6*h**2 - 4*h - 9. Solve t(o) = 0.
1, 2, 38
Let i = -68 + 74. Let f be 1 + 69*i/126 + -4. Find z, given that -f*z + 0 + 8/7*z**2 + 8/7*z**4 - 2/7*z**5 - 12/7*z**3 = 0.
0, 1
Let d be (-131)/(-21) - (-979)/(-267). Factor d*r + 6/7*r**2 - 2/7*r**3 + 10/7.
-2*(r - 5)*(r + 1)**2/7
Let h be ((-3)/3)/(-3 - -1). Let d = -3482362 + 3482364. Factor -3/2*l + 3/2*l**3 + 1 - h*l**d - 1/2*l**4.
-(l - 2)*(l - 1)**2*(l + 1)/2
Let s(a) be the third derivative of a**7/1050 + 47*a**6/150 + 187*a**5/300 - 988*a**2. Factor s(c).
c**2*(c + 1)*(c + 187)/5
Let q(m) be the third derivative of m**7/315 - m**6/30 + 11*m**5/90 - m**4/6 + 330*m**2. Solve q(d) = 0.
0, 1, 2, 3
Let o = -704 + 829. Let p(b) be the first derivative of 1/4*b**4 + 75/2*b**2 + 14 + o*b + 5*b**3. What is v in p(v) = 0?
-5
Let g = 61836/5 + -247329/20. Let 0*l + 9/4*l**3 + 0 - g*l**4 - 3/2*l**2 = 0. Calculate l.
0, 1, 2
Let n(r) be the second derivative of 0 - 40*r - 13/21*r**3 + 13/70*r**5 + 11/42*r**4 - 12/7*r**2 + 1/105*r**6. Suppose n(u) = 0. What is u?
-12, -1, 1
Let z(v) be the second derivative of v**6/96 + 13*v**5/96 - 25*v**4/48 - 47*v**3/2 + v - 8. Let f(t) be the second derivative of z(t). What is o in f(o) = 0?
-5, 2/3
What is n in -96/7*n**2 - 2/7*n**3 + 206/7*n + 300/7 = 0?
-50, -1, 3
Let u(l) be the first derivative of 0*l - 1/14*l**4 - 4/105*l**5 + 180 + 1/63*l**6 + 8/63*l**3 + 4/21*l**2. What is s in u(s) = 0?
-1, 0, 2
Let y(a) be the first derivative of -a**3/15 - 50*a**2 - 12500*a + 1084. Suppose y(m) = 0. Calculate m.
-250
Suppose 0 = 253*i - 251*i - 4. Suppose -8*v**i - v**2 + 12 + 10*v**2 + 7*v = 0. Calculate v.
-4, -3
Suppose 252*j**3 - 235*j**4 + 996*j**2 + 39*j**5 - 432 - 1116*j - 129*j**3 + 13*j**4 = 0. What is j?
-2, -4/13, 2, 3
Let j be 36*(-36)/(-1728) - (-61)/(-92). Suppose -8/23*b + 4/23*b**2 + 8/23*b**3 - 6/23 + j*b**4 = 0. What is b?
-3, -1, 1
Let n = 835988 - 4179903