7
Let u(z) be the first derivative of z**6/48 + z**5/5 + 19*z**4/32 + 19*z**3/24 + z**2/2 + 54*z + 90. Let q(d) be the first derivative of u(d). Factor q(p).
(p + 1)**2*(p + 4)*(5*p + 2)/8
Find n such that -12*n + 54696*n**3 - 27342*n**3 - 116*n + 263*n**2 - 225 - 192*n - 27348*n**3 = 0.
-45, -1/2, 5/3
Let v = -114151013/24764818 - -2463/22151. Let r = 1/559 - v. Solve -12*h**2 - 21/2*h**3 - r*h**4 - 3/4*h**5 - 27/4*h - 3/2 = 0.
-2, -1
Suppose -1832*z + 1829*z - 2*p = 2, 3*p = 2*z - 16. Factor -1/5*i**5 + 0*i + 0 + 1/5*i**4 - 1/5*i**z + 1/5*i**3.
-i**2*(i - 1)**2*(i + 1)/5
Suppose -8 = l + 2*j, l - 15*j = -12*j + 17. Let s(c) be the second derivative of 0*c**l - 3*c + 1/20*c**5 + 0 + 1/6*c**4 - 1/30*c**6 + 0*c**3. Factor s(g).
-g**2*(g - 2)*(g + 1)
Let v(b) be the first derivative of -b**4/48 + 7*b**3/12 - 49*b**2/8 + 65*b + 59. Let p(j) be the first derivative of v(j). Factor p(y).
-(y - 7)**2/4
Let l(i) be the third derivative of i**7/105 - 5*i**6/12 + 5*i**5/2 + 375*i**4/4 - 661*i**2 - 2*i. Let l(f) = 0. Calculate f.
-5, 0, 15
Suppose 20 - 16 = g. Factor f**2 + 106 + g*f**2 - f**3 - 106.
-f**2*(f - 5)
Let p = -132215/42 - -3148. Let s(u) be the second derivative of p*u**4 + 1/7*u**2 + 0 + 3*u - 2/21*u**3. Factor s(v).
2*(v - 1)**2/7
Let u(f) be the second derivative of f**5/10 - 7*f**4/3 + 25*f**3/3 - 12*f**2 - f + 1948. Factor u(s).
2*(s - 12)*(s - 1)**2
Let i(a) = -6*a**4 - 12*a**3 + 13*a**2 - 2*a - 7. Let n(r) = -2*r**4 - 4*r**3 + 4*r**2 - 2. Let y(s) = -4*i(s) + 14*n(s). Factor y(o).
-4*o*(o - 1)*(o + 1)*(o + 2)
Let l(n) be the second derivative of 31/20*n**5 + 0 + 68*n - 49/12*n**4 + 19/12*n**3 + 33/20*n**6 - 27/28*n**7 - 1/4*n**2. Find q such that l(q) = 0.
-1, 1/9, 1
Let m(o) be the second derivative of -o**4/15 - 266*o**3/15 - 524*o**2/5 - 990*o. Let m(b) = 0. Calculate b.
-131, -2
Let p(o) = -6*o**2 + 84*o - 878. Let y be 32/(-40) + (4 - 44/20). Let v(h) = -h**2 + 1. Let a(t) = y*p(t) - 4*v(t). Find x such that a(x) = 0.
21
Let q(p) = p**3 - 38*p**2 + 253*p - 580. Let i(n) = 2*n**3 - 77*n**2 + 503*n - 1155. Let c(y) = -4*i(y) + 9*q(y). Factor c(o).
(o - 24)*(o - 5)**2
Suppose 167 = 3*c - 13*k + 83, 5*c = 4*k + 34. Let v(u) be the first derivative of -1/3*u**3 - 46 + u**c + 0*u. Find o such that v(o) = 0.
0, 2
Let t be ((-9)/(-6) + -1)*110*(-68)/(-20570). Find a such that -258/11*a**2 - 159014/11 - t*a**3 - 11094/11*a = 0.
-43
Let s(t) be the first derivative of t**6/9 + 28*t**5/15 + 26*t**4/3 - 16*t**3/3 - 96*t**2 + 778. Suppose s(l) = 0. Calculate l.
-6, -4, 0, 2
Let f be 4/2*21/12*2 + -6. Let z(m) be the first derivative of 0*m - 4/9*m**3 - f - 2*m**2. Solve z(u) = 0 for u.
-3, 0
Let j(t) be the third derivative of 75*t**8/28 + 68*t**7/7 - 388*t**6/15 - 2032*t**5/15 - 248*t**4/3 - 64*t**3/3 - 1037*t**2. Find k, given that j(k) = 0.
-2, -2/15, 2
Let z = 1166/359 + -1255/718. Let 0 + 0*p**2 - z*p**3 + p**4 + 0*p + 1/2*p**5 = 0. What is p?
-3, 0, 1
Let y(m) = 79*m - 242. Let f be y(5). Factor -136*r**3 - 72*r**2 - 26*r**2 - 552*r + 458*r**2 + 337*r**2 + 144 - f*r**3.
-(r - 1)*(17*r - 12)**2
Let p(c) be the third derivative of 0*c**4 - 1/1008*c**8 + c**2 + 0*c**5 + 0*c - 1/90*c**6 + 26 + 0*c**3 - 2/315*c**7. Factor p(a).
-a**3*(a + 2)**2/3
Suppose -3*v = -76 - 32. Let i be v/75*(6 - (-39)/(-9)). Solve 4/5*p**3 + 2/5*p**2 + 0 - 2/5*p**4 - i*p = 0 for p.
-1, 0, 1, 2
Let z(i) be the third derivative of i**7/1680 + i**6/144 + i**5/80 - 3*i**4/16 + 71*i**3/6 - 19*i**2. Let m(t) be the first derivative of z(t). Factor m(w).
(w - 1)*(w + 3)**2/2
Let n = 76 + -71. Factor -21*w**2 - 20*w + 107 - 4*w**3 + n*w**2 - 115.
-4*(w + 1)**2*(w + 2)
Suppose 34*k - 8275 = 9*k. Suppose k = -11*d + 353. Solve -2/5*f**d + 4/5 + 2*f - 12/5*f**3 = 0.
-2/3, -1/2, 1
Determine o, given that -2565*o - 222*o + 2707 + 701 + 4*o**2 + 53*o - 678*o = 0.
1, 852
Let f = 617274 - 617271. Determine b, given that -6*b**2 + 6 + 3/7*b - 3/7*b**f = 0.
-14, -1, 1
Factor -19376 - 19*v + 38751 - 5*v**3 + 85*v**2 - 19375 - 61*v.
-5*v*(v - 16)*(v - 1)
Let a(g) be the first derivative of g**4/27 + 125*g**3/27 + 62*g**2/9 - 270*g + 297. Let f(c) be the first derivative of a(c). Factor f(j).
2*(j + 62)*(2*j + 1)/9
Let i(s) = -12*s**3 + 43*s**2 + 610*s + 3170. Let t(r) = r**3 - 2*r**2 + r - 1. Let n(o) = -2*i(o) - 22*t(o). Find b, given that n(b) = 0.
-9, 39
Let i(d) be the first derivative of 111/2*d**2 + 1/2*d**3 + 4107/2*d + 224. Factor i(n).
3*(n + 37)**2/2
Let q be 2/6 + 4/(24/(-3026)). Let l = 728 + q. Factor 12*o - 5 + 5 + 239*o**3 + 21*o**4 - 48*o**2 - l*o**3.
3*o*(o - 1)*(o + 2)*(7*o - 2)
Let q = 11 - 7. Let k(v) = 7*v**2 + 7398*v - 52129. Let w be k(7). Find z, given that 0 - 2*z**5 - 8/3*z**q + 2/3*z**3 + w*z + 4/3*z**2 = 0.
-1, 0, 2/3
Let w(a) be the first derivative of a**6/280 - 3*a**4/14 + 8*a**3/7 - 147*a**2/2 - 290. Let n(g) be the second derivative of w(g). Factor n(c).
3*(c - 2)**2*(c + 4)/7
Solve 52*x + 0 + 209/4*x**2 + 1/4*x**3 = 0.
-208, -1, 0
Let d(s) be the second derivative of -s**7/420 - s**6/120 + s**5/120 + s**4/24 - 109*s**2/2 + 108*s. Let g(o) be the first derivative of d(o). Factor g(p).
-p*(p - 1)*(p + 1)*(p + 2)/2
Let z be 8*(-272)/(-1536) + 2/(-3). Let d(f) be the second derivative of -3/80*f**5 - 1/8*f**4 + z*f**2 + 0 + 1/8*f**3 - 6*f. Let d(x) = 0. Calculate x.
-2, -1, 1
Let c(g) be the first derivative of 2*g**3/3 - 24*g**2 - 290*g - 6509. What is w in c(w) = 0?
-5, 29
Let w(l) be the first derivative of -l**5/30 - l**4/16 + l**3/12 - 2*l**2 + l - 52. Let k(u) be the second derivative of w(u). Factor k(c).
-(c + 1)*(4*c - 1)/2
Let k(y) be the first derivative of y**4/2 - 4*y**3/3 + y**2 + 2115. Factor k(o).
2*o*(o - 1)**2
Let a(t) be the first derivative of -188*t**3/3 - 238*t**2 - 288*t + 2246. Let a(d) = 0. Calculate d.
-72/47, -1
Let f(j) be the third derivative of j**7/3780 - j**6/30 + 9*j**5/5 + 41*j**4/24 + j**3/3 - 2*j**2 + 2. Let m(k) be the second derivative of f(k). Factor m(l).
2*(l - 18)**2/3
Let k(y) be the second derivative of y**7/210 - y**6/30 + y**5/15 - y**3/6 - 21*y**2 - 2*y - 18. Let f(u) be the second derivative of k(u). Factor f(m).
4*m*(m - 2)*(m - 1)
Let n be (((-200)/150)/(-1 - -2))/(-2 - -1). Let a(f) be the first derivative of 5/9*f**3 + 14 + n*f + 1/6*f**4 - 11/6*f**2. Factor a(k).
(k - 1)*(k + 4)*(2*k - 1)/3
Let a = -1464533/3 + 488178. Factor -5/3*u + 0 + a*u**2.
u*(u - 5)/3
Let i(r) = -9 + 0*r**3 + 14*r**2 - 12*r + r**3 - 26*r**2. Let k be i(13). What is d in -k*d + 16*d**2 - 12*d**2 - 8*d**2 = 0?
-1, 0
Let w = 1536 + -1532. Let l = 52/189 - -2/189. Factor l*v + 0 - 8/7*v**2 + 10/7*v**3 - 4/7*v**w.
-2*v*(v - 1)**2*(2*v - 1)/7
Let l be 7 + 1000/(-80)*(-4)/(-10) + 1. Let 0 + 6/7*c - 2/7*c**l - 4/7*c**2 = 0. Calculate c.
-3, 0, 1
Let b be -1 + 1 - (-37)/(2775/200). Let g be (16/(-60))/((-2)/100). Factor g*d + b + 1120/3*d**4 - 190/3*d**2 + 6272/3*d**5 - 1000/3*d**3.
2*(4*d + 1)**3*(7*d - 2)**2/3
Let s(y) be the first derivative of 56*y**5/9 + 149*y**4/18 + 2*y**3/3 - 2*y**2 + 37. Solve s(q) = 0.
-3/4, -3/5, 0, 2/7
Let p(i) be the second derivative of -i**4/6 + 29*i**3/3 - 28*i**2 - 766*i + 2. Let p(t) = 0. What is t?
1, 28
Let r(z) be the first derivative of 51/2*z**2 - 54*z + 82 + z**3. Factor r(a).
3*(a - 1)*(a + 18)
Let a = 569/3408 - 1/3408. Factor 0*m + 1/3*m**2 + 0 + 0*m**4 - a*m**5 + 1/2*m**3.
-m**2*(m - 2)*(m + 1)**2/6
Find k such that 2/13*k**3 + 596/13 + 898/13*k + 304/13*k**2 = 0.
-149, -2, -1
Solve -452/9*u**3 - 6*u**4 + 2560/9*u + 1024/3 - 304/3*u**2 - 2/9*u**5 = 0 for u.
-12, -8, -1, 2
Let i(f) be the first derivative of -8/3*f**3 + 0*f**2 - 1/720*f**6 - 8 + 1/80*f**5 - 1/24*f**4 + 0*f. Let y(x) be the third derivative of i(x). Solve y(u) = 0.
1, 2
Let t(m) be the third derivative of 0 - 160/3*m**3 + 0*m - 133*m**2 - 1/300*m**5 - 2/3*m**4. Factor t(v).
-(v + 40)**2/5
Let s(a) be the first derivative of 2/3*a**3 + 5*a**2 - 12*a - 15. Determine v, given that s(v) = 0.
-6, 1
Factor 1/8*f**3 + 4489/2*f + 67/2*f**2 + 0.
f*(f + 134)**2/8
Let c = 7/360 - -115337/360. Let d = c + -320. Factor 2/5*y**3 - 2/5*y + 2/5*y**4 + 0 - d*y**2.
2*y*(y - 1)*(y + 1)**2/5
Let n(h) be the second derivative of -h**6/10 + 3*h**5/10 + 9*h**4/4 - 9*h**3 + 2*h - 927. Factor n(a).
-3*a*(a - 3)*(a - 2)*(a + 3)
Let z(n) = -6*n**2 +