)**2
Factor 573 - 570*y + 561/4*y**2 + 3/4*y**3.
3*(y - 2)**2*(y + 191)/4
Let i(u) be the third derivative of 10*u**2 - 1/60*u**6 - 1/4*u**4 + 1/10*u**5 + 2*u + 1/3*u**3 + 0. What is c in i(c) = 0?
1
Let z(j) be the third derivative of j**5/12 + 815*j**4/24 + 805*j**3/3 - 2924*j**2. Factor z(c).
5*(c + 2)*(c + 161)
Let c(k) = -k**3 - 27*k**2 + k + 27. Suppose 0 = 11*t + 5 - 49. Let b(l) = -5*l**3 - 108*l**2 + 5*l + 108. Let h(f) = t*b(f) - 18*c(f). Factor h(x).
-2*(x - 27)*(x - 1)*(x + 1)
Let s = 11/1267 + 1201/7602. Let p(r) be the second derivative of 2/9*r**3 + 0 + r + s*r**4 + 1/30*r**5 + 0*r**2. Factor p(u).
2*u*(u + 1)*(u + 2)/3
Let u = 28267/18850 + 4/9425. Determine q, given that -49/8*q + u + 1/2*q**2 = 0.
1/4, 12
Suppose -2*p = 2*i + 4, p + 11 = -2*i + 4*i. Suppose n + 1 - 2 = l, -4*l = i*n - 10. Factor -h**n - 263*h - 324 + 191*h - 3*h**2.
-4*(h + 9)**2
Factor -85 - 4*j**2 + 2*j + 33*j - 110*j - 49*j + 349.
-4*(j - 2)*(j + 33)
Let m(g) = 57*g**3 + 511*g**2 - 995*g + 537. Let r(k) = -31*k**3 - 256*k**2 + 497*k - 270. Let o(v) = 6*m(v) + 11*r(v). Find h, given that o(h) = 0.
-252, 1
Let u(n) be the first derivative of -3/5*n**2 - 1/5*n**3 + 36 + 3/10*n**4 + 0*n + 3/25*n**5. Find d, given that u(d) = 0.
-2, -1, 0, 1
Let y = -336 - -358. Let b(h) = -5*h + 110. Let w be b(y). Factor -1/3*l + w - 5/3*l**2 - 4/3*l**3.
-l*(l + 1)*(4*l + 1)/3
Let v be 17/(10829/52)*28. Let i be -6 + 2 + (1 - -5). Factor 1/7*k**i + 8/7*k + v.
(k + 4)**2/7
Let n(s) = s**3 - 37*s**2 - 244*s + 7830. Let p be n(38). Factor r**3 + r**5 - 5/2*r**4 + 1/2 - p*r + 2*r**2.
(r - 1)**3*(r + 1)*(2*r - 1)/2
Let x(c) be the third derivative of -2 + 0*c - 1/24*c**6 + 5/2*c**4 + 0*c**3 - 11*c**2 - 11/12*c**5. Factor x(o).
-5*o*(o - 1)*(o + 12)
Let f(j) be the first derivative of -j**6/10 - 27*j**5/25 - 33*j**4/10 - 6*j**3/5 + 69*j**2/10 + 9*j - 2697. Determine w so that f(w) = 0.
-5, -3, -1, 1
Let j(h) be the first derivative of 24*h + 1/2*h**3 - 15 - 15/2*h**2. Solve j(l) = 0 for l.
2, 8
Let x(l) be the third derivative of -l**6/84 - 151*l**5/105 - 10*l**4/7 - 26*l**2 - 16*l. Factor x(j).
-2*j*(j + 60)*(5*j + 2)/7
Let w(s) be the first derivative of 2*s**4/13 - 178*s**3/39 + 362*s**2/13 - 170*s/13 - 1535. Solve w(r) = 0 for r.
1/4, 5, 17
Let f(u) = 8*u**2 + 4*u - 16. Let q(z) be the third derivative of 3/8*z**4 - 31/6*z**3 + 0*z + 0 + 1/4*z**5 - 11*z**2. Let s(i) = 7*f(i) - 4*q(i). Factor s(p).
-4*(p - 1)*(p + 3)
Let v be (-3 - -10) + 8766/45. Let x = -201 + v. Let 0*q - x + 4/5*q**2 = 0. Calculate q.
-1, 1
Let k = 78406/9 - 8711. Let q(y) be the second derivative of -49/6*y**2 - 1/36*y**4 - 8*y + 0 - k*y**3. Let q(j) = 0. What is j?
-7
Let p(h) be the second derivative of -h**4/32 + 369*h**3/16 + 837*h**2/4 - 1480*h. Let p(s) = 0. What is s?
-3, 372
Let i = 2567/8457 + 84/2819. Find n, given that -i*n**2 - 8/3*n + 3 = 0.
-9, 1
Find r, given that -39*r**2 + 1040*r**4 + 1035*r**4 + 528*r - 72*r**3 - 432 + 11*r**2 - 2071*r**4 = 0.
-3, 1, 2, 18
Let s(i) = -18*i**2 + 15*i + 1. Suppose 0 = -2*p - 28 + 24. Let z(o) = o**2. Let l(g) = p*z(g) - s(g). Factor l(m).
(m - 1)*(16*m + 1)
Let b(w) be the second derivative of -2/25*w**5 + 4/15*w**3 - 50*w + 0 - 8/5*w**2 + 1/4*w**4 + 1/150*w**6. Factor b(g).
(g - 4)**2*(g - 1)*(g + 1)/5
Suppose 0*m - 5*m + 35 = 0. Suppose m - 19 = -4*i. Factor i*a**4 + 4*a**4 - 16*a**2 - 10*a**3 - 9*a**4 - 8*a.
-2*a*(a + 1)*(a + 2)**2
Solve 91/3 - 215/6*v - 1/6*v**3 + 17/3*v**2 = 0 for v.
1, 7, 26
Let g(b) = -b. Let o(u) = -u**2 + 45*u + 87. Let r(l) = 5*g(l) - o(l). Let z(d) = -5*d**2 + 300*d + 525. Let j(t) = -35*r(t) - 6*z(t). Let j(q) = 0. What is q?
-7, -3
Let w be (-4)/(-5)*(-9 + 138/12). Determine b, given that 12*b**w - 8*b**3 - 4*b**3 - 18*b + 11*b**2 + 0*b**2 + 10*b**2 = 0.
0, 3/4, 2
Determine h, given that 307 - 4*h**4 + 19*h - 589 + h**3 - 9*h**3 + 32*h**2 + 318 + 53*h = 0.
-3, -1, 3
Let m(l) be the third derivative of 0*l**3 + 4/175*l**7 + 0*l + 1/420*l**8 - 2/25*l**5 + 2/75*l**6 - 1/6*l**4 - l**2 + 36. Solve m(a) = 0 for a.
-5, -1, 0, 1
Let 4/15*v**3 - 8/15*v**2 + 2/15*v**4 + 0 - 16/15*v = 0. Calculate v.
-2, 0, 2
Let v(b) = 51*b - 202. Let w be v(4). Let m(d) be the first derivative of 1/18*d**3 + 1/3*d - 1/4*d**w - 6. Factor m(z).
(z - 2)*(z - 1)/6
Let j(y) be the second derivative of 5*y**7/147 + 104*y**6/105 - 13*y**5/35 - 52*y**4/21 + y**3 + 783*y + 3. Let j(b) = 0. Calculate b.
-21, -1, 0, 1/5, 1
Let g(l) = 8*l**3 - 207*l**2 - 565*l. Let h(t) = 3*t**3 - 69*t**2 - 186*t. Let n(s) = -6*g(s) + 17*h(s). Factor n(u).
3*u*(u + 4)*(u + 19)
Let m(z) be the third derivative of -z**7/70 - 3*z**6/20 + 3*z**5/4 - z**4 + 198*z**2 - 1. Find j such that m(j) = 0.
-8, 0, 1
Factor -164/3*i - 128/3 + 14/3*i**3 - 22/3*i**2.
2*(i + 1)*(i + 2)*(7*i - 32)/3
Let z(l) be the first derivative of 5*l**5/42 - 9*l**4/28 + 2*l**3/21 - 5*l**2/2 + l - 1. Let n(u) be the second derivative of z(u). What is o in n(o) = 0?
2/25, 1
Factor -6*t**2 - 5/2*t**3 - 40 + 1/2*t**4 + 38*t.
(t - 5)*(t - 2)**2*(t + 4)/2
Let t(b) be the second derivative of b**4/30 - b**3/5 - 8*b**2 + b + 1122. Let t(v) = 0. What is v?
-5, 8
Let j be (225/(-350))/(9/(-7)). Factor 1/4*a**4 - j*a**3 - 3/4*a**2 + a + 1.
(a - 2)**2*(a + 1)**2/4
Suppose 173876614/15 - 2/15*r**3 - 392498/5*r + 886/5*r**2 = 0. What is r?
443
Let w(q) be the second derivative of 33/5*q**5 - 2*q + 32*q**2 - 3 + 56*q**3 + 8/15*q**6 + 88/3*q**4. Factor w(t).
4*(t + 2)**2*(t + 4)*(4*t + 1)
Factor 387/4*b + 1/4*b**2 - 387/4*b**3 - 1/4.
-(b - 1)*(b + 1)*(387*b - 1)/4
Let b(j) be the first derivative of -3*j**5 + 95 + 0*j - 3/4*j**6 - 10/3*j**3 - 37/8*j**4 - j**2. Determine g so that b(g) = 0.
-1, -2/3, 0
Let m(d) be the third derivative of -d**6/1020 - 9*d**5/34 - 2025*d**4/68 - 30375*d**3/17 - 148*d**2 - d - 11. Solve m(r) = 0 for r.
-45
Solve -2/7*d**5 + 50/7*d + 0 - 48/7*d**3 + 20/7*d**2 - 20/7*d**4 = 0.
-5, -1, 0, 1
Let i be (35/35 + (-2)/2)/3. Let s(k) be the third derivative of 1/230*k**5 - 1/69*k**4 + 0 + i*k**3 + 13*k**2 + 1/1380*k**6 + 0*k. Suppose s(p) = 0. What is p?
-4, 0, 1
Let n(m) = 5*m**4 + m**2 + m + 1. Let y(l) = 19*l**4 - 9*l**3 - 20*l**2 - 16*l + 4. Let s(f) = 4*n(f) - y(f). Suppose s(h) = 0. Calculate h.
-5, -2, 0
Let w(o) be the third derivative of 5*o**8/336 + 11*o**7/14 + 29*o**6/4 + 83*o**5/3 + 45*o**4 - 1453*o**2. Suppose w(y) = 0. What is y?
-27, -2, 0
Let h(f) = 2*f**3 + 156*f**2 + 268*f + 183. Let d(o) = 3*o**3 + 179*o**2 + 268*o + 184. Let s(z) = -3*d(z) + 4*h(z). Factor s(g).
-(g - 90)*(g + 1)*(g + 2)
Suppose 0 = 2*s + 4*c - 32, 15*s - 17*s + 7*c = 34. Suppose 0 - 3/2*p + 3/2*p**2 + 3/2*p**3 - 3/2*p**s = 0. Calculate p.
-1, 0, 1
Find d such that 2/11*d**2 + 0 + 1022/11*d = 0.
-511, 0
Let o(c) be the third derivative of -c**5/120 - 43*c**4/48 - 55*c**3/2 + 2*c**2 + c + 535. Determine i so that o(i) = 0.
-33, -10
Let q = -1360 - -1999. Solve -q - 2*g**4 - 4*g**2 - 6*g**3 + 639 = 0 for g.
-2, -1, 0
Let x(v) be the third derivative of v**5 - 55/24*v**4 + 0*v**3 + 0 + 3*v - 2*v**2 - 1/24*v**6. Determine r so that x(r) = 0.
0, 1, 11
Let c(w) be the third derivative of 0*w - 4/15*w**5 - 14 + w**2 - 8/3*w**3 + 1/42*w**7 + 2*w**4 - 1/10*w**6. Solve c(p) = 0.
-2, 2/5, 2
Let u(g) be the third derivative of -g**8/3360 + g**7/630 - g**6/360 + 29*g**4/8 + 3*g**2 - 5*g. Let w(p) be the second derivative of u(p). Factor w(s).
-2*s*(s - 1)**2
Let j(l) = l**2 - 32*l + 23. Let t be j(23). Let b be (t/12)/(4/(-6)). Solve 5*k**5 + 10*k**2 + b*k**4 - 3*k**4 + 7*k**3 + 18*k**3 = 0.
-2, -1, 0
Let l be 3/(-12) - 39/(-12). Let q = 3369 + -3364. Factor 166*m - 166*m - q*m**l.
-5*m**3
Factor -464/5*x + 156/5 - 12/5*x**2.
-4*(x + 39)*(3*x - 1)/5
Let s be (-1)/8 + -122*13/(-9360). Let i(w) be the second derivative of 0 + 0*w**4 + 1/135*w**6 + 0*w**2 + 16*w + 0*w**3 - s*w**5. Factor i(q).
2*q**3*(q - 4)/9
Let q(j) be the second derivative of -j**6/840 - 11*j**5/420 - 4*j**4/21 - 2*j**3/3 - 24*j**2 - 64*j. Let o(a) be the first derivative of q(a). Factor o(g).
-(g + 2)**2*(g + 7)/7
Let h(x) = 4*x - 44. Let v be h(20). Let c be (v/60)/((-2)/(-70)). Solve 4*z**2 - c - 6*z**3 - z**4 - 6*z**2 + z**2 + 5 + 24*z = 0.
-4, 1
Let t = -9268 + 9272. Let w(i) be the second derivative of -23*i + 2/9*i**3 + 0 + 4*i**2 - 1/9*i**t. Factor w(o).