/12*3. Factor 8*m**3 + r*m**3 + 2*m**3 - 23*m**3 - 3*m**2.
-3*m**2*(m + 1)
Suppose b = 6*b - 34*b + 116. Let w(s) be the second derivative of -5/24*s**3 + 0 + 5/48*s**4 - 15/4*s**2 + b*s. Solve w(v) = 0.
-2, 3
Let l(n) be the third derivative of n**6/360 + n**5/18 + 25*n**4/72 - 75*n**2 - 1. Factor l(h).
h*(h + 5)**2/3
Suppose 14 - 44 = 6*h. Let c(r) = 40*r**4 + 205*r**3 + 260*r**2 + 105*r + 20. Let p(t) = -t**4 - t**3 - t + 1. Let b(x) = h*p(x) + c(x). Solve b(y) = 0.
-3, -1, -1/3
Let v = 339 + -334. Suppose 0 = -3*i + 113 + 7. Factor v*b**2 + 43*b - 93*b + i*b.
5*b*(b - 2)
Let u(n) be the first derivative of 91 - 5*n**3 + 5/6*n**6 + 0*n + 0*n**2 + 3*n**5 - 5/4*n**4. Suppose u(w) = 0. What is w?
-3, -1, 0, 1
Suppose -5*l + 6*b = 10*b - 27, 5*l - 12 = b. Solve 752*g**2 - 64 + 392*g**4 + 1532*g**l - 674*g - 196*g**5 + 562*g - 144*g**3 = 0 for g.
-1, -2/7, 2/7, 4
Suppose 3*l - p = 13, 10*l - 6*l - 24 = 3*p. Factor -37*b**l - 136*b**2 + 176*b**2 + 5*b**5 + 107*b**3 + 35*b**4.
5*b**2*(b + 1)*(b + 2)*(b + 4)
Let m(o) be the first derivative of -15*o**4/4 - 175*o**3/3 + 40*o**2 - 80*o + 92. Let q(w) be the first derivative of m(w). Factor q(s).
-5*(s + 8)*(9*s - 2)
Let h(d) be the third derivative of -d**8/168 - 34*d**7/105 - 77*d**6/12 - 242*d**5/5 + 467*d**2. Factor h(w).
-2*w**2*(w + 11)**2*(w + 12)
Let t(c) = -11*c**4 + 25*c**3 + 235*c**2 + 383*c + 192. Let h(v) = -3*v**4 - v**3 - v + 3. Let n(a) = 4*h(a) - t(a). Determine j so that n(j) = 0.
-15, -12, -1
Let u be (-2431)/(-572) - (-27)/(-12). Determine y so that 0 + 8/7*y - 6/7*y**3 - 4/7*y**u + 1/7*y**4 + 1/7*y**5 = 0.
-2, 0, 1, 2
Let u = -542 + 544. Factor -8*p**2 + 4*p**u - 3*p - 2*p**3 + 3*p**3 + 18.
(p - 3)**2*(p + 2)
Let a(g) be the first derivative of -5*g**6/21 - 34*g**5/35 + g**4 + 136*g**3/21 + 24*g**2/7 + 573. Find r such that a(r) = 0.
-3, -2, -2/5, 0, 2
Let o be 3/3 + (-3)/(-1). Suppose 22*g - 91*g + 270 = -213. Factor -9*y**2 + 8*y**2 - 12*y**3 - g*y**o + 20*y**3.
-y**2*(y - 1)*(7*y - 1)
Let w(m) = -3*m**5 - 2*m**4 - m**3 + m**2 + 1. Let b(t) = 20*t**5 + 22*t**4 + 16*t**3 - 16*t**2 - 12*t - 6. Let q(v) = b(v) + 6*w(v). Find s such that q(s) = 0.
-3, -2, -1, 0, 1
Suppose -5*t = -2*g - 15, 4*t - 2*g + 2 = 14. Factor 1 + 2*o**t + 12*o**2 + 8*o + 2*o**3 - 1.
4*o*(o + 1)*(o + 2)
Factor -18*o**2 - 110*o + 30*o**2 + 105 - 7*o**2.
5*(o - 21)*(o - 1)
Factor 3773934*m - 3773934*m + 2*m**4 + 6*m**2 - 8*m**3.
2*m**2*(m - 3)*(m - 1)
Let b = 1349285/867357 - 7/96373. Factor 98/9*j**3 - 22/3*j - b*j**2 - 2.
2*(j - 1)*(7*j + 3)**2/9
Let z = 13465 - 13462. Let 2/5*x**z + 2/5*x**2 + 0*x + 0 = 0. What is x?
-1, 0
Let x(o) = -o**2 - 47*o + 239. Let l(c) = -c - 8. Let t be l(-2). Let b = -181 + 177. Let w(v) = 46*v - 240. Let r(f) = b*x(f) + t*w(f). Factor r(k).
4*(k - 11)**2
Let z = 392452/81765 - -4/16353. Factor 3*i**3 - z*i - 3/5*i**5 - 12/5 - 3/5*i**2 + 3/5*i**4.
-3*(i - 2)**2*(i + 1)**3/5
Suppose 4*f**2 - 11451477 - 8104781 - 4*f**2 - 2*f**2 - 12508*f = 0. What is f?
-3127
Let l(d) be the first derivative of d**4/6 - 646*d**3/9 + 8640*d**2 + 17496*d + 1059. Let l(i) = 0. Calculate i.
-1, 162
Let f = -4853/4085 + 1134/817. Let f + 3/5*y**2 - 1/5*y**3 - 3/5*y = 0. What is y?
1
Suppose -131*k = -321*k + 570. Let x(o) be the third derivative of 2/33*o**k + 0 + 2/165*o**5 - 16*o**2 - 1/660*o**6 + 0*o - 5/132*o**4. What is j in x(j) = 0?
1, 2
Let r be 0/(((-18)/(-21))/(4/14)). Let v(b) = -b + 7. Let z be v(r). Determine o so that 8*o**3 + z + 15*o**4 - 36*o**2 + 9 - 3*o**4 = 0.
-2, -2/3, 1
What is o in 1/3*o**3 - 25/3*o**2 + 0 + 0*o = 0?
0, 25
Let k(s) be the third derivative of 2*s**7/105 - 11*s**6/30 + 8*s**5/5 - 93*s**2 + 4. Factor k(f).
4*f**2*(f - 8)*(f - 3)
Suppose 5*o + 25 = 0, -14*g + 15*g + 2*o + 10 = 0. Let p(a) be the second derivative of 16/15*a**3 + 64/5*a**2 + g + 1/30*a**4 + 12*a. Factor p(j).
2*(j + 8)**2/5
Let z(c) = 23*c**4 - 450*c**3 - 704*c**2 + 1097*c - 17. Let r(o) = -8*o**4 + 152*o**3 + 234*o**2 - 366*o + 6. Let p(l) = 17*r(l) + 6*z(l). Factor p(f).
2*f*(f - 60)*(f - 1)*(f + 3)
Let c(b) = 1. Let k(d) = -3*d**3 + 3*d**2 - 3*d - 3. Let r(u) = -2*c(u) - k(u). Let a be r(2). Factor -30*j - 2*j**2 - 14*j + 30 - 3*j**2 + a*j.
-5*(j - 1)*(j + 6)
Let z(h) be the third derivative of h**5/330 - 13*h**4/66 + 133*h**3/33 - 32*h**2. Factor z(g).
2*(g - 19)*(g - 7)/11
Let i(t) be the first derivative of 5/6*t**6 + 6*t**5 + 0*t + 20*t**3 + 10*t**2 - 124 + 65/4*t**4. Factor i(o).
5*o*(o + 1)**2*(o + 2)**2
Factor -25000 + 995/2*d**2 - 5/2*d**3 - 24500*d.
-5*(d - 100)**2*(d + 1)/2
Suppose 0 = -f + 4*x + 604, -x - 460 = -2*f + 727. What is k in f*k**2 + 162*k**4 - 1476*k**3 - 931*k + 64 + 1427*k + 162*k**4 = 0?
-2/9, 1, 4
Let v = -19/45 - -17/36. Let q(j) be the third derivative of -v*j**5 + 0 - 5*j**2 - j**3 + 0*j + 3/8*j**4. Suppose q(m) = 0. What is m?
1, 2
Let j(i) be the second derivative of -5/12*i**4 + 36 + 25/6*i**3 + 35*i**2 + 2*i. Let j(d) = 0. Calculate d.
-2, 7
Let g = 5054/8115 - 37/1623. Factor -1/5 + 4/5*d - g*d**2.
-(d - 1)*(3*d - 1)/5
Let v(l) = -15*l**3 + 48*l**2 + 444*l - 1100. Let s(m) = -4*m**3 - 3. Let p(o) = 4*s(o) - v(o). What is c in p(c) = 0?
-34, -16, 2
Let a(h) be the second derivative of -1/34*h**5 - 24/17*h**2 + 136*h + 0 - 44/51*h**3 + 19/51*h**4. Suppose a(x) = 0. Calculate x.
-2/5, 2, 6
Factor 5*r**4 - 1635*r**2 - 3046*r**2 + 3940*r + 2246*r**2 + 470*r**3 - 1980.
5*(r - 2)**2*(r - 1)*(r + 99)
Let 3 + 175232/3*a**5 + 27340/3*a**2 + 314*a + 47384*a**3 + 89984*a**4 = 0. Calculate a.
-1/2, -3/148
Let p(r) = 55*r**4 + 230*r**3 + 90*r**2 - 1690*r + 650. Let m(t) = 3*t**4 - t**3 - t**2 - t + 1. Let g(o) = 10*m(o) - p(o). Determine l, given that g(l) = 0.
-8, -4, 2/5, 2
Let n(i) be the first derivative of 2*i**3/33 + 34*i**2/11 + 6*i + 1180. Factor n(u).
2*(u + 1)*(u + 33)/11
Suppose 0 = -430*x + 2215*x + 1039 - 8179. Factor 14/3*d + x - 10/3*d**2.
-2*(d - 2)*(5*d + 3)/3
Let c(z) be the third derivative of z**7/60 + 113*z**6/240 + 401*z**5/120 + 55*z**4/48 + 718*z**2. Factor c(g).
g*(g + 5)*(g + 11)*(7*g + 1)/2
Let w(c) be the first derivative of -4*c**5/5 - 3*c**4 - 4*c**3 - 2*c**2 + 1485. Factor w(x).
-4*x*(x + 1)**3
Let d be (-32)/(-24)*(-9)/(-6). Let w be d + 3 - 33/11. What is s in 7 + 9*s**2 - 12*s - 2*s**3 - 1 - w = 0?
1/2, 2
Let f(b) be the third derivative of -1/24*b**6 - 105/2*b**4 - 176*b**2 + 0*b - 17/6*b**5 + 0 + 540*b**3. Suppose f(g) = 0. What is g?
-18, 2
Let d(f) be the third derivative of 0*f + 0 + 1/30*f**5 + 7/30*f**4 - 1/5*f**3 + 34*f**2. Factor d(b).
2*(b + 3)*(5*b - 1)/5
Let m(o) be the third derivative of 9/160*o**6 - 1/448*o**8 - 271*o**2 - 1/4*o**4 + 0*o - 31/240*o**5 + 5/6*o**3 + 11/840*o**7 + 0. Find k such that m(k) = 0.
-2, -1, 2/3, 1, 5
Let z = 19 - 12. Suppose 0 = -q + 3, 3*y + z = -q + 22. Determine l so that 439 + 2*l**2 - y*l - 4*l**2 - 441 = 0.
-1
Let k(z) = -z**4 - z**3 - 4*z**2 + z + 4. Let t(p) = 24*p**4 + 84*p**3 - 160*p**2 + 492*p - 412. Let w(m) = 28*k(m) + t(m). Factor w(x).
-4*(x - 5)**2*(x - 3)*(x - 1)
Suppose 867*p = 873*p - 48. Suppose 0 = -68*b + p*b. Factor 6/5*o**2 - 6/5*o**3 + b*o + 0.
-6*o**2*(o - 1)/5
Let z(w) be the second derivative of -8/7*w**2 + 0 - 4/21*w**3 - 49*w - 1/84*w**4. Factor z(u).
-(u + 4)**2/7
Let t(p) be the first derivative of -4*p - 2/3*p**3 + 2/15*p**5 + 11/3*p**2 + 71 - 1/2*p**4. Determine r so that t(r) = 0.
-2, 1, 3
Let i = 147497/78 - 11345/6. Factor i + 4/13*n + 2/13*n**2.
2*(n + 1)**2/13
Let r(d) = 9*d**3 + 13*d**2 + 5*d - 6. Let o(h) = h**3 + h**2 + h. Let n = 198 + -212. Let t(z) = n*o(z) + 2*r(z). Factor t(q).
4*(q - 1)*(q + 1)*(q + 3)
Let -3/5*l**3 - 96/5 + 33/5*l**2 - 12*l = 0. What is l?
-1, 4, 8
Let k be 228/(-42) + 5 + (-692)/(-14). Let k + 55 + 36*s - 4*s**2 + 9 - 25 = 0. Calculate s.
-2, 11
Let p(w) = -6*w**2 + 12*w - 26. Let i be p(11). Let b be 2 + i/90 - 6/(-1). Factor 2/9*d**4 + 8/9*d + 0 + 16/9*d**2 + b*d**3.
2*d*(d + 1)*(d + 2)**2/9
Solve 1144/9*x**2 + 0 - 2/3*x = 0.
0, 3/572
Solve 6/13*x**4 + 216/13 - 54/13*x**2 + 2/13*x**5 - 50/13*x**3 + 216/13*x = 0 for x.
-6, -2, -1, 3
Let d(w) be the first derivative of -5*w**6/6 + 13*w**5 + 5*w**4/2 - 130*w**3/3 - 5*w**2/2 + 65*w + 4832. Let d(t) = 0. What is t?
-1, 1, 13
Let d be -1 + (-1044)/(-24)*(-12)/(-9). Suppose -4*k - 20 = -c, 