*w**2 = 0.
-3, 36
Let h be 5080/1136 - 78/(-2769). Factor 6*j**3 - 6 + 3/2*j**4 - 6*j + h*j**2.
3*(j - 1)*(j + 1)*(j + 2)**2/2
Let b(y) = 2*y**2 + 8*y - 34. Let h(w) = 237 - 477 + 2*w + 241. Let c(k) = -b(k) + 8*h(k). Suppose c(n) = 0. What is n?
-3, 7
Let t = -6216463/3 + 2072165. Solve -85*c**2 - 1/3*c**4 - 32/3*c**3 + t*c + 256/3 = 0 for c.
-16, -1, 1
Let c = 4207 + -4205. Let r(j) be the first derivative of -j**3 + 3*j - 3/4*j**4 + 3/2*j**c - 3. Factor r(f).
-3*(f - 1)*(f + 1)**2
Let c be (-10)/6*(2 + -5). Suppose 4*l + g = 13, -c*l + 3*g - 10 = -g. Factor l*i - 2 + 0*i**2 + 2*i**2 - 2*i.
2*(i - 1)*(i + 1)
Let g(y) be the second derivative of y**7/840 - y**6/120 - y**5/30 - y**3/6 - 2*y**2 - 6*y. Let b(i) be the second derivative of g(i). Factor b(m).
m*(m - 4)*(m + 1)
Let j(b) be the third derivative of -b**6/360 + b**4/24 + 71*b**3/3 + 61*b**2. Let c(z) be the first derivative of j(z). Let c(t) = 0. Calculate t.
-1, 1
Let m be (-716)/(-9) + (-12)/(-27). Suppose 60*k**3 + 92*k**4 + 20*k + m*k**2 - 48*k**4 + 45*k**3 + k**4 = 0. Calculate k.
-1, -2/3, 0
Let y = 293405 - 293399. What is n in 0*n + 2*n**4 + y*n**3 + 0 + 10/3*n**2 - 2/3*n**5 = 0?
-1, 0, 5
Let i = -307717/13 + 23673. Factor -i - 2/13*u**2 - 16/13*u.
-2*(u + 4)**2/13
Let l be (10/28)/((-36)/(-504)). Let s be (-2640)/(-198) - (-1 + l)/1. Let -4/3*w**3 + 4/3*w**4 + 52/3*w - s*w**2 - 8 = 0. What is w?
-3, 1, 2
Let p(k) be the first derivative of -k**6/12 - 11*k**5/5 - 27*k**4/2 - 100*k**3/3 - 32*k**2 - 3909. Find z, given that p(z) = 0.
-16, -2, 0
Let o(w) = -18*w**5 - 22*w**4 - 118*w**3 - 194*w**2 - 144*w - 32. Let g(f) = -2*f**5 + f**4 + 1. Let r(d) = -8*g(d) + o(d). Factor r(k).
-2*(k + 1)**3*(k + 2)*(k + 10)
Let a(x) = 1189*x - 10697. Let d be a(9). Factor -1/4*g**d + 5/2*g**2 - 9/4 + 2*g - 2*g**3.
-(g - 1)**2*(g + 1)*(g + 9)/4
Let r be ((-60)/(-8) - 8)*-2*3/(12 + -9). Factor 7/4*a + 1/8*a**3 + r + 7/8*a**2.
(a + 1)*(a + 2)*(a + 4)/8
Suppose -2*h - 3*p + 989 = 0, 8*p - 984 = -2*h + 4*p. Suppose -2*b = -h + 498. Factor 2*j**b - 3/4*j + 5/4*j**5 + 9/2*j**4 + 11/2*j**3 - 1/2.
(j + 1)**4*(5*j - 2)/4
Let r(m) = -m**3 - 8*m**2 - 18*m + 5. Let j be r(-6). Let b = -38 + j. Factor -21*g + g**2 - b*g - 3*g**3 - 16*g**2 - 12.
-3*(g + 1)*(g + 2)**2
Let w(x) be the second derivative of -x**8/252 + 4*x**7/105 - 2*x**6/15 + 8*x**5/45 - 23*x**2 - 42*x. Let h(l) be the first derivative of w(l). Factor h(y).
-4*y**2*(y - 2)**3/3
Let s be (-234351)/(-78)*4/6. Let x = 4009/2 - s. Determine t so that 24 + 12*t + x*t**2 = 0.
-4
Let z(a) be the third derivative of a**6/90 - 296*a**5/45 + 295*a**4/18 - 3*a**2 - a - 344. Factor z(k).
4*k*(k - 295)*(k - 1)/3
Let q be 21/(-6)*((-23)/(-70) + 16/(-40)). Let k(j) be the first derivative of -q*j**4 - 4 + 5/3*j**3 - 7/2*j**2 + 3*j. Factor k(u).
-(u - 3)*(u - 1)**2
Let k = 550 + -546. Let u(b) = 58*b**4 - 62*b**3 + 2*b + 2. Let f(c) = c**5 + c**4 - c - 1. Let m(x) = k*f(x) + 2*u(x). Suppose m(l) = 0. Calculate l.
-31, 0, 1
Find z, given that -5491/2*z - 25/8*z**3 + 13735/4*z**2 + 549 = 0.
2/5, 1098
Let a be (1839/4291)/((-891)/300 + 3). Factor -a + 20/7*g - 1/7*g**2.
-(g - 10)**2/7
Let r(x) = -x - 7. Let m be r(-10). Suppose 0 = -d + m*t + 12, 5*t = 2*d + 2*d - 69. Factor 36 + 0*s + 0*s**2 - 3*s + 4*s**2 - d*s.
4*(s - 3)**2
Suppose 0 = -7271*j + 7249*j + 110. Let x(y) be the third derivative of 0 + 0*y**4 + 0*y**3 + 36*y**2 - 1/180*y**6 - 1/45*y**j + 0*y. Factor x(o).
-2*o**2*(o + 2)/3
Let r(p) = 49*p**2 + 1712*p + 183184. Let b(t) = -29*t**2 - 856*t - 91592. Let x(a) = 5*b(a) + 3*r(a). Factor x(s).
2*(s + 214)**2
Let o be (3 - (-1 - 1)) + 51/(-17). Factor -25*j**3 + 25 + 5*j**2 + 40*j + 3*j**5 - 5 - 5*j**4 + o*j**5.
5*(j - 2)**2*(j + 1)**3
Factor -129/2*t**2 - 77*t + 12*t**3 + 0 - 1/2*t**4.
-t*(t - 14)*(t - 11)*(t + 1)/2
Suppose 0 = 71*o - 69*o - 4. Let h(p) be the third derivative of 0*p - 24*p**o + 1/12*p**3 + 1/72*p**4 - 1/360*p**5 + 0. Factor h(v).
-(v - 3)*(v + 1)/6
Let i(m) be the second derivative of -5*m**4/12 - 13460*m**3/3 - 18117160*m**2 - 1745*m. Factor i(y).
-5*(y + 2692)**2
Let i(t) = -16307*t**2 + 1 + 16306*t**2 - t**3 - 2. Let v(w) = -18*w**3 - 3*w**2 + 33*w + 3. Let h(y) = -15*i(y) + v(y). Suppose h(f) = 0. Calculate f.
-1, 6
Let a(g) = g**2 + 2*g - 15. Let l be a(-5). Let z = -14747 - -14747. Let -1/9*k**3 + 1/3*k**2 + z*k + l = 0. What is k?
0, 3
Let g = 211827/85 + -2492. Let b = 15/17 - g. Factor -b*s**2 + 24/5*s - 36/5.
-4*(s - 3)**2/5
Let p(i) be the second derivative of 49*i**4/4 + 589*i**3/6 + 2*i**2 - 4997*i. Suppose p(r) = 0. Calculate r.
-4, -1/147
Let j = -117053 + 117055. Solve 4/3*s + 2/3*s**3 + 2*s**j + 0 = 0.
-2, -1, 0
Let v = -20162 - -20182. Let i(z) be the second derivative of -2/15*z**6 - 3/10*z**5 + 0*z**4 + 0*z**3 + 0*z**2 + 1/21*z**7 - v*z + 0. Factor i(t).
2*t**3*(t - 3)*(t + 1)
Let x(z) be the second derivative of -43 + 1/2*z**4 + 30*z**2 - 47/3*z**3 - z. Solve x(b) = 0 for b.
2/3, 15
Let r = -113317/20 + 5666. Let z(b) be the second derivative of -1/4*b**4 + r*b**5 + 1/20*b**6 + 3/4*b**2 - 1/28*b**7 + 0 + 6*b - 1/4*b**3. Factor z(y).
-3*(y - 1)**3*(y + 1)**2/2
Let s(i) be the second derivative of -i**5/5 + 215*i**4 + 2*i**3/3 - 1290*i**2 + 392*i - 6. What is w in s(w) = 0?
-1, 1, 645
Let g(o) be the second derivative of -o**5/20 - 43*o**4/12 - 218*o**3/3 + 240*o**2 - 106*o - 2. Solve g(i) = 0 for i.
-24, -20, 1
Let f(l) be the first derivative of 4/7*l**4 + 50/7*l + 9 + 4/7*l**3 + 2/35*l**5 - 40/7*l**2. Factor f(r).
2*(r - 1)**2*(r + 5)**2/7
Find f such that 3/2*f**4 + 45 - 39/2*f**3 - 93/2*f**2 + 39/2*f = 0.
-2, -1, 1, 15
Let f = -25340/11 - -2308. Let i = -133/33 + f. Determine z, given that 0 + 2/3*z**3 + i*z**4 + 0*z + 1/3*z**2 = 0.
-1, 0
What is p in -758 - 402 - 561*p - 270*p**2 - 8*p**3 - 680*p + 2381*p + 3*p**3 = 0?
-58, 2
Suppose 3*q - 89*q = -1462. Let y(d) be the first derivative of 2/9*d**3 + q - 8/3*d**2 + 32/3*d. Factor y(u).
2*(u - 4)**2/3
Suppose -n + 22 = 117. Let b = n + 666/7. Let 0*s + 0 + b*s**2 = 0. Calculate s.
0
Let i(c) be the second derivative of 0*c**5 - 3*c - 15/2*c**2 + 1/420*c**6 - 1/84*c**4 + 0 + 0*c**3. Let u(j) be the first derivative of i(j). Factor u(n).
2*n*(n - 1)*(n + 1)/7
Suppose -6 = 2*i - 0, -4*i = -u + 25. Factor u*r + 37 + 27*r**2 + 77*r + 38.
3*(3*r + 5)**2
Let u(n) be the second derivative of n**5/110 - 4*n**4/33 + 7*n**3/33 + 902*n. Factor u(t).
2*t*(t - 7)*(t - 1)/11
Suppose -4*k + 5*n + 9 = 6*n, -5*k + n = -18. Find x, given that 2*x**k + 244*x - 38*x**2 - 244*x = 0.
0, 19
Let -21/5*f**4 - 540*f + 0 - 10812/5*f**2 - 4773/5*f**3 = 0. Calculate f.
-225, -2, -2/7, 0
What is i in 0*i + 0 - 98/5*i**2 - 2/5*i**3 = 0?
-49, 0
Let m(l) be the second derivative of 16*l**6/15 + 22*l**5/5 + l**4/3 - 44*l**3/3 - 18*l**2 - 6939*l. Suppose m(x) = 0. Calculate x.
-9/4, -1, -1/2, 1
Determine f so that -2868/7*f**2 - 218430704/7 + 1370904/7*f + 2/7*f**3 = 0.
478
Suppose -1604*s + 857*s + 895*s = 0. What is z in 0 + s*z - 10/3*z**2 + 2/3*z**3 = 0?
0, 5
Let n(f) be the first derivative of f**5/20 - 7*f**4/16 + f**3/2 + 4*f**2 - 8*f - 4290. Factor n(z).
(z - 4)**2*(z - 1)*(z + 2)/4
Factor 1/5*v**3 + 8904*v + 423/5*v**2 - 44944/5.
(v - 1)*(v + 212)**2/5
Factor 13*s**2 - 6247430 - 11136*s - 48*s**2 - 1503226 + 31*s**2.
-4*(s + 1392)**2
Factor -392*d - 10*d**2 - 114 - 151 + 37 - 154.
-2*(d + 1)*(5*d + 191)
Let k(y) be the second derivative of 2*y + 7/20*y**5 + 1/6*y**4 - 17 + 0*y**2 + 2/15*y**6 - 1/6*y**3. Find q such that k(q) = 0.
-1, 0, 1/4
Let s be ((-6)/21)/(18 - 1045/57). Factor 6/7*v**3 - s*v**2 + 0 + 2/7*v - 2/7*v**4.
-2*v*(v - 1)**3/7
Let m(b) = -6*b**2 - 12*b - 12. Let u be m(-4). Let s = u - -63. Factor 51*z**2 + 8*z**3 - 15 + z**3 - 48*z + 3*z**s.
3*(z - 1)*(z + 5)*(4*z + 1)
Let p(w) be the second derivative of 7*w**3 - 1/2*w**4 + 0 + 157*w - 3/40*w**5 - 24*w**2. Factor p(m).
-3*(m - 2)**2*(m + 8)/2
Let s = -167 + 351. Suppose 20*u**2 + 27*u + 4 - 36*u**2 - 48*u + s*u**2 - 29*u - 72*u**3 = 0. What is u?
1/6, 2
Let d(n) = 359*n - 1431. Let t be d(4). Let j(v) be the first derivative of -1/18*v**4 - t + 2/27*v**3 + 1/9*v**2 + 0*v - 2/45*v**5. Factor j(c).
-2*c*(c - 1)*(c + 1)**2/9
Let p(y) be the third derivative of -y**5/60 + 119*y**4/24 - 1566*y**2. What is f in p(f) = 0?
0, 1