 that 30*j**2 - 3520*j + 192076 - 966476 - 5*j**2 - 29*j**2 = 0.
-440
Let k(s) be the second derivative of s**4/6 + 166*s**3 + 62001*s**2 + 27*s + 9. Factor k(j).
2*(j + 249)**2
Let v(a) = 7*a + 114. Let p be v(-16). Let g be ((-180)/25)/(-3) - p. Suppose 28/5*s**4 + 1/5*s**3 + 0 - g*s**2 + 0*s = 0. Calculate s.
-2/7, 0, 1/4
Let q be 48/(-15) + -6*18/27. Let f = -88/15 - q. Find i, given that f*i**2 + 0 + 2*i - 2/3*i**3 = 0.
-1, 0, 3
Let n = 24/28081 - -758139/56162. Find m such that 3/2*m**2 + 27/2*m - n - 3/2*m**3 = 0.
-3, 1, 3
Let k(f) be the second derivative of f**7/168 + f**6/20 + 13*f**5/80 + f**4/4 + f**3/6 - 774*f + 2. Factor k(q).
q*(q + 1)**2*(q + 2)**2/4
Let i be 6 + -31 - ((-408)/17 - 1). Factor -9/2*g**3 + i*g + 9*g**2 + 1/2*g**4 + 0.
g**2*(g - 6)*(g - 3)/2
Suppose -67*q - 7 + 61 = -80. Let r(w) be the first derivative of 4/5*w**5 - 6 + 0*w + 0*w**q + 4*w**4 + 0*w**3. Suppose r(g) = 0. What is g?
-4, 0
Let p(c) be the first derivative of -2*c**3/69 - 19*c**2/23 + 8*c - 254. Factor p(i).
-2*(i - 4)*(i + 23)/23
Let q(b) be the first derivative of 37*b**4/4 + 224*b**3/9 + 115*b**2/6 + 2*b/3 - 5631. Solve q(m) = 0.
-1, -2/111
Find r such that 1/2*r**4 - 102*r + 0 - 25/2*r**3 + 74*r**2 = 0.
0, 2, 6, 17
Solve 12/13*g**4 + 218/13*g**3 + 1188/13*g**2 + 256/13 + 1728/13*g = 0.
-8, -2, -1/6
Suppose 278/9*b - 2/9*b**3 - 88/9*b**2 - 188/9 = 0. Calculate b.
-47, 1, 2
Let t(m) = -3*m**2 + 155*m - 436. Let w be t(3). Let r(d) be the first derivative of -4*d + 42 + 4*d**w - 4/3*d**3. Factor r(h).
-4*(h - 1)**2
Let g(b) be the first derivative of -5*b**6/6 - 16*b**5 - 80*b**4 + 5722. Solve g(f) = 0 for f.
-8, 0
Let w(j) be the second derivative of -1/15*j**3 + 3/25*j**5 + j + 0*j**2 - 1/12*j**4 - 2. Factor w(l).
l*(3*l - 2)*(4*l + 1)/5
Let y = -1/11694 + 175417/81858. Let c(d) be the first derivative of 75/7*d + 40 + 1/7*d**3 + y*d**2. Factor c(n).
3*(n + 5)**2/7
Let d be (-1 + 22/4)*(-1432)/(-2685). Let i(w) be the first derivative of d*w**2 + 48/5*w + 7 + 1/5*w**3. Factor i(f).
3*(f + 4)**2/5
Suppose 0 = -18*g + 19*g + 4*x + 7, -4*g - 5*x = -5. What is l in -2 - 20*l + 84*l**2 + 2 - 116*l**3 - 9906*l**5 + 9898*l**g + 60*l**4 = 0?
0, 1/2, 1, 5
Let c(a) be the third derivative of 3*a**8/28 - 53*a**7/70 - 41*a**6/20 + 207*a**5/20 + 17*a**4 + 10*a**3 + 2*a**2 - 993*a. Let c(f) = 0. Calculate f.
-2, -1/3, -1/4, 2, 5
Suppose 5*x - 32 = 3*a - 33, -a - 4*x + 23 = 0. Let o(q) be the first derivative of a + 49/5*q**5 + 22*q**2 + 8*q + 6*q**3 - 119/4*q**4. Factor o(t).
(t - 2)*(t - 1)*(7*t + 2)**2
Suppose -24/11*v**4 + 120/11*v + 0 - 30/11*v**3 - 2/11*v**5 + 112/11*v**2 = 0. Calculate v.
-10, -3, -1, 0, 2
Let d(t) be the third derivative of -t**6/30 + 31*t**5/15 - 40*t**4 + 2*t**2 - 309. Solve d(m) = 0 for m.
0, 15, 16
Solve 347967*p - 7872*p**2 + 187/3*p**3 - 3101445/2 - 1/6*p**4 = 0.
5, 123
Let f(b) = -2*b**2 - b - 2. Let i(d) = 4*d**3 - 39*d**2 + 14*d + 6. Let x = 646 - 644. Let v(w) = x*i(w) + 6*f(w). Factor v(s).
2*s*(s - 11)*(4*s - 1)
Let r(z) be the second derivative of -z**7/336 + z**5/40 - 6178*z. Factor r(g).
-g**3*(g - 2)*(g + 2)/8
Let c(m) be the second derivative of -4*m**7/15 - 278*m**6/75 - 68*m**5/5 + 5*m**4/3 + m - 8839. Determine k, given that c(k) = 0.
-5, 0, 1/14
Suppose 0 = -2*k + 4*k - 120. Let q = k + -59. What is r in r - 14*r + 17 - 3*r + 4*r**2 - q = 0?
2
Factor -116*t**3 + 183*t**2 - 1804*t + 8712 - 773*t**2 - 4*t**4 - 54*t**2 - 384*t**2.
-4*(t - 2)*(t + 9)*(t + 11)**2
Determine n, given that -4*n**5 + 28*n**4 + 8*n**4 + 158*n**2 + 123*n**3 + 64*n + 4*n**5 - 8*n**4 - n**5 = 0.
-2, -1, 0, 32
Let s(j) be the third derivative of -2*j**7/105 - j**6/6 - j**5/3 + 5*j**4/6 + 4*j**3 - 1549*j**2. Solve s(g) = 0.
-3, -2, -1, 1
Let v(k) = 2*k**2 + 15*k - 29. Let n be v(2). Solve 20*l - 5*l**3 + 4*l**2 + 2*l**2 + n*l**2 + 0*l = 0 for l.
-1, 0, 4
Let r(j) = 7*j**2 - 11*j. Let s = -106 - -133. Let n(m) = 48*m**2 - 75*m. Let k(o) = s*r(o) - 4*n(o). Factor k(h).
-3*h*(h - 1)
Let j(v) be the second derivative of v**6/120 - v**5/16 + v**4/24 + 5*v**3/6 - 3*v**2 + 29*v + 8. Let j(q) = 0. What is q?
-2, 2, 3
Let i = -28 + 30. Suppose 2*s + i*s - 4*q = 32, -5*q = -2*s + 31. Suppose -14*l**4 + 11*l**2 - 55*l**s + l**2 + 33*l**3 = 0. Calculate l.
-2, 0, 3/7
Let i(j) = -5*j**3 + 816*j**2 + 338*j. Let k(a) = -2*a**3 + 408*a**2 + 170*a. Let f(p) = -3*i(p) + 5*k(p). Find l such that f(l) = 0.
-2/5, 0, 82
Let n be (-609)/(-4060)*(-2)/(-90). Let y(m) be the third derivative of n*m**5 + 0*m - 3*m**2 + 1/120*m**4 - 1/5*m**3 + 0. Factor y(l).
(l - 2)*(l + 3)/5
Let h be (-761)/(-379) - (-17)/((-204)/24). Let j = 2313/4927 - h. Factor -j + 8/13*a - 2/13*a**2.
-2*(a - 3)*(a - 1)/13
Suppose -191*a + 186*a = -z - 16, 0 = 2*a - 3*z - 48. Factor o**3 - 12/5*o - 1/5*o**4 + a + 8/5*o**2.
-o*(o - 6)*(o - 1)*(o + 2)/5
Let b be (-2)/24*(-306)/54 - 0. Let x = b + 1/36. Let -1/4*a**3 - 1/2*a**2 + 1/4*a + x = 0. What is a?
-2, -1, 1
Let x be 4098/1140 + (-60)/(-570) - 3. Determine i so that -1/5 + 2/5*i**2 - x*i = 0.
-1/4, 2
Factor -2/9*y**2 + 4*y + 14.
-2*(y - 21)*(y + 3)/9
Let w be (0/(-1)*(-89)/178)/(-2). Suppose 0*v**2 + 24/5*v - 6/5*v**3 + w = 0. What is v?
-2, 0, 2
Let m be 119/34 + (-2)/(-4). Factor -k + 92*k**2 + 4*k**m + 9*k + 90*k**2 - 194*k**2.
4*k*(k - 1)**2*(k + 2)
Let t = -1531 - -6421/4. Factor -t*d - 3/4*d**3 - 63/4*d**2 + 363/4.
-3*(d - 1)*(d + 11)**2/4
Let p(g) = g**2 + 3*g - 3302. Let m be p(-59). Let s(b) be the first derivative of -4/57*b**3 + 1/38*b**4 + 1/19*b**m + 14 + 0*b. Factor s(i).
2*i*(i - 1)**2/19
Let a be ((6 + 2)/2)/(-14 - -15). Let c(p) = -p**3 + 4*p**2 + 5. Let b be c(a). Factor 5*t**5 + 3*t**5 + 4*t**3 - 2*t - 5*t**b - 5*t**5.
-2*t*(t - 1)**2*(t + 1)**2
Suppose 4*m - 4*j = 40, -168*m + 172*m + j - 35 = 0. Suppose m*i - 3*i**2 + 2 - 2 + 26*i + 76*i = 0. What is i?
0, 37
Let z(j) be the second derivative of -j**4/90 + j**3/3 + 406*j**2/15 - 2911*j. Factor z(t).
-2*(t - 29)*(t + 14)/15
Suppose 13*b - 2 = 12*b. What is r in 7*r**4 + 20*r - 42*r**2 + 37*r**2 - b*r**4 - 20*r**3 = 0?
-1, 0, 1, 4
Let f(h) be the third derivative of h**6/30 + 7*h**5/15 + 5*h**4/2 + 6*h**3 - 8520*h**2 + 2. Factor f(r).
4*(r + 1)*(r + 3)**2
Let k(y) be the second derivative of -8/3*y**6 + 16/3*y**3 + 39/5*y**5 - 10*y**4 + 2/7*y**7 - 163*y + 0*y**2 + 0. Solve k(j) = 0.
0, 2/3, 1, 4
Let d(b) be the second derivative of b**7/1260 - b**6/18 + 5*b**5/4 + 7*b**3/2 + b**2/2 + b - 40. Let i(m) be the second derivative of d(m). Factor i(a).
2*a*(a - 15)**2/3
Let u(a) be the second derivative of -a**4/60 - 78*a**3/5 - 27378*a**2/5 + 2023*a. Suppose u(j) = 0. Calculate j.
-234
Let b be (-2515)/(-20)*(1818/915 + -2). Let a = -3/61 - b. Solve -2*q**4 + 0*q + a + 36/5*q**3 - 34/5*q**2 = 0.
-2/5, 1, 2
What is f in -1/4*f**2 - 385641/4 + 621/2*f = 0?
621
Let p(j) be the third derivative of -5*j**3 - 35/24*j**4 - 1/12*j**5 - 2*j + 0 - 17*j**2. Solve p(z) = 0 for z.
-6, -1
Let k(c) = 2*c**3 + 189*c**2 - 405*c + 205. Let q(i) = -i**3 - 2*i**2. Let d(z) = -k(z) + 3*q(z). Factor d(y).
-5*(y - 1)**2*(y + 41)
Let c be 9896/1300 + 756/567*3/50. Factor c*m + 0 - 2/13*m**4 + 24/13*m**3 - 90/13*m**2.
-2*m*(m - 5)**2*(m - 2)/13
Let -252*z**2 - 445*z**2 - 348100 - 3545*z + 693*z**2 + 1185*z = 0. What is z?
-295
Let a = 161/968 + 1131/4840. Find o, given that 2/5*o**4 - 4/5*o**2 + a + 0*o + 0*o**3 = 0.
-1, 1
Let x(a) = a**3 + 5*a**2 - 7*a - 10. Let u be x(-6). Let h be 9*160/360*(-2)/u. Factor -6*c**3 + 16/3*c + 2*c**h - 8/3.
-2*(c + 1)*(3*c - 2)**2/3
Let z(i) = 25*i**3 - 65*i**2 - 118*i + 202. Let c(j) = 9*j**3 - 21*j**2 - 40*j + 68. Let x(w) = -11*c(w) + 4*z(w). Suppose x(p) = 0. What is p?
-2, 1, 30
Let d(t) be the first derivative of 3*t**5/5 - 21*t**4/4 + 15*t**3 - 27*t**2/2 - 1382. Determine l, given that d(l) = 0.
0, 1, 3
Let t(p) be the first derivative of 4/3*p**3 - 44 - 84*p**2 + 1764*p. Let t(f) = 0. What is f?
21
Let v(f) = 6*f - 58. Let p be v(10). Suppose 4*k**3 - 3*k**2 + 15*k**p - 13*k**5 - 12*k**4 + 32*k**5 - 10*k**5 - 13*k**5 = 0. Calculate k.
-3, -1, 0, 1
Let y(h) be the third derivative of -h**5/390 - 23*h**4/156 + 2*h**3 - 2*h**2 - 467. Factor y(b).
-2*(b - 3)*(b + 26)/13
Let a(j) be the third derivative of -1/504*j**8 + 1/315*j**7 + 0*j + 1/60*j**6 - 1/18*j**5 + 0 + 1/1