Factor 132 - 563*c**3 - 33 + 237*c + 18 + 566*c**3 + 123*c**2.
3*(c + 1)**2*(c + 39)
Suppose -28 = -41*z + 54. Let v(k) be the third derivative of 0*k + 2*k**z + 1/20*k**5 + 0*k**3 + 0 - 1/4*k**4 + 3/40*k**6. Factor v(y).
3*y*(y + 1)*(3*y - 2)
Let h = 5528/3 - 1842. Factor -1/3 + 2/3*c - h*c**3 + 0*c**2 + 1/3*c**4.
(c - 1)**3*(c + 1)/3
What is p in 2/3*p**3 + 8/3*p - 8 + 14/3*p**2 = 0?
-6, -2, 1
Let d(n) = 5*n**5 + 4*n**4 - 19*n**3 + 12*n**2 - 4*n. Let r(s) = 21*s**5 + 15*s**4 - 75*s**3 + 48*s**2 - 18*s. Let j(h) = 9*d(h) - 2*r(h). Factor j(k).
3*k**2*(k - 1)**2*(k + 4)
Let p(s) be the third derivative of -s**8/84 - 68*s**7/105 - 16*s**6/15 + 34*s**5/15 + 11*s**4/2 - s**2 + 171*s. Determine r, given that p(r) = 0.
-33, -1, 0, 1
Let l(p) = p**2 - 5*p - 5. Let q = 5 + 2. Let v be l(q). Find i, given that 3 - 3*i**4 - v*i + 5*i**3 + i**3 + 0 + 3*i = 0.
-1, 1
Let i(l) be the second derivative of -l**10/90720 - l**9/45360 + l**8/20160 + l**7/7560 + 3*l**4/4 - 5*l. Let z(n) be the third derivative of i(n). Factor z(g).
-g**2*(g - 1)*(g + 1)**2/3
Suppose -23*y = -4*y + 23*y - 84. Factor -3/5*p**3 + 9/5*p - 6/5 + 0*p**y.
-3*(p - 1)**2*(p + 2)/5
Find b such that 0*b**3 - 2*b**4 + 0*b + 0 - 2/7*b**5 + 0*b**2 = 0.
-7, 0
Find k, given that 15*k**2 - 45 - 23*k**3 - 71*k**4 - 21*k**5 + 41 - k + 17*k - 32*k**3 = 0.
-2, -1, 2/7, 1/3
Let v be (-5)/15 + (-26)/(-6). Find j such that -12*j**3 + 16*j**3 - 4*j**2 - 5*j + 4*j**v + j = 0.
-1, 0, 1
Let h(z) be the second derivative of z**7/70 - 71*z**6/50 + 2589*z**5/50 - 1541*z**4/2 + 25921*z**3/10 - 36501*z**2/10 + z. Determine i, given that h(i) = 0.
1, 23
Let m(k) = -7*k**4 + 9*k**3 - k**2 + 5. Let w(o) = 6*o**4 - 10*o**3 + 2*o**2 + 4*o - 6. Let q(v) = 2*m(v) + 3*w(v). Suppose q(f) = 0. Calculate f.
-1, 1, 2
Let l = 368 + -368. Let d(n) be the third derivative of 0 - 1/144*n**4 - 1/360*n**5 + l*n - 6*n**2 + 0*n**3. Factor d(g).
-g*(g + 1)/6
Let q(g) be the first derivative of -3*g**5/35 + 3*g**4/28 + 2*g**3/7 + 239. Determine c so that q(c) = 0.
-1, 0, 2
Let d = 2/217 + 25600/651. Let z = d - 39. Determine t so that 0*t - t**4 + 0 + t**3 - 1/3*t**2 + z*t**5 = 0.
0, 1
Let a be 13 + (6 - 11) + (-4 - (-16)/(-5)). Factor -a*j + 2/5 + 2/5*j**2.
2*(j - 1)**2/5
Let q(a) be the first derivative of -2/21*a**3 + 4/7*a - 1/7*a**2 + 9. Factor q(x).
-2*(x - 1)*(x + 2)/7
Let k(w) be the first derivative of -w**4/18 - 26*w**3/27 - 40*w**2/9 - 8*w - 28. Determine u so that k(u) = 0.
-9, -2
Let u = -98 - -98. Let f(v) be the third derivative of -3*v**2 + 0*v + 1/60*v**5 - 1/3*v**3 + u - 1/24*v**4. Factor f(c).
(c - 2)*(c + 1)
Let t be -2 + 639/630 + 1. Let g(s) be the second derivative of 1/105*s**6 + 0 + s + t*s**5 - 1/21*s**4 + 0*s**2 + 0*s**3. Factor g(u).
2*u**2*(u - 1)*(u + 2)/7
Factor -4 + 1/2*s**3 + 4*s**2 - 1/2*s.
(s - 1)*(s + 1)*(s + 8)/2
Let s be (27/(-90))/(16/(-1620)). Let g(q) be the first derivative of 13 - 6*q - 24*q**2 - 45/2*q**3 + s*q**4. Let g(f) = 0. Calculate f.
-2/9, 1
Suppose 55*z**3 + 62500*z + 39527 + 3750*z**2 + z**4 + 45*z**3 + 351098 = 0. Calculate z.
-25
Let f(w) = -4*w**2 + 10*w + 14 - 11 - 11. Let r(u) = 8*u**2 - 19*u + 16. Let t be 1/(-6)*-3*-4. Let a(z) = t*r(z) - 5*f(z). Find l such that a(l) = 0.
1, 2
Suppose -30*i = -34*i + 2*d, 2*d = -i. Factor 0*p**2 + 1/5*p - 1/5*p**3 + i.
-p*(p - 1)*(p + 1)/5
Let v(i) be the third derivative of i**5/75 - 2*i**4/15 - 64*i**3/15 - 3*i**2 - 12. Determine c, given that v(c) = 0.
-4, 8
Let i(s) be the third derivative of -s**9/12096 + s**7/1008 - s**5/60 + 12*s**2. Let h(m) be the third derivative of i(m). Let h(t) = 0. What is t?
-1, 0, 1
Let j(b) be the second derivative of -b**4/16 + b**3/2 + 135*b**2/8 - 193*b. Solve j(u) = 0.
-5, 9
Let q(s) = 3*s**2 - 12*s + 9. Let h be q(5). Determine z, given that -15*z**3 - 4*z**2 - 12*z**4 + 7*z**2 + h*z**3 = 0.
-1/4, 0, 1
Let x = 4464 + -8927/2. Factor -1/4*i**4 + 1/4*i - 1/4 + 1/4*i**5 + x*i**2 - 1/2*i**3.
(i - 1)**3*(i + 1)**2/4
Let o(w) = w**3 - 95*w**2 - 1242*w - 1161. Let u(b) = b**3 - 191*b**2 - 2486*b - 2319. Let c(r) = -5*o(r) + 3*u(r). What is h in c(h) = 0?
-24, -1
Let p(k) be the third derivative of -k**5/120 - 7*k**4/48 + 2*k**3/3 + 2*k**2 + 64. Solve p(i) = 0.
-8, 1
Let f = -105 + 226. Solve 8 - 245*i**2 + 144*i**2 - 28*i + f*i**2 = 0 for i.
2/5, 1
Let o be ((-3)/(-9))/((-2548)/636 - -4). Let w = o + 57. Find f such that -2/3*f**5 + 0 + 2/3*f - 4/3*f**2 + 0*f**3 + 4/3*f**w = 0.
-1, 0, 1
Suppose 565 = 4*y - 431. Suppose y*g = 251*g - 4. Suppose 1/5*p**g + 1/5*p - 2/5 = 0. What is p?
-2, 1
Let k = 446 + -2218/5. Factor -2/5*x**2 - 18/5 - k*x.
-2*(x + 3)**2/5
Let r = 309/130 - -8/65. Let y(v) be the first derivative of -4/3*v**3 + 8 - r*v**2 + 2*v + 3/4*v**4. Find f such that y(f) = 0.
-1, 1/3, 2
Let a(u) be the first derivative of -2*u**5/15 - 2*u**4 - 98*u**3/9 - 26*u**2 - 80*u/3 - 964. Determine b, given that a(b) = 0.
-5, -4, -2, -1
Let m = 768 - 538. Determine l, given that -155*l**3 + 7*l + 12*l + m*l**4 - 20*l**2 + l - 88*l**5 + 13*l**5 = 0.
-1/3, 0, 2/5, 1, 2
Let b(w) be the second derivative of -w**4/108 + 7*w**3/27 + 5*w**2/6 + 140*w + 1. Determine n so that b(n) = 0.
-1, 15
Let l(w) be the first derivative of -2*w**2 + 15 + 6*w + 2/9*w**3. Find k, given that l(k) = 0.
3
Let o(z) be the second derivative of -z**4/3 - 8*z**3/3 + 64*z**2 - 410*z. Determine u so that o(u) = 0.
-8, 4
Let w(f) be the first derivative of -f**5/4 - 5*f**4/4 + 10*f**3/3 - 16*f - 16. Let c(x) be the first derivative of w(x). Determine o, given that c(o) = 0.
-4, 0, 1
Let h(w) = w**2 + w. Let z(x) = -14*x**2 + 14*x - 36. Let l(v) = 10*h(v) + z(v). Suppose l(q) = 0. What is q?
3
Let l(s) be the third derivative of s**6/480 - s**4/32 + s**3/12 - 10*s**2. Factor l(z).
(z - 1)**2*(z + 2)/4
Let p(a) be the first derivative of 1/3*a**2 - 1/6*a**4 + 8/15*a - 53 - 2/75*a**5 - 2/15*a**3. Determine y, given that p(y) = 0.
-4, -1, 1
Suppose -5*p - 9 = -5*w + 31, 0 = 5*w + 5*p - 50. Suppose -w + 0 = -3*s. Solve -3*u**3 - 2 + u**2 + 5*u**4 + u**4 + s*u - 5*u**4 = 0.
-1, 1, 2
Suppose -7*z + 280 = -56. Factor -6*d**4 - 9*d - 27*d + z*d**2 - 9*d**3 - 126*d**2 - 31*d**3.
-2*d*(d + 3)**2*(3*d + 2)
Let j be ((133/504)/(2/(-3)))/(-1). Let z = j - 1/16. Factor 1/3*w**5 + 5/3*w + 5/3*w**4 + 10/3*w**2 + 10/3*w**3 + z.
(w + 1)**5/3
Let a(t) be the third derivative of t**7/1155 - 29*t**6/660 + 9*t**5/10 - 405*t**4/44 + 486*t**3/11 - 7*t**2 - 26*t. Factor a(v).
2*(v - 9)**3*(v - 2)/11
Let g(k) be the first derivative of k**4/2 + 8*k**3/3 + 4*k**2 - 50. Factor g(m).
2*m*(m + 2)**2
Let h(g) = -g**3 - 5*g**2 + 21*g + 51. Let f be h(-7). Let r(b) be the first derivative of 1/8*b**f + 1/2*b - 1/12*b**3 - 2. Factor r(y).
-(y - 2)*(y + 1)/4
Let g(r) be the second derivative of -r**5/40 + 7*r**3/4 + 5*r**2 + 94*r. Find o such that g(o) = 0.
-4, -1, 5
Let o(s) = s**2 + 13*s + 20. Let u be o(-13). Let u + 30*m - 191*m**3 - 159*m**3 + 245*m**4 + 1365*m**2 + 70*m - 1380*m**2 = 0. Calculate m.
-2/7, 1
Let o(k) = -k**3 - 3*k**2 - 4*k - 2. Suppose 20 = -4*j + 16. Let z be o(j). Factor -2/9*y**2 + 0 + z*y.
-2*y**2/9
Let s(v) be the first derivative of -2*v**3/15 - 3*v**2/5 - 4*v/5 + 64. Factor s(g).
-2*(g + 1)*(g + 2)/5
Let g(i) be the third derivative of 5*i**6/6 - 77*i**5 + 5929*i**4/2 - 913066*i**3/15 + 5*i**2 + 10. Find t such that g(t) = 0.
77/5
Let f(o) = 11*o - 7. Let g(p) = 12*p - 6. Let s(d) = -3*f(d) + 4*g(d). Let k be s(3). Solve -k*n**3 + 44*n**3 - 157*n**3 - 176*n - 25*n**3 - 312*n**2 - 32 = 0.
-2/3, -2/5
Let x(u) be the second derivative of u**6/30 - u**5/15 - 2*u**4/3 + 8*u**3/3 + 9*u**2 + 27*u. Let r(i) be the first derivative of x(i). Factor r(m).
4*(m - 2)*(m - 1)*(m + 2)
Suppose -3*p - 5*u = -6 - 9, -2*u + 20 = 4*p. Let t be (p - 1) + (-90)/24. Solve -1 - 7/4*l + t*l**3 - 1/2*l**2 = 0 for l.
-1, 4
Let d be 2 - 88/(-28) - (-1)/(-7). Let n(g) be the second derivative of 1/100*g**d - 1/30*g**4 + 0*g**2 + 1/30*g**3 + 0 - g. Determine a, given that n(a) = 0.
0, 1
Find t, given that 2/7 + 0*t**3 - 4/7*t**2 + 0*t + 2/7*t**4 = 0.
-1, 1
Let i = -5 + 5. Suppose k - l = -i*l + 8, k + 5*l = -10. Factor -4*c**2 - 2*c**k + 2 + 4*c**3 + 0*c**4 - 13*c + 11*c + 2*c**4.
-2*(c - 1)**3*(c + 1)**2
Suppose 45*t - 566 + 276 + 65 = 0. Factor 0*k + 0*k**3 + 1/2*k**t - 