272*k - 49063*k**2 - 3*k**5 + 2*k**5 - 24*k**4 - 109*k**3 + 49249*k**2 = 0. What is k?
-17, -8, -1, 0, 2
Factor -2/7*a + 0 + 0*a**2 + 2/7*a**3.
2*a*(a - 1)*(a + 1)/7
Let m(x) be the third derivative of -x**9/60480 - x**8/1440 + x**7/336 + 37*x**5/20 - 5*x**2. Let t(d) be the third derivative of m(d). Solve t(h) = 0.
-15, 0, 1
Let u(d) = d**3 - 42*d**2 + 7*d - 147. Let n be u(42). Let f be (-630)/n - 5/(-1). Factor -1/7*g**3 - f - 11/7*g - g**2.
-(g + 1)**2*(g + 5)/7
Let z(m) be the third derivative of m**6/320 - 85*m**5/32 - 107*m**4/4 - 429*m**3/4 + 227*m**2 + m. Factor z(h).
3*(h - 429)*(h + 2)**2/8
Let k(g) = 2*g**4 - g**3 + g**2 - 2*g. Let t(f) = 595*f**4 + 720*f**3 - 1100*f**2 - 205*f - 10. Let a(j) = -5*k(j) - t(j). Suppose a(x) = 0. Calculate x.
-2, -1/11, 1
Let k be (-727431)/56390*(-10)/12. Suppose -1/4*s**3 + 1/4*s + 43/4 - k*s**2 = 0. What is s?
-43, -1, 1
Let y(i) be the first derivative of i**3/3 + 695*i**2/2 + 694*i + 318. Factor y(q).
(q + 1)*(q + 694)
Let b(w) be the third derivative of w**6/180 + 13*w**5/15 + 38*w**4/9 - 3932*w**2. Determine r, given that b(r) = 0.
-76, -2, 0
Let h(y) = 2*y**3 + 70*y**2 + 212*y + 150. Let l be (-6 - (-5 - -5)) + -2. Let c(u) = -7*u**3 - 210*u**2 - 637*u - 450. Let k(i) = l*h(i) - 3*c(i). Factor k(a).
5*(a + 1)*(a + 3)*(a + 10)
Let j(u) be the first derivative of u**4/6 + 18*u**3 - 517*u**2/3 + 290*u - 2363. Factor j(t).
2*(t - 5)*(t - 1)*(t + 87)/3
Let n = 184052/15 - 12270. Factor 8/5*j + 0 + n*j**2.
2*j*(j + 12)/15
Solve 480 - 200*a - a**2 - 46*a**2 - 333*a**2 - 43*a**4 - 4*a**5 + 9*a**5 + 30*a**3 + 108*a**4 = 0 for a.
-12, -2, 1, 2
Let r be (-27)/12*16/(-6) + (-715)/121. Let n(w) be the second derivative of 1/44*w**4 - 1/330*w**6 - r*w**2 + 0 - 14*w + 1/220*w**5 - 1/66*w**3. Factor n(g).
-(g - 2)*(g - 1)*(g + 1)**2/11
Let n(h) be the second derivative of -h**7/504 - 5*h**6/144 - h**5/4 - h**4/6 + 13*h**3/6 - 13*h. Let g(d) be the third derivative of n(d). Factor g(q).
-5*(q + 2)*(q + 3)
Suppose -525/4 + 5/4*o**2 + 20*o = 0. Calculate o.
-21, 5
Let y(a) = -5*a**4 + a**3 - 8*a. Let s(l) be the first derivative of 4*l**5/5 - l**3/3 + 3*l**2 - 117. Let w(b) = -4*s(b) - 3*y(b). Factor w(r).
-r**2*(r - 1)*(r + 4)
Let c(o) = -7*o**4 - 135*o**3 + 483*o**2 - 457*o + 3. Let k(a) = 10*a**4 + 270*a**3 - 965*a**2 + 915*a - 5. Let j(v) = -5*c(v) - 3*k(v). Factor j(w).
5*w*(w - 23)*(w - 2)**2
Suppose 3*p - 1415 = -5*g, 0 = g + 2*p + 76 - 352. Let y = -547/2 + g. Factor -y*i + 125/4 + 5/4*i**2.
5*(i - 5)**2/4
Find r, given that 908/7*r**3 + 103968/7 + 2/7*r**4 - 207024/7*r + 102146/7*r**2 = 0.
-228, 1
Factor 411/2*r - 204 - 3/2*r**2.
-3*(r - 136)*(r - 1)/2
Suppose -246*r + 579 = 190*r - 293. Let i(b) be the third derivative of 0*b**3 + 1/84*b**4 + 32*b**r + 3/140*b**5 + 0*b + 0. Factor i(a).
a*(9*a + 2)/7
Factor 839487/7*q**2 + 507/7*q**4 - 41418/7*q**3 + 20172/7 + 261252/7*q.
3*(q - 41)**2*(13*q + 2)**2/7
Factor 1/3*x**3 + 415*x**2 + 71473375/3 + 172225*x.
(x + 415)**3/3
Let v(c) be the first derivative of -14*c - 10/3*c**3 + 23/2*c**2 - 38 + 1/4*c**4. Factor v(n).
(n - 7)*(n - 2)*(n - 1)
Suppose 6*i - 3 = 33. Suppose 0 = i*x - 12*x + 18. Factor -5*s**x + 4*s**3 - 3*s**3 - s**2 - 3*s**2.
-4*s**2*(s + 1)
Let 9319 - 55*m - 2*m**2 - 18668 + 9549 + m**3 = 0. What is m?
-8, 5
Factor 25*d**2 + 89*d + 359*d - 580 + 257*d.
5*(d + 29)*(5*d - 4)
Let u(j) = -j**3 - 3*j**2 + 2*j + 1. Let i(t) = 5*t**3 - 1229*t**2 + 190954*t + 192197. Let a(g) = 2*i(g) + 6*u(g). Factor a(o).
4*(o - 310)**2*(o + 1)
Suppose 116 = -11*r + 127. Let y be r + -9 + (-4017)/(-6). Let -y*k**2 + 126*k - 6 = 0. Calculate k.
2/21
Let j be ((-2)/(-7))/((288/(-28) - -11)/1). Let x(f) be the second derivative of 1/3*f**4 + 19*f + 0*f**3 + 0*f**2 + 1/10*f**6 + 0 - j*f**5. Factor x(w).
w**2*(w - 2)*(3*w - 2)
Let u(a) be the second derivative of a**5/30 + 7*a**4/12 + 4*a**3 + 119*a**2 - 67*a - 2. Let f(p) be the first derivative of u(p). Factor f(j).
2*(j + 3)*(j + 4)
Let i(t) be the first derivative of t**5/5 - 7*t**4/4 + 2*t**3 + 3507. Determine d, given that i(d) = 0.
0, 1, 6
Suppose -4*x - y + 486 = 0, 0 = -3*x + 2*x - 4*y + 114. Let 128*r**2 - 3*r**3 - 2*r**4 + 3*r**3 + 4*r - x*r**2 = 0. What is r?
-1, 0, 2
Suppose 559*l = 1656*l - 5485. Determine b so that b + 13/8*b**2 - 3/8*b**3 - 3/2 - 5/8*b**4 - 1/8*b**l = 0.
-3, -2, 1
Let h(c) be the third derivative of 0 - 3/20*c**4 + 0*c - 1/25*c**5 - 4/15*c**3 - 1/300*c**6 - 50*c**2. Let h(u) = 0. What is u?
-4, -1
Let c(t) be the first derivative of -t**7/42 + t**6/5 - 3*t**5/5 + 5*t**4/6 - t**3/2 - 139*t + 7. Let m(o) be the first derivative of c(o). Factor m(j).
-j*(j - 3)*(j - 1)**3
Let h(v) = 5*v**3 - 38*v**2 + 31*v + 6. Let i be h(1). Factor -i - 2/7*m**2 + 18/7*m.
-2*(m - 7)*(m - 2)/7
Let i be 696/(-12528) - ((-212)/(-72) - 3). Suppose 4/9*f - 2/9*f**2 + 2/3*f**4 - 8/9*f**3 + i = 0. Calculate f.
-2/3, 0, 1
Factor 0 - 3/2*x**3 - 189*x + 69/2*x**2.
-3*x*(x - 14)*(x - 9)/2
Let u(j) = 217*j**2 + 707*j + 695. Let z(m) = 130*m**2 + 354*m + 347. Let p(d) = -6*u(d) + 10*z(d). Factor p(r).
-2*(r + 1)*(r + 350)
Let w(d) be the third derivative of -d**10/37800 - 13*d**9/3024 - d**5/60 + 5*d**4/6 - 54*d**2 + 2. Let k(p) be the third derivative of w(p). Factor k(q).
-4*q**3*(q + 65)
Let y(v) be the third derivative of -3*v**6/80 - 31*v**5/30 - 89*v**4/48 + 13*v**3/6 - v**2 + 392*v - 2. Factor y(f).
-(f + 1)*(f + 13)*(9*f - 2)/2
Let v(b) = -b**3 - 2*b**2 - 2. Let l(c) = 6*c**3 - 868*c**2 + 192721*c + 10. Let r(n) = l(n) + 5*v(n). Factor r(h).
h*(h - 439)**2
Let v(t) be the second derivative of 85*t + 0*t**2 + 0 - 4/3*t**4 + 8/3*t**3 + 2/15*t**6 - 1/5*t**5. Let v(h) = 0. What is h?
-2, 0, 1, 2
Factor 0*b**3 - 2*b**3 - 2*b**4 - 15 + 4*b**3 + 18*b**2 + 10*b**3 - 12*b - b**4.
-3*(b - 5)*(b - 1)*(b + 1)**2
Let w = -42300 - -126904/3. Solve 2/3*d**4 + 2/9*d + 2/3 + 2/9*d**5 - 4/9*d**3 - w*d**2 = 0 for d.
-3, -1, 1
Let a(g) = -g**2 - 27*g - 24. Let v be a(-26). Find h, given that -15 - 15*h + 1361*h**2 + 10*h**3 - 1346*h**v + 5 = 0.
-2, -1/2, 1
Let i(v) be the second derivative of -289*v**5/120 + 527*v**4/36 + 920*v**3/9 + 200*v**2 - 8628*v. Factor i(p).
-(p - 6)*(17*p + 20)**2/6
Let t(q) be the first derivative of -4/21*q**3 - 1/14*q**4 + 289 + 0*q + 8/7*q**2. Factor t(f).
-2*f*(f - 2)*(f + 4)/7
Let y(x) be the first derivative of 3*x**4/28 - 23*x**3/7 - 36*x**2/7 + 4779. Factor y(v).
3*v*(v - 24)*(v + 1)/7
Let w(u) be the first derivative of -u**6/3600 + u**5/400 + 3*u**4/40 - 40*u**3/3 - 72. Let i(g) be the third derivative of w(g). Factor i(b).
-(b - 6)*(b + 3)/10
Suppose -201 - 1110 = -497*a + 180. Factor -8/13*y + 16/13 - 4/13*y**2 + 2/13*y**a.
2*(y - 2)**2*(y + 2)/13
Suppose -37*g - 411*g + 1384 = 244*g. Find k such that -6/5 - 9/5*k + 0*k**g + 3/5*k**3 = 0.
-1, 2
Suppose -4*w + 4*x + 28 = -4, 2*w + 19 = -5*x. What is n in -5*n**w + 7*n**2 + 60*n**5 - 56*n**5 - 7*n**3 - 16*n + 8*n**4 - 39*n**2 = 0?
-2, -1, 0, 2
Factor 5*m**4 + 269115*m**2 - 34663 + 34663 - 271445*m + 1586*m**3 + 739*m**3.
5*m*(m - 1)*(m + 233)**2
Let h = 160 - 157. Solve 2*v - 5*v**3 + 4*v**4 - 2 + h*v**3 + 4*v**2 + 2*v**5 - 2*v**3 - 6*v**4 = 0.
-1, 1
Let z(f) be the third derivative of -f**5/20 - 313*f**4/4 - 97969*f**3/2 - 370*f**2. Factor z(a).
-3*(a + 313)**2
Let z(g) be the second derivative of g**5/240 - 23*g**4/96 - g**3 - 162*g**2 + 222*g. Let n(v) be the first derivative of z(v). Let n(b) = 0. What is b?
-1, 24
Let y(x) be the third derivative of 5/8*x**4 + 1/24*x**6 + 0*x**3 + 2*x**2 + 0 - 1/3*x**5 - 17*x. Factor y(i).
5*i*(i - 3)*(i - 1)
Find s, given that -10*s + 5*s**2 - 126*s + 206*s + 225 = 0.
-9, -5
Factor 60/13*q**2 - 166/13*q - 2/13*q**3 + 108/13.
-2*(q - 27)*(q - 2)*(q - 1)/13
Let r(p) = 16*p**3 + 21*p**2 - 40*p + 9. Let h(y) = 9 - 50*y + 21*y**2 - 81*y + 18*y**3 + 92*y. Let i(w) = 2*h(w) - 3*r(w). Suppose i(x) = 0. What is x?
-3, 1/4, 1
Let a(w) be the second derivative of -3/5*w**5 + 1/15*w**3 - 1 - 47*w - 1/35*w**7 + 3/5*w**2 - 3/5*w**4 - 17/75*w**6. What is q in a(q) = 0?
-3, -1, 1/3
Let u(n) = -26*n - 41*n - 10*n - 802 - n. Let v(b) = -b**2 + 77*b + 803. Let i(y) = -3*u(y) - 2*v(y). Solve i(x) = 0.
-20
Let t = 21077 - 1475389/70. Let f(x) be the third derivative of 0 + 0*x + 8*x**3 + 37*x**2 + 1/20*x**5 + t*x**7 - 3/