)/9
Let n(r) be the second derivative of -r**4/4 - 1816*r**3 - 4946784*r**2 - 1122*r. What is s in n(s) = 0?
-1816
Let f(a) be the second derivative of a**5/80 + 3*a**4/8 + 15*a**3/8 + 5904*a. Factor f(s).
s*(s + 3)*(s + 15)/4
Let s(q) = q**2 - q + 11. Let v be s(4). Suppose -27 = -n + v. Let 5*j + 53 + n - 93 - 5*j**2 = 0. Calculate j.
-1, 2
Let r = 2192/323 + -27850/4199. Factor r*x**2 + 24/13 + 14/13*x.
2*(x + 3)*(x + 4)/13
Factor -8/17*l**2 + 2/17*l**4 + 0 - 48/17*l + 12/17*l**3.
2*l*(l - 2)*(l + 2)*(l + 6)/17
Let o(m) be the third derivative of 5/2*m**3 - 7/30*m**5 + 83*m + 3/20*m**6 + 0 - 17/24*m**4 - 1/210*m**7 + 2*m**2 - 1/336*m**8. Let o(t) = 0. What is t?
-5, -1, 1, 3
Let i be ((-121)/1210)/(3/35) - (-13133)/66. Factor -2048/11 - 130/11*f**2 - i*f - 2/11*f**3.
-2*(f + 1)*(f + 32)**2/11
Let v(o) be the third derivative of 0*o**3 + 14/45*o**5 - 1/60*o**6 + 44*o**2 + 0*o + 5/9*o**4 + 0. Let v(y) = 0. Calculate y.
-2/3, 0, 10
Suppose 3*j + 2*n = 6, n - 3 = -2*j + 3*j. Let z = -1/1008400 - -504203/3025200. Find y such that 0 + j*y + 3/2*y**3 + z*y**4 + 4/3*y**2 = 0.
-8, -1, 0
Suppose -30 = -687*l - 30. Factor 0*a**2 - 3/2*a**3 + l - 1/2*a**4 + 0*a.
-a**3*(a + 3)/2
Solve -10*o**3 - 10*o**3 + 336 - 61 - 234*o**4 + 133*o**2 - 580*o + 229*o**4 + 197*o**2 = 0 for o.
-11, 1, 5
Let h(a) be the second derivative of -8*a**2 + 0 + 4/3*a**3 + 5*a + 1/3*a**4 - 1/10*a**5. Let h(y) = 0. Calculate y.
-2, 2
Let v(c) = 14*c**2 + 4874*c + 419036. Let r(j) = 2*j**2 + 696*j + 59862. Let o(d) = -15*r(d) + 2*v(d). Factor o(b).
-2*(b + 173)**2
Let o(v) be the first derivative of -2*v - 1/4*v**4 - v**3 + 1/5*v**5 + 52 + 5/2*v**2. Factor o(c).
(c - 1)**3*(c + 2)
Let j be (-150)/(-20)*(-2)/(-5). Let y(l) = -3*l**3 + l. Let u be y(-1). Solve -27*b**j - 15*b**u + 20*b + 32*b**3 - 5*b**2 = 0 for b.
0, 2
Let y(q) be the third derivative of 4*q**7/35 + 9*q**6/10 + 33*q**5/40 + q**4/4 - 13*q**2 - 5. Factor y(p).
3*p*(p + 4)*(4*p + 1)**2/2
Suppose 25*h**5 + 6*h**2 + 29865*h**4 - 29863*h**4 - 23*h**5 - 10*h**3 = 0. Calculate h.
-3, 0, 1
Let n(s) be the third derivative of -s**6/320 - 7*s**5/40 - 13*s**4/16 + 2*s**2 - 1809. Find r, given that n(r) = 0.
-26, -2, 0
Suppose 79*b - 84*b - 6*k + 40 = 0, 5*k = 25. Let w(y) be the second derivative of b*y + 0 + 0*y**2 + 1/4*y**4 - 3/20*y**5 + y**3. Determine i so that w(i) = 0.
-1, 0, 2
Let b(g) be the first derivative of 9/2*g**2 - 6*g + 241 + 12*g**3 + 21/4*g**4. Factor b(m).
3*(m + 1)**2*(7*m - 2)
Suppose -30*i + 118 - 58 = 0. Find l such that -75/4*l - 3/8*l**i - 1875/8 = 0.
-25
Let q be (-4)/26 - (-83721)/429. Factor -q + 5*o**3 - 26*o - 3*o**3 - 4*o**2 + 175.
2*(o - 5)*(o + 1)*(o + 2)
Suppose 3*g + 0*g = 9*g. Factor 4*b + g*b - 3*b**2 + 12*b + 12 + 7*b**2.
4*(b + 1)*(b + 3)
Let v = -622783/2398 - -115/218. Let c = -259 - v. Find p, given that -4/11*p + c + 2/11*p**2 = 0.
1
Suppose -8*r + 5*r = -9. Let c(s) = 64*s - 190. Let j be c(r). What is i in -1/6*i**3 + 0*i - 1/2*i**j + 2/3 = 0?
-2, 1
Suppose 4*y + 48 = -124. Let k = y - -48. Factor k*s**2 - 88*s**4 - 5*s + 0*s + 5*s**3 + 83*s**4.
-5*s*(s - 1)**2*(s + 1)
Let x(z) be the first derivative of -1/20*z**5 - 13/3*z**3 - 16*z + 3/4*z**4 + 12*z**2 + 9. Factor x(p).
-(p - 4)**2*(p - 2)**2/4
Factor -2856 + 13570*d - 30*d**4 + 7858*d + 44775*d**3 - 95*d**4 - 26532*d**2 - 27078*d**2.
-(d - 357)*(5*d - 2)**3
Let y(w) = -1346*w + 1 + w**3 + 1346*w. Let q(x) = 9*x**3 + 24*x**2 + 20*x + 5. Let l(s) = q(s) - 5*y(s). Factor l(z).
4*z*(z + 1)*(z + 5)
Let f(u) = -4*u**2 - 91*u - 10. Let b(k) = 2. Let x(n) = 6*n**2 + 136*n + 8. Let c(g) = -4*b(g) - x(g). Let y(h) = 5*c(h) - 8*f(h). Factor y(a).
2*a*(a + 24)
Let n(y) be the first derivative of y**4/6 - 398*y**3/9 + 10379*y**2/3 - 94090*y/3 - 7430. Factor n(w).
2*(w - 97)**2*(w - 5)/3
Suppose -22 - 3 = 5*y, -3*p - 2*y + 5 = 0. Suppose -2*s - 4*t + 0*t = 0, -p*t = -s. Solve s + 2/5*g**2 + 4/5*g = 0.
-2, 0
Suppose 81*k - 160 = 49*k. Let x(h) be the first derivative of -h**2 + 2/3*h**3 + 0*h + 16 + 1/2*h**4 - 2/5*h**k. Determine i so that x(i) = 0.
-1, 0, 1
Let k(m) = -m**5 - 2*m**2 - 2*m. Let r(p) = -2*p**5 + 8*p**4 + 194*p**3 + 858*p**2 + 1173*p + 500. Let l(g) = -k(g) + r(g). Solve l(n) = 0.
-5, -1, 20
Let n be ((429/(-44))/(-13))/((-2)/(-8)). Let r be 2 + n/(-12) + (-5)/(-4). Find x such that -1/2*x**4 + 1/6*x**r - 2/3*x**5 + 0*x + 0*x**2 + 0 = 0.
-1, 0, 1/4
Solve -4175*h**2 - 649 + 4170*h**2 - 11 + 340*h = 0.
2, 66
Factor -2/5*r**3 - 588/5*r**2 + 0 + 0*r.
-2*r**2*(r + 294)/5
Factor 0*z**2 - 470596 + 2744*z - 13*z**2 - 12*z**2 + 21*z**2.
-4*(z - 343)**2
Suppose 229 = -7*n - 44. Let o be (-26)/n + 79/3. Factor 12 - 6*h**3 - o*h + 18*h**2 + 11*h**3 - 8*h**3.
-3*(h - 4)*(h - 1)**2
Suppose 16 = -984*t + 966*t + 52. Suppose -5*u = -12 - 3. Solve 13*j - 40*j**3 - u*j**t + 3 - j + 9 + 37*j**3 = 0.
-2, -1, 2
Suppose 3*s + l + 268 = 278, -2*l + 6 = -s. Determine u, given that -5/6 + 1/3*u**s - 1/12*u**3 + 7/12*u = 0.
-2, 1, 5
Let o(r) be the first derivative of r**8/7560 + 2*r**7/945 + 13*r**6/1620 + r**5/90 - r**3/3 - 81. Let u(s) be the third derivative of o(s). Solve u(j) = 0.
-6, -1, 0
Solve -95535*d**3 + 180 - 11*d**2 + 95538*d**3 + 92*d**2 - 264*d = 0 for d.
-30, 1, 2
Let z(i) = -i + 30. Let t be z(22). Suppose -8 = 5*s + 4*d, t*s + 5*d = 4*s - 10. Factor 15 + s + 2*o**2 + 3 + 12*o.
2*(o + 3)**2
Factor -1280 + 4*p**2 - 162*p - 2*p**2 + 87*p + 123*p.
2*(p - 16)*(p + 40)
Factor 12/7*o**2 - 2/7*o**3 - 12/7 + 2/7*o.
-2*(o - 6)*(o - 1)*(o + 1)/7
Let f(d) be the first derivative of -16*d - 1/3*d**3 + 19 + 17/2*d**2. Factor f(m).
-(m - 16)*(m - 1)
Let i(q) be the first derivative of -16*q**5 + 2370*q**4 - 1575*q**3 + 295*q**2 - 727. Find t, given that i(t) = 0.
0, 1/4, 118
Let k(s) = s**2 + 31*s - 10. Let y be k(-36). Factor -y*m**2 + 42*m + 8 + 143*m**2 + 16.
-3*(m - 2)*(9*m + 4)
Let i(y) be the third derivative of -y**8/28 - 23*y**7/350 + 17*y**6/200 + 23*y**5/100 + 3*y**4/40 + 53*y**2 + 17*y. Solve i(h) = 0.
-1, -3/20, 0, 1
Let s(w) be the second derivative of 11*w**2 + 0*w**3 + 1/12*w**5 + 0 + 5/24*w**4 + 4*w. Let a(c) be the first derivative of s(c). Let a(x) = 0. What is x?
-1, 0
Let d(n) = 33*n - 288. Let i(t) = -8*t - 41. Let v be i(-5). Let c(a) = a**2 - a + 1. Let s(x) = v*c(x) + d(x). Factor s(h).
-(h - 17)**2
Let m = -109 + 65. Let v = m + 48. Factor -w**3 + w**4 + w**v - w**3 + 0*w**4.
2*w**3*(w - 1)
Let o(a) = -88*a**3 - 1488*a**2 - 2236*a + 546. Let l(w) = 58*w**3 + 992*w**2 + 1490*w - 363. Let v(d) = -10*l(d) - 7*o(d). Factor v(f).
4*(f + 2)*(f + 12)*(9*f - 2)
Let g = 62042/217 + -8686/31. Suppose -g + 4/7*m**3 - 4*m + 16/7*m**2 = 0. Calculate m.
-5, -1, 2
Let a(p) be the second derivative of 0*p**3 + 4/25*p**5 - 278*p + 0*p**2 + 16/15*p**4 + 1/150*p**6 + 0. Find w, given that a(w) = 0.
-8, 0
Let t(m) be the second derivative of m**5/30 + m**4/3 + m**3 - 31*m**2 - 4*m - 3. Let d(x) be the first derivative of t(x). Factor d(a).
2*(a + 1)*(a + 3)
Suppose 3*p - 3*i = -0*p + 36, -4*i - 27 = -p. Factor 11*x**4 + 12*x**2 - 7*x**3 - 9*x**3 - p*x**4.
4*x**2*(x - 3)*(x - 1)
Let k(r) be the second derivative of r**6/1440 - 7*r**5/120 - 73*r**3/6 + 24*r. Let a(s) be the second derivative of k(s). Solve a(n) = 0 for n.
0, 28
Suppose -f + 16 = -26. Let g be ((-136)/f)/((-30)/(-45)) - -6. Factor -u - g + 1/7*u**2.
(u - 8)*(u + 1)/7
Let u be (42 + (-31 - 5))/(0 - -2). Let o be 3/36 - (-1)/4. Solve 0 - o*c**4 - 2/3*c**u + 2/3*c + 1/3*c**2 = 0 for c.
-2, -1, 0, 1
Factor 1361 - 1400*a - 1960*a**2 + 5*a**3 + 1139 + 2025*a**2.
5*(a - 10)*(a - 2)*(a + 25)
Let r = -158 + 154. Let h be ((-145)/35 - r)*-8. Solve h*s + 20/7*s**2 + 0 = 0 for s.
-2/5, 0
Let p be (-88 - (-1261)/13) + 239/(-26) + (-2)/(-4). Find a such that -2/13*a + 4/13*a**2 + 2/13*a**3 - p = 0.
-2, -1, 1
Suppose -10 - 12 = -3*k - 5*w, -5*w + 30 = 5*k. Suppose 4*i - 18 = -2*s, -i - 3*i = -k*s. Factor -14 + 22 + 7 - i*z**2 + 12*z.
-3*(z - 5)*(z + 1)
Let h(n) be the second derivative of -n**5/90 - 7*n**4/36 - 6*n**2 + 4*n + 3. Let f(o) be the first derivative of h(o). Factor f(m).
-2*m*(m + 7)/3
Let v(y) be the second derivative of y**7/42 + 2*y**6/15 + y**5/10 - y**4/3 - y**3/2 - 972*y. Factor v(m).
m*(m - 1)*(m + 1)**2*(m + 3)
Suppose -32 = 13*s - 5*s. Let p be (-26 + s)*((-3)/(-42))/(-1)