-2, -1
Let k(s) be the third derivative of -s**8/84 - 2*s**7/105 + s**6/10 + s**5/3 + s**4/3 + 12*s**2 + 5. Find j, given that k(j) = 0.
-1, 0, 2
Let q = -7 - -9. Suppose -k**3 + 0*k**3 + 5*k**3 + 0*k**3 + 12*k**q + 12*k + 4 = 0. Calculate k.
-1
Let b(t) be the third derivative of -t**6/480 + 19*t**5/240 - 7*t**4/6 + 8*t**3 - 346*t**2. Determine x, given that b(x) = 0.
3, 8
Let l = 1744 + -1740. Factor 3*c**2 + 0*c - 3/2*c**l + 0 + 3/2*c**3.
-3*c**2*(c - 2)*(c + 1)/2
Let p(o) be the second derivative of -o**6/30 + 3*o**5/10 - 3*o**4/4 + 2*o**3/3 + 2*o - 10. Determine t, given that p(t) = 0.
0, 1, 4
Let i(l) be the first derivative of -441*l**4/2 - 1904*l**3/9 - 220*l**2/3 - 32*l/3 - 174. Factor i(v).
-2*(7*v + 2)**2*(27*v + 4)/3
Let v(d) be the second derivative of -d**7/14 - 3*d**6/5 - 21*d**5/10 - 4*d**4 - 9*d**3/2 - 3*d**2 + 52*d - 2. Find i such that v(i) = 0.
-2, -1
Let d(t) be the second derivative of -8*t + 0 + 7/15*t**3 - 1/60*t**4 - 49/10*t**2. Factor d(s).
-(s - 7)**2/5
Suppose 0*a + 120 = 30*a. Let n(k) be the third derivative of 0*k**3 + 0*k - 8*k**2 + 0*k**a - 1/420*k**5 + 0. Factor n(m).
-m**2/7
Let d = -10619 - -10622. Factor 1/4*z**d + 0 + 0*z**2 - z.
z*(z - 2)*(z + 2)/4
Let q(t) = -t**3 + 11*t**2 + 32*t - 237. Let s be q(12). Let 6*x**s - 12 + 45/4*x**2 - 6*x + 3/4*x**4 = 0. Calculate x.
-4, -1, 1
Let o = 296 - 291. Suppose o*u = 48 - 38. Let -2/5*s - 6/5*s**3 + 0 - 6/5*s**u - 2/5*s**4 = 0. Calculate s.
-1, 0
Suppose -22*n = -28*n + 18. Let k(o) be the third derivative of 1/240*o**5 - n*o**2 + 0*o + 0*o**3 + 0 + 0*o**4 + 1/480*o**6. Factor k(p).
p**2*(p + 1)/4
Let g be 1*2/4*7/((-7)/(-4)). Find b such that 6/5*b**4 + 0 + 3/5*b - 6/5*b**g + 0*b**3 - 3/5*b**5 = 0.
-1, 0, 1
Let k be (-2)/4 - 721/(-14). Suppose 5*t - 4*m - k = 0, -3*t - 2*t + 3*m + 47 = 0. Suppose 3*s - 3*s**2 - s**2 - 2*s + t*s = 0. Calculate s.
0, 2
Solve 0 + 10*z**3 - 50/3*z - 5/3*z**4 - 5*z**2 = 0.
-1, 0, 2, 5
Suppose 7 + 37 = 22*n. Let o(s) be the first derivative of -1/12*s**3 + 0*s - 4 + 1/20*s**5 + 1/16*s**4 - 1/24*s**6 + 0*s**n. Determine w, given that o(w) = 0.
-1, 0, 1
Solve 12/5*d + 0 + 6/5*d**4 + 3*d**3 - 33/5*d**2 = 0.
-4, 0, 1/2, 1
Let x be 2/(-60)*(-16)/96. Let p(z) be the third derivative of 0*z**3 - 1/36*z**4 + 0*z + 0 + 3*z**2 + x*z**5. Factor p(o).
o*(o - 2)/3
Let j(v) be the second derivative of 1/5*v**5 - 2/3*v**4 + 1/5*v**6 - 2/3*v**3 + v**2 + 12*v + 0. Factor j(m).
2*(m - 1)*(m + 1)**2*(3*m - 1)
Let w**4 - 3*w + 2*w**2 + 259 + 237 + 7*w**3 + 12*w**2 - w**2 - 514 = 0. What is w?
-3, -2, 1
Let l(o) be the third derivative of o**8/10080 - 7*o**6/1080 + o**5/30 + o**4/12 + 16*o**2. Let p(s) be the second derivative of l(s). Factor p(u).
2*(u - 2)*(u - 1)*(u + 3)/3
Let i(d) be the second derivative of 0 + 5/6*d**3 - 5/42*d**7 + 19*d + 0*d**2 + 5/6*d**4 - 1/3*d**6 + 0*d**5. Factor i(w).
-5*w*(w - 1)*(w + 1)**3
Let v = -8 + 10. Find r, given that 15*r**3 + 2*r**5 + 3*r**4 - 12*r - 2*r**5 + v*r**5 - 15*r**2 - 5*r**5 + 12 = 0.
-2, -1, 1, 2
Let m(p) = -p**3 - 74*p**2 - 1116*p - 157. Let b be m(-53). What is h in 1/4*h**b - 7/4*h - 2 = 0?
-1, 8
Let f(n) = -n**2 - n + 13. Let i(g) = -g. Let r(s) = -f(s) + 3*i(s). Let x be r(-3). Solve 2/7 - 3/7*v - 2/7*v**x = 0 for v.
-2, 1/2
Let o = 11/69 + 197/207. What is c in 0*c + 0 - 2/3*c**5 - 4/9*c**3 + 0*c**2 + o*c**4 = 0?
0, 2/3, 1
Factor -486/5 + 513*m + 33/5*m**3 + 588/5*m**2.
3*(m + 9)**2*(11*m - 2)/5
Let l be (208/13)/64*16. Suppose -6/5*p**2 - 2/5*p + 0 - 2/5*p**l - 6/5*p**3 = 0. Calculate p.
-1, 0
Suppose -4*a = -q + 31, 3*a - 7 = -q - q. Let m = 22 - q. What is l in 2*l**5 + 10*l**4 + 16*l**3 - 2*l**3 - 13*l - 8 - m*l + 8*l - 2*l**2 = 0?
-2, -1, 1
Let j be 96/80 + (-4)/5. Let k(f) be the second derivative of 0 - 7/3*f**3 + f + 1/7*f**7 - f**4 - 2*f**2 + j*f**5 + 8/15*f**6. Suppose k(t) = 0. What is t?
-1, -2/3, 1
Suppose 2*d = 190 - 186. Suppose 3*o = -5*a + 20, a = 3*a + 2*o - 12. Factor -25*q**2 - 2 + 26*q**d + a + q**3 - q.
(q - 1)*(q + 1)**2
Let w = 93 - 89. Let c be (w/(-6) - (-20)/(-24))*-2. Factor 0*m + 1/3*m**c + 1/3*m**2 + 0.
m**2*(m + 1)/3
Let v(t) be the third derivative of 0 + 35*t**2 + 0*t + 2*t**3 + 1/30*t**5 - 5/12*t**4. Factor v(c).
2*(c - 3)*(c - 2)
Suppose -4 = -t - 2. Let j = t + 1. Determine a so that 10*a**2 + 3*a**3 - 8 - a**j - 4*a**2 = 0.
-2, 1
Let z(o) be the first derivative of -1/20*o**5 - 32 + 0*o - 1/4*o**3 - 1/8*o**2 - 3/16*o**4. Factor z(d).
-d*(d + 1)**3/4
Let p be 2/(-6) - 45004/(-30). Let c = 1505 - p. Factor 18/5*b**5 - 4/5*b**2 + c*b**3 - 48/5*b**4 + 0*b + 0.
2*b**2*(b - 2)*(3*b - 1)**2/5
Suppose 0 = -47*n + 34*n + 52. Let a(g) be the first derivative of 0*g - 5/9*g**3 + 4 - 1/15*g**5 - 1/3*g**2 - 1/3*g**n. Factor a(x).
-x*(x + 1)**2*(x + 2)/3
Let c = -63 - -67. Suppose -s - 5 = -3*b, -2*b - 3*s - 19 = -c. Find n such that 0*n + b + 0*n**2 + 3/4*n**5 + 0*n**3 + 3/4*n**4 = 0.
-1, 0
Suppose -2*y - 3*y - 14 = 2*j, 5*j + 2*y - 7 = 0. Let z = 36 - 36. Factor 4*b**j - 6*b**3 + 2*b + z*b**3.
-2*b*(b - 1)*(b + 1)
Let h be 3 - (1175/80)/5. Let d(m) be the third derivative of -1/80*m**5 - h*m**4 - 5*m**2 + 0 + 3/8*m**3 + 0*m. Factor d(i).
-3*(i - 1)*(i + 3)/4
Let j(y) be the third derivative of 3*y**5/80 + y**4/48 - 2*y**2 + 4*y. Determine f, given that j(f) = 0.
-2/9, 0
Let q = 1666 + -1664. Determine x so that -8*x - 8/3 - 6*x**2 + 4/3*x**3 + q*x**4 = 0.
-1, -2/3, 2
Let j(t) be the third derivative of 0 - 2/3*t**3 + 10*t**2 - 1/30*t**5 - 1/120*t**6 + 0*t + 7/24*t**4. Determine g, given that j(g) = 0.
-4, 1
Suppose b = -24 + 29, 36 = 4*i + 4*b. Let -4/7*o**3 + 0*o**2 - 6/7*o**i + 0*o - 2/7*o**5 + 0 = 0. Calculate o.
-2, -1, 0
Let y(u) = -453*u**2 + 120*u - 14. Let p(s) = -452*s**2 + 120*s - 12. Let n(a) = -3*p(a) + 2*y(a). Find b such that n(b) = 0.
2/15
Let h(z) be the first derivative of z**4/78 + z**3/39 - 7*z - 5. Let b(o) be the first derivative of h(o). Let b(t) = 0. Calculate t.
-1, 0
Let v = 907/2520 - 5/14. Let j(b) be the third derivative of 0*b + 0 + 0*b**3 + v*b**6 - 1/180*b**5 + 0*b**4 + 8*b**2. Let j(q) = 0. Calculate q.
0, 1
Suppose -4*x = -3*n - 15, -3*x + 4*x = -2*n - 10. Suppose s + 3*s - 4 = x, -3*w + s = -5. Factor -1 - 1/2*m**w - 3/2*m.
-(m + 1)*(m + 2)/2
Suppose 0 - 90/23*o + 2/23*o**3 + 88/23*o**2 = 0. Calculate o.
-45, 0, 1
Let d(j) = 50*j**3 - 75*j**2 + 45*j - 5. Let y(f) = -13*f**3 + 19*f**2 - 11*f + 1. Let g(l) = -4*d(l) - 15*y(l). Factor g(o).
-5*(o - 1)**3
Let o be 2*1/(-12) - (-30)/(-36). Let d be (-6)/(-27) + 1 + o. Find m such that 0 - d*m**2 + 0*m = 0.
0
Let w(n) be the first derivative of 2*n**3/45 - 34*n**2/3 + 2890*n/3 + 1. Factor w(i).
2*(i - 85)**2/15
Let h(w) = -w**3 - 27*w**2 - 50*w + 17. Let g be h(-25). Let p = g + -13. Factor -j**2 + 5/2*j**3 - 2*j**p + 0 + 1/2*j**5 + 0*j.
j**2*(j - 2)*(j - 1)**2/2
Let v be 60/15 + (-33)/9. Factor 2/3 + v*a**2 + a.
(a + 1)*(a + 2)/3
Let s(h) be the third derivative of -h**5/15 - 17*h**4/6 - 32*h**3/3 - 425*h**2. Determine f so that s(f) = 0.
-16, -1
Let s(l) be the third derivative of -l**9/36288 + l**7/3024 - 13*l**5/60 - 17*l**2. Let h(r) be the third derivative of s(r). Determine t so that h(t) = 0.
-1, 0, 1
Let m(d) = 6*d**3 - 12*d**2 + 9. Let o(l) = 9*l - 6*l - 4*l. Let c be o(3). Let u(q) = q**3 - q - 1. Let h(a) = c*u(a) - m(a). Factor h(j).
-3*(j - 1)**2*(3*j + 2)
Let q(o) be the second derivative of -4*o**2 + 1/5*o**5 + 19*o + 0 + 10/3*o**3 - 4/3*o**4. Solve q(j) = 0.
1, 2
Let d(z) = -z**2 + 9*z + 30. Let p(k) = 9*k**2 - 71*k - 241. Let q(u) = -51*d(u) - 6*p(u). Factor q(a).
-3*(a + 4)*(a + 7)
Let s(r) = 5*r**3 - 20*r**2 - 10*r. Let m(j) = 3*j**3 - 10*j**2 - 4*j. Let l(k) = -5*m(k) + 2*s(k). Let l(p) = 0. What is p?
0, 2
Let t(x) be the third derivative of 1/52*x**4 - 1/780*x**6 - 6*x**2 + 0 - 2/39*x**3 + 0*x**5 + 0*x. Let t(p) = 0. Calculate p.
-2, 1
Let n(w) be the third derivative of w**7/1680 - 223*w**6/240 + 49729*w**5/80 - 11089567*w**4/48 + 2472973441*w**3/48 + 8*w**2 + 23. Factor n(p).
(p - 223)**4/8
Let w be (-70)/2352*1/(-45). Let d(h) be the third derivative of 0*h**3 + 0*h**5 + 0 + 0*h**7 + 0*h - w*h**8 - 4*h**2 - 1/108*h**4 + 1/270*h**6. Solve d(b) = 0.
-1, 0, 1
Factor 42520*v + 2592 + 31*v**3 + 26*v**3 - 3*v**4 - 54*v**2 - 45112*v.
-3*(v - 12)**2*(v - 1)*(v + 6)
Let d = 5 