- 3*p**4/4 - 19*p**3/6 - 192*p**2. Find g, given that s(g) = 0.
-1, 19
Let n(h) be the first derivative of -h**6/30 + h**5/5 + 2*h**4/3 - 19*h**2/2 + 1. Let t(d) be the second derivative of n(d). Factor t(w).
-4*w*(w - 4)*(w + 1)
Let y(s) be the third derivative of -s**9/60480 + s**8/3360 - s**7/420 + s**6/90 + 29*s**5/60 - 23*s**2. Let c(l) be the third derivative of y(l). Factor c(r).
-(r - 2)**3
Let v(h) be the first derivative of -h**5/5 - 13*h**4/4 - 16*h**3 - 18*h**2 - 54. Let v(i) = 0. Calculate i.
-6, -1, 0
Let l = 6594 - 19780/3. Factor -4/3*q**2 + l*q - 2/3*q**3 + 4/3.
-2*(q - 1)*(q + 1)*(q + 2)/3
Let f(t) be the third derivative of -t**7/42 - 3*t**6/2 - 69*t**5/2 - 675*t**4/2 - 3375*t**3/2 - t**2 + 79*t. Factor f(q).
-5*(q + 3)**2*(q + 15)**2
Let j(r) be the first derivative of r**4 + 8*r**3/3 + 74. Factor j(h).
4*h**2*(h + 2)
Let d(h) be the third derivative of -h**6/40 - 27*h**5/5 - 729*h**4/2 - 115*h**2 + h. Find g, given that d(g) = 0.
-54, 0
Suppose x - 15 = 3*j, 4*x = -0*j - 2*j + 130. Factor 295*d**2 - 185*d**3 + 19*d**4 - 91*d + x - 84*d + 16*d**4.
5*(d - 3)*(d - 1)**2*(7*d - 2)
Let i = 9784/3 - 3261. Solve -2/9 - 1/9*c**2 + i*c = 0.
1, 2
Let 4/7*v**3 + 64/7*v**2 + 208/7*v + 192/7 = 0. What is v?
-12, -2
Let p(t) = 5*t + 1. Let h be p(2). Suppose 8*o = h*o - 39. Factor -3*d**5 + d - 4*d + o*d**3 - 7*d**3.
-3*d*(d - 1)**2*(d + 1)**2
Let k = 126 + -123. Factor 42 - 42 + 2*h**2 - 5*h**4 + k*h**4.
-2*h**2*(h - 1)*(h + 1)
Let z be (-550)/33*(-2 - (3 - 2)). Find d such that -z*d**2 + 104*d**2 + 5*d**4 + 25*d**5 - 54*d**2 = 0.
-1/5, 0
Let w = 37/410 + -1/738. Let r(d) be the second derivative of -10*d - 2/63*d**7 + 0*d**3 + 0 + 0*d**2 + 0*d**4 - 1/15*d**5 + w*d**6. Factor r(j).
-4*j**3*(j - 1)**2/3
Suppose 5/2*a**2 + 2645/2 + 115*a = 0. What is a?
-23
Let t(j) be the second derivative of -2*j**5/15 + 11*j**4/27 + 2*j**3/9 - 4*j**2/9 - 4*j + 12. Let t(c) = 0. Calculate c.
-1/2, 1/3, 2
Let g(d) = d**3 - d**2. Let t = -72 + 36. Let b(a) = -2*a**3 - 10*a**2 + 8*a + 4. Let l(q) = t*g(q) - 4*b(q). Factor l(k).
-4*(k - 2)*(k - 1)*(7*k + 2)
Let g(f) be the first derivative of -f**6/120 - 7*f**5/80 - 13*f**4/48 + f**3/8 + 9*f**2/4 - 20*f - 5. Let o(h) be the first derivative of g(h). Factor o(m).
-(m - 1)*(m + 2)*(m + 3)**2/4
Suppose 2*d - 10 = p, -3*p + 6 = -6*p. Let f(v) be the second derivative of -1/13*v**2 - 1/26*v**d + 0 - 4/39*v**3 - 8*v. Suppose f(n) = 0. Calculate n.
-1, -1/3
Let u = 2403/2 - 1197. Let -u*s**2 + 1/2*s**3 - 7/2 + 15/2*s = 0. Calculate s.
1, 7
Let z(t) be the first derivative of 10*t**3 + 43*t**2 - 12*t - 78. Suppose z(b) = 0. What is b?
-3, 2/15
Factor -26*j**4 - 229*j**5 + 121*j**5 - 4*j**4 + 113*j**5 + 270*j**2 - 405*j.
5*j*(j - 3)**3*(j + 3)
Suppose 5*l + 29 = 4*p + 141, -3*p = 4*l - 102. Suppose -19*o**2 - l*o + 18 + 40*o**2 + 3 - 18*o**2 = 0. What is o?
1, 7
Let b be (0/2)/((-4)/2). Let r be (13/((-312)/16))/(6/(-27)). Factor -1/5*v**r + 0 + 1/5*v**2 + b*v.
-v**2*(v - 1)/5
Let p(q) be the third derivative of q**10/252000 - q**8/33600 + q**5/20 + 12*q**2. Let n(w) be the third derivative of p(w). Factor n(t).
3*t**2*(t - 1)*(t + 1)/5
Suppose 0*q = -2*q + 8. Suppose q*u = -4*d - 8, u - 3*d = -0 + 6. Factor u*n - 2*n**2 + 4 - 4*n - 2*n**2 + 4*n**3.
4*(n - 1)**2*(n + 1)
Let b = -1906/5 - -413. Let m = -156/5 + b. Factor -m*z**4 + 9/5*z**2 - 12/5*z + 6/5*z**3 - 12/5.
-3*(z - 2)**2*(z + 1)**2/5
Let t(r) be the third derivative of -r**8/50400 + r**7/1260 - r**6/72 - 17*r**5/60 - 8*r**2. Let a(c) be the third derivative of t(c). Let a(b) = 0. What is b?
5
Let a(r) be the second derivative of -21*r + 1/8*r**4 + r**3 + 0 - 15/4*r**2. Factor a(t).
3*(t - 1)*(t + 5)/2
Let r(q) be the third derivative of -2/15*q**3 + 1/30*q**4 + 0 + 0*q + 7*q**2 - 1/300*q**5. Factor r(c).
-(c - 2)**2/5
Let o(s) = 6*s. Let j be o(2). Suppose j*u = 5*u. Factor 2/9*n - 2/3*n**2 + u - 2/9*n**4 + 2/3*n**3.
-2*n*(n - 1)**3/9
Find a such that -6*a**5 + 266*a**4 - 326*a**4 + 55*a**3 - 29*a**5 - 20*a + 14*a**2 + 46*a**2 = 0.
-2, -1, 0, 2/7, 1
Let m(t) be the third derivative of t**9/5040 + t**8/1120 + t**7/840 - 7*t**4/24 - 11*t**2. Let p(j) be the second derivative of m(j). Factor p(n).
3*n**2*(n + 1)**2
Let y(g) be the third derivative of -g**6/420 + 2*g**5/35 + 13*g**4/84 + 17*g**2 - 2*g. Suppose y(l) = 0. What is l?
-1, 0, 13
Let u(l) = -5*l**3 + 5*l**2 + 2*l - 2. Let q(p) = -14*p**2 + 24*p**3 - 11*p**2 - 12*p + 10 + p**2 + 2*p. Let f(j) = 3*q(j) + 14*u(j). Solve f(v) = 0 for v.
-1, 1
Let k(n) be the third derivative of n**7/840 - n**6/480 - n**5/30 + n**4/8 + 3*n**2 + 14*n. Factor k(t).
t*(t - 2)**2*(t + 3)/4
Factor 25*h + 35*h**3 - 3872*h**2 + 1758*h**2 + 1934*h**2.
5*h*(h - 5)*(7*h - 1)
Let k(p) = p**3 - 10*p**2 + 9*p + 4. Let v be k(9). Let w be (-1 + v)/(-1 - -2). Factor -g**2 - w*g + 0*g - 2*g**2.
-3*g*(g + 1)
Let c(z) = z**2 + z + 30. Let l be c(0). Let x = l + -27. Solve -4/9*g**x + 2/9*g - 2/9*g**4 - 2/9 + 4/9*g**2 + 2/9*g**5 = 0 for g.
-1, 1
Let h(s) = 13*s**2 - 335*s + 252. Let o be h(25). Factor 1/3*f**5 - 40/3*f - 7*f**3 - 1/3*f**4 - 4 - 47/3*f**o.
(f - 6)*(f + 1)**3*(f + 2)/3
Determine i so that -4*i - 105/4*i**3 + 18*i**2 + 29/2*i**4 + 0 - 9/4*i**5 = 0.
0, 4/9, 1, 4
Let v(l) be the second derivative of -l**5/160 + l**4/8 - 15*l**3/16 + 27*l**2/8 - 289*l. Factor v(g).
-(g - 6)*(g - 3)**2/8
Let p be (9/12)/(9/3). Let b(a) be the third derivative of -1/30*a**5 + a**2 - p*a**4 - 2/3*a**3 + 0*a + 0. Factor b(g).
-2*(g + 1)*(g + 2)
Find l such that 32*l**4 + 67*l - 118*l**2 + 3*l**5 - 2*l**5 + 14*l**2 + 12*l**3 - 3*l - 5*l**5 = 0.
-2, 0, 1, 8
Let p be 8/(-60) - (-368)/60. Factor -2*g**3 - p*g**4 + g**4 + 0*g**3 + g**2 + 6*g**4.
g**2*(g - 1)**2
Let k(d) = -3*d**5 - 6*d**4 - 8*d**2. Let n(l) = -9*l**5 - 18*l**4 - 22*l**2. Let x(q) = -11*k(q) + 4*n(q). Factor x(p).
-3*p**4*(p + 2)
Factor -24/7 - 3*j**3 - 54/7*j**2 - 3/7*j**4 - 60/7*j.
-3*(j + 1)*(j + 2)**3/7
Let g(u) be the first derivative of u**6/120 - 3*u**5/10 + 9*u**4/2 + 10*u**3 + 35. Let f(r) be the third derivative of g(r). Factor f(p).
3*(p - 6)**2
Let d(w) be the first derivative of w**5/15 + 85*w**4/12 + 812*w**3/3 + 12152*w**2/3 + 21952*w/3 + 890. Factor d(v).
(v + 1)*(v + 28)**3/3
Let v = -23 - -34. Suppose -3*u - 5*l = -0*l + 5, 4*l + v = -u. Suppose -17*q**3 + 2 - u*q + 5*q + 2*q**4 + q**3 + 8*q**5 - 4*q**2 + 8*q = 0. Calculate q.
-1, -1/4, 1
Let d(x) be the second derivative of x**6/60 + x**5/10 + x**4/6 + 11*x**2 + 2*x. Let c(i) be the first derivative of d(i). Suppose c(s) = 0. What is s?
-2, -1, 0
Let f(h) be the third derivative of 9*h**2 - 1/630*h**7 - 4/9*h**3 + 0*h + 5/18*h**4 + 7/360*h**6 - 1/10*h**5 + 0. Find z, given that f(z) = 0.
1, 2
Find n, given that 112/9*n**3 + 104/9*n**2 - 112/9*n + 4/9*n**4 - 12 = 0.
-27, -1, 1
Suppose 4*w + w = 40. Let n be (0 + 2/w)/1. Factor 1/4*z + 0 + n*z**4 + 3/4*z**3 + 3/4*z**2.
z*(z + 1)**3/4
Let p be (-110)/(-24) - 4*4/(-24). Let m(q) be the first derivative of -9/5*q**5 + p*q**4 + 0*q + 0*q**3 - 3 - 6*q**2. Factor m(x).
-3*x*(x - 2)*(x - 1)*(3*x + 2)
Let b(i) be the third derivative of i**7/70 - i**6/4 + 2*i**5/5 + 5*i**4/4 - 9*i**3/2 + 78*i**2. Factor b(z).
3*(z - 9)*(z - 1)**2*(z + 1)
Let z(f) = -16*f - 4. Let n be z(-4). Factor -84*r - 12 - 91*r**2 - n*r**2 + 4*r**2.
-3*(7*r + 2)**2
Let f be 8 - -3*35/(-21). Let o(t) be the second derivative of -6*t + 0 + 1/8*t**4 + 1/4*t**f - 3/2*t**2. Factor o(c).
3*(c - 1)*(c + 2)/2
Factor -1/2*w**3 + 1/2*w - 1 - 1/2*w**4 + 3/2*w**2.
-(w - 1)**2*(w + 1)*(w + 2)/2
Let k = 5875 + -23497/4. Suppose k*n + 0 - 3/4*n**3 + 0*n**2 = 0. What is n?
-1, 0, 1
Let l(o) be the first derivative of o**3/12 + 121*o**2/8 - 61*o/2 - 5. Factor l(r).
(r - 1)*(r + 122)/4
Factor -325*z**2 + 322*z**2 + z - z**4 + 5*z**4.
z*(z + 1)*(2*z - 1)**2
Let s(p) = -p**2 - p + 30. Let z be s(-6). Suppose z = -0*l - 7*l - l. Find x such that l + 6/5*x + 3/5*x**4 - 9/5*x**2 + 0*x**3 = 0.
-2, 0, 1
Let f(z) = z**2 - 3*z + 8. Let s(d) = 3*d**2 - 7*d + 16. Let p be (-3)/(-6) - 39/(-6). Let c(o) = p*f(o) - 3*s(o). Factor c(g).
-2*(g - 2)*(g + 2)
Let i(x) be the third derivative of -x**9/60480 + x**8/6720 - x**7/2520 - x**5/10 + 24*x**2. Let c(g) be the third derivative of i(g). Solve c(a) = 0.
0, 1, 2
Let a(z) be the first de