t v(n) be the third derivative of 0*n**5 + 0*n**4 + 0*n - 1/24*n**6 + 0 + 0*n**3 - 18*n**2. What is a in v(a) = 0?
0
Factor 1/2*t**2 - 18 + 0*t.
(t - 6)*(t + 6)/2
Suppose 5*c + 17 = 47. Let n(h) be the third derivative of 0*h - 1/70*h**7 + 0 + 3/20*h**c - 13/20*h**5 - 10*h**2 - 2*h**3 + 3/2*h**4. Let n(s) = 0. What is s?
1, 2
Let i(t) = -t**5 - t**4 + t - 1. Let o(w) = 9*w**4 + 12*w**3 + 3*w**2 + 6*w - 6. Suppose 0 = -14*d + d - 13. Let g(v) = d*o(v) + 6*i(v). Factor g(s).
-3*s**2*(s + 1)**2*(2*s + 1)
Let f(q) = 2*q**2 + q - 6. Let r be f(-3). Suppose r*p = -5*p - p. Suppose p - 3*d**5 + 8/3*d**3 + 1/3*d + 2*d**4 - 2*d**2 = 0. What is d?
-1, 0, 1/3, 1
Let b(n) be the second derivative of -n**7/378 - n**6/270 + n**5/30 - n**4/54 - 5*n**3/54 + n**2/6 + 41*n. Suppose b(l) = 0. Calculate l.
-3, -1, 1
Determine b, given that 2/3*b - 2/21*b**3 - 4/21*b**2 - 8/21 = 0.
-4, 1
Let p(u) = -u**3 + 2*u**2 + u - 3. Let k(r) = -2*r**3 - 23*r**2 - 31*r + 3. Let d(y) = -k(y) - p(y). Factor d(s).
3*s*(s + 2)*(s + 5)
Let q(f) = 5*f**2 + 55*f. Let c(z) = z**2 + 9*z. Let d = 816 + -812. Suppose 3*a + 91 = -4*m, -m + 8 = a + 30. Let g(j) = d*q(j) + m*c(j). Factor g(v).
-5*v*(v + 1)
Suppose 110*h**3 + 52/3*h + 238/3*h**2 + 0 + 10/3*h**5 + 154/3*h**4 = 0. Calculate h.
-13, -1, -2/5, 0
Let g = -23 + 25. Let 0*j - j**g - j - 4*j + 6*j = 0. Calculate j.
0, 1
Factor 8/5*y**2 + 6/5*y**3 + 0 - 4/5*y**4 - 2/5*y**5 - 8/5*y.
-2*y*(y - 1)**2*(y + 2)**2/5
Let g(w) be the third derivative of 1/6*w**4 - 1/120*w**6 + 1/60*w**5 - 2/3*w**3 + 0*w + 0 + 49*w**2. Solve g(u) = 0 for u.
-2, 1, 2
Let x(i) be the second derivative of -i**7/147 - i**6/105 + i**5/35 + 87*i. Factor x(q).
-2*q**3*(q - 1)*(q + 2)/7
Factor -4096 + 197*t - t**2 - 32*t - 37*t.
-(t - 64)**2
Let o = 52104 - 52102. Let w = -2/45 + 49/90. Determine f so that 1/2*f**o - 1/2 - 1/2*f**3 + w*f = 0.
-1, 1
Let o(l) = -7*l**4 + 25*l**3 - 27*l**2 + 3*l + 3. Let f(q) = -36*q**4 + 124*q**3 - 136*q**2 + 16*q + 16. Let s(m) = -3*f(m) + 16*o(m). Solve s(p) = 0.
0, 1, 6
Suppose 2*j + 2*l + 40 = 0, 2*j + 0*l + 3*l + 45 = 0. Let r = 17 + j. Factor u + 2*u**2 + r - 3*u + 6*u.
2*(u + 1)**2
Factor -3/2*z**4 + 3*z**2 + 3/4*z**5 + 3*z - 9/4*z**3 + 0.
3*z*(z - 2)**2*(z + 1)**2/4
Let p(y) be the first derivative of -y**3/6 + y**2/4 - 77. Determine v, given that p(v) = 0.
0, 1
Factor 67/10*m - 3/5*m**2 - 11/10.
-(m - 11)*(6*m - 1)/10
Let z(x) be the first derivative of x**4/16 - 13*x**3/12 + 11*x**2/4 + 167. Factor z(s).
s*(s - 11)*(s - 2)/4
Suppose -83 + 6 = -2*c - 3*o, -2*o - 178 = -4*c. Let l = c - 128/3. Let 4/3*h**3 + 0*h**4 - h - 2/3*h**2 - l*h**5 + 2/3 = 0. Calculate h.
-2, -1, 1
Let m(t) be the first derivative of 4/7*t**5 - 8/21*t**3 + 0*t - 8 + 3/7*t**4 + 0*t**2. Factor m(c).
4*c**2*(c + 1)*(5*c - 2)/7
Suppose 37*t = 24*t. Let r(l) be the third derivative of 1/300*l**6 - 1/150*l**5 + t + 1/15*l**3 + 0*l + 9*l**2 - 1/60*l**4. Factor r(n).
2*(n - 1)**2*(n + 1)/5
Let k(z) be the first derivative of -1/2*z**4 + 2/65*z**5 + 2 + 128/13*z + 40/13*z**3 - 112/13*z**2. Suppose k(w) = 0. What is w?
1, 4
Let 0*m + 0 - 2/7*m**4 + 4/7*m**2 - 2/7*m**3 = 0. What is m?
-2, 0, 1
Let o be 3 + (36/3)/(-3). Let g be (-12)/(-24)*(3 - o). Factor -21 + 21 - 2*z**3 + 0*z**3 + g*z**5.
2*z**3*(z - 1)*(z + 1)
Let t be (18/(-12))/(3/(-24)). Let k be ((-104)/(-28) + -3)*t/15. Suppose 0*n**3 - 2/7*n + 0 - 4/7*n**4 + 2/7*n**5 + k*n**2 = 0. What is n?
-1, 0, 1
Solve 2*v**4 - 4*v**3 + v**5 - 2 - 6*v**3 + 7*v + 2*v**5 + 0*v**5 = 0.
-2, -1, 1/3, 1
Let r(x) be the second derivative of x**6/20 - 3*x**5/20 - 280*x. Determine k so that r(k) = 0.
0, 2
Let u = 1900 + -1898. Factor -15/2*v + 3*v**u - 3 + 15/2*v**3.
3*(v - 1)*(v + 1)*(5*v + 2)/2
Let k(v) be the second derivative of -v**7/28 + 2*v**6/5 + 99*v**5/40 - 13*v + 6. Factor k(t).
-3*t**3*(t - 11)*(t + 3)/2
Let w(v) = 5*v**2 + 3*v**2 - 3*v - 4*v**3 + 6*v**2 + 3 - 17*v**2. Let a(l) = l**3 + l - 1. Let c(x) = 3*a(x) + w(x). Factor c(q).
-q**2*(q + 3)
Let o(x) be the second derivative of -x**5/5 + 2*x**3/3 + 38*x. Factor o(h).
-4*h*(h - 1)*(h + 1)
Let a = -40 + 43. Factor -5*b**a - 7*b**2 + 35*b - 3*b**2 + 0*b**3 + 2 - 22.
-5*(b - 1)**2*(b + 4)
Let o(u) be the first derivative of -15 + 3/2*u**3 + 27/8*u**2 + 0*u + 3/16*u**4. Find c, given that o(c) = 0.
-3, 0
Suppose -4*h + 8*h - 11 = v, -v - 3*h + 17 = 0. What is u in -5*u**4 + 0*u**5 + 3*u**4 + 3*u**3 + u**v - u**2 - u**4 = 0?
0, 1
Let o be (-1*2/4)/(7/(-42)). Suppose -2 = 2*k - o*k. Factor -10/3*f**4 - 10/3*f - 2/3 - 2/3*f**5 - 20/3*f**3 - 20/3*f**k.
-2*(f + 1)**5/3
Let n = 2363 + -2363. Let -6/19*z**3 + 0*z - 4/19*z**2 + 2/19*z**5 + 0 + n*z**4 = 0. Calculate z.
-1, 0, 2
Let n(x) be the third derivative of -x**6/150 - 4*x**5/25 - 7*x**4/10 + 196*x**3/15 - x**2 + 137*x. Factor n(o).
-4*(o - 2)*(o + 7)**2/5
Let v = -114 + 115. Let g(u) be the first derivative of -1/6*u**4 - v - 2/3*u**3 - u**2 - 2/3*u. Factor g(r).
-2*(r + 1)**3/3
Determine v so that 1/2*v**4 - 8*v + 0*v**2 - 8 + 2*v**3 = 0.
-2, 2
Let i = -1481/12 + 495/4. Let 0 + 0*h - 4/3*h**3 + i*h**4 + 4/3*h**5 - 1/3*h**2 = 0. Calculate h.
-1, -1/4, 0, 1
Suppose -11*k - 251 + 295 = 0. Let t(b) be the third derivative of -2/3*b**3 - 1/60*b**5 + 0*b + 7*b**2 + 1/6*b**k + 0. Factor t(a).
-(a - 2)**2
Let y(q) = q**2 - 7*q + 6. Let d be y(6). Let p be ((-6)/52)/((-28)/182). Factor -p*c**2 - 3/4*c**5 + 3/4*c**3 + 0 + 3/4*c**4 + d*c.
-3*c**2*(c - 1)**2*(c + 1)/4
Suppose -34/9*h + 10/9*h**2 - 14/3 + 2/9*h**3 = 0. Calculate h.
-7, -1, 3
Let i be -3 + (-1830)/(-9) + 4/(-3). Let x = i - 2983/15. Suppose -2/5*r + 4/15 + x*r**2 = 0. Calculate r.
1, 2
Suppose 17*q = 5*q + 24. Factor -9/7*a + 3/7*a**3 + 0*a**q - 6/7.
3*(a - 2)*(a + 1)**2/7
Suppose -9*g = -14*g, 4*g = v + 12. Let h = v - -14. Factor 3/5*c**h - 3/5*c + 0.
3*c*(c - 1)/5
Let u = 23 - 114/5. Let y be 24/(-10) + (5 - 2). Let 2/5*g + 0 + u*g**3 - y*g**2 = 0. Calculate g.
0, 1, 2
Let q(l) be the first derivative of l**3 + 3*l**2/2 - 36*l + 232. Factor q(z).
3*(z - 3)*(z + 4)
Let y = -40271/9 - -4475. Let -4/3*c**3 - 8/9*c + y*c**5 - 4/9*c**4 + 20/9*c**2 + 0 = 0. Calculate c.
-2, 0, 1
Let u(q) = 3*q**2 + 18*q - 4. Let i = -23 - -15. Let g be u(i). Find x such that -g*x + x**3 - 4*x**4 + 33*x**2 + 16 + 3*x**2 - 5*x**3 = 0.
-4, 1
Suppose 40*f = 34*f + 36. Let u(n) be the second derivative of 0*n**2 + 3/70*n**5 - 2/105*n**f - 4*n + 0*n**4 - 1/21*n**3 + 0. What is j in u(j) = 0?
-1/2, 0, 1
Let b(d) be the third derivative of -6*d**2 + 0*d**3 + 1/2*d**4 + 0 + 1/20*d**5 + 0*d. Find k such that b(k) = 0.
-4, 0
Let n be (-5)/((-1 - 6)/7). Let u(m) be the first derivative of -3/22*m**4 - 1/11*m**2 + n + 10/33*m**3 - 2/11*m. Suppose u(a) = 0. Calculate a.
-1/3, 1
Let l(u) be the first derivative of -u**5/30 + 145*u**4/6 - 21025*u**3/3 + 3048625*u**2/3 - 442050625*u/6 - 579. Factor l(r).
-(r - 145)**4/6
Suppose -4*o + 32 = 4*d, 5*d - 10 = -28*o + 33*o. Let k(y) be the second derivative of 3/16*y**4 + 3/8*y**3 - 11*y + 3/80*y**d + 0 + 3/8*y**2. Solve k(z) = 0.
-1
Let w = 40 - 36. Solve 3*f - 6*f + 9*f + 2*f**2 + w = 0.
-2, -1
Let v = -65 - -67. Let g be (-1 + -1 + v)/1. Factor -2/5*r + 2/5*r**3 + g*r**2 + 0.
2*r*(r - 1)*(r + 1)/5
Let j(s) be the third derivative of 0*s + 0 - 2/3*s**3 - 1/8*s**4 + 8*s**2 + 1/60*s**5. Factor j(q).
(q - 4)*(q + 1)
Let p(m) = 2*m**3 + 10*m**2 + 16*m - 4. Let k(v) = -4*v**3 - 19*v**2 - 33*v + 9. Let w(l) = 4*k(l) + 9*p(l). Factor w(i).
2*i*(i + 1)*(i + 6)
Suppose 9*i - 20*i - 39*i = 0. Let u(r) be the first derivative of 6/55*r**5 + 1/33*r**6 + 0*r**2 + i*r - 5 + 3/22*r**4 + 2/33*r**3. Solve u(k) = 0 for k.
-1, 0
Let 2*o**3 - 3249*o - 125 + 8*o**3 + 50*o**3 - 180*o**4 + 295*o**2 + 3199*o = 0. Calculate o.
-5/6, 1
Factor 1/3*u**3 + 16/3*u + 10/3*u**2 + 0.
u*(u + 2)*(u + 8)/3
Let x be -10 - (-1204)/119 - 14*4/(-680). Factor 0*t - 1/5*t**3 - 1/5*t**4 + 1/5*t**2 + 0 + x*t**5.
t**2*(t - 1)**2*(t + 1)/5
Factor -5*r**3 - 20528*r + 483*r**2 - 31687*r + 419323 + 402*r**2 + 607572.
-5*(r - 59)**3
Let j = 146359/11 - 13305. Factor 2/11*z**5 + 2/11*z**4 - 6/11*z**3 - 10/11*z**2 + 0 - j*z.
2*z*(z - 2)*(z + 1)**3/11
Let j(g) be the second derivative of g**8/952 - 8*g**7/1785 + g**6/255 - 13*g**2/2 - 12*g. Let k(u) be the first derivative of j(u). Factor k(f).
2*f*