be the first derivative of -r**6/2 + 27*r**5/5 + 195*r**4/4 - 729*r**3 + 1848*r**2 - 1728*r + 3340. Find c such that a(c) = 0.
-9, 1, 8
Let z(a) = 53*a + 323. Let t be z(-23). Let p be (6/(-88))/(336/t). Solve -6/11*r**3 - 6/11*r**2 - 2/11*r**4 - p*r + 0 = 0.
-1, 0
Let z(q) be the first derivative of 162*q**5/5 - 2250*q**4 + 122984*q**3/3 + 28000*q**2 + 6272*q - 1981. Factor z(v).
2*(v - 28)**2*(9*v + 2)**2
Let t(k) be the third derivative of -1/3*k**4 + 0 + 12*k**2 + 7/60*k**6 + 0*k**5 + 0*k**3 + 0*k + 1/35*k**7. Factor t(n).
2*n*(n + 1)*(n + 2)*(3*n - 2)
Let m = 245417/2 - 122707. Factor -m*r**3 - r**4 + 1/4*r**5 + 5/4*r + r**2 + 0.
r*(r - 5)*(r - 1)*(r + 1)**2/4
Let 0 - 12/5*k - 3*k**2 + 1833/5*k**3 = 0. What is k?
-1/13, 0, 4/47
Let m(n) be the first derivative of -1/15*n**4 + 0*n**3 + 42 + 0*n**2 + 0*n - 2/75*n**5. What is l in m(l) = 0?
-2, 0
Let t = -1214683 - -1214686. Suppose 15/7 - 106/7*i - 86/7*i**t + 5/7*i**4 + 172/7*i**2 = 0. What is i?
1/5, 1, 15
Let q(j) be the first derivative of 5*j**3/3 - 1655*j**2/2 - 6700*j + 3074. Solve q(h) = 0 for h.
-4, 335
Let z(y) be the third derivative of -y**6/120 + 3*y**5/40 - 41*y**3/3 + 22*y**2 - 2*y. Let o(m) be the first derivative of z(m). Factor o(n).
-3*n*(n - 3)
Let l(w) = 2*w**2 + 19*w - 32. Let v be l(2). Suppose -3*b - 5*a = v, -a + 36 - 38 = b. Factor -1/6*d**b + 2*d - 6.
-(d - 6)**2/6
Suppose -3*m + 5*t = m - 540, 500 = 4*m + 5*t. Let j = m + -71. Factor -594 - 336*w**3 - 174 - j*w**4 - 1056*w**2 - 3*w**5 + 8*w**4 - 1536*w.
-3*(w + 1)*(w + 4)**4
Let u(r) be the first derivative of 2*r**5/105 + 137*r**4/14 - 1660*r**3/21 + 4996*r**2/21 - 2224*r/7 + 11088. Factor u(s).
2*(s - 2)**3*(s + 417)/21
Suppose -23*v - 57*v + 78 = -242. Find n such that 10/7*n - 18/7*n**2 + 2*n**v - 10/7*n**3 + 4/7 = 0.
-1, -2/7, 1
Let -2346/5 + 776/5*f + 2/5*f**2 = 0. Calculate f.
-391, 3
Suppose -48944 = -12*j + 88*j. Let p = 646 + j. Factor -8*z**p + 4/3 + 20/3*z.
-4*(z - 1)*(6*z + 1)/3
Let o(x) be the third derivative of -x**6/60 + 5*x**5/18 - 11*x**4/9 + 4*x**3/3 - x**2 + 2144*x. Suppose o(w) = 0. Calculate w.
1/3, 2, 6
Let j(k) be the first derivative of -9/8*k**3 + 21/8*k**2 + 9 + 3/32*k**4 + 0*k. Suppose j(f) = 0. Calculate f.
0, 2, 7
Let w(m) be the first derivative of 4*m**3 + 0*m - 3/5*m**5 + 161 + 3/4*m**4 - 6*m**2. Factor w(l).
-3*l*(l - 2)*(l - 1)*(l + 2)
Let q(n) be the second derivative of n**5/40 + n**4 + 23*n**3/12 - 305*n + 5. Factor q(h).
h*(h + 1)*(h + 23)/2
Let n be 1/2*(-22 - -60). Suppose -2*w**4 - n*w**2 - 9*w**2 - 8*w**3 + 28*w**3 - 4*w**2 = 0. What is w?
0, 2, 8
Let o(m) be the second derivative of m**4 + 1187*m**3/3 - 198*m**2 - 1105*m + 1. Determine b so that o(b) = 0.
-198, 1/6
Let p(j) = 26*j**2 + 2*j + 3. Let m be p(-1). Factor 9 + 2*n**2 + 27 + 14 - 7*n + m*n.
2*(n + 5)**2
Suppose 6*h**4 - 2751 + 5556 - 15*h**3 + 303*h**2 - 2760 - 249*h - 96*h**3 + 6*h**4 = 0. What is h?
1/4, 1, 3, 5
Let x(i) = -5*i**4 - 130*i**3 + 45*i**2 + 400*i + 170. Let f(p) = -p**2 + 3. Let c(z) = -30*f(z) - x(z). Solve c(j) = 0 for j.
-26, -1, 2
Suppose 10*w + 0 = -31*w - 0. Let y(a) be the third derivative of 1/210*a**5 + 1/84*a**4 - 11*a**2 + w + 0*a + 0*a**3. Find j, given that y(j) = 0.
-1, 0
Let w(z) be the third derivative of z**6/200 - 3*z**5/20 - 33*z**4/40 - 17*z**3/10 + 7886*z**2. Determine r so that w(r) = 0.
-1, 17
Let h(x) = -9*x**2 + 82*x - 288. Let z(i) = -7*i**2 + 75*i - 288. Let w(f) = 3*h(f) - 4*z(f). Factor w(l).
(l - 48)*(l - 6)
Let a(s) = 6*s**2 - 3*s - 1. Suppose -22*v + 21*v - 3 = 0. Let w(b) = -6*b**2 + 2*b + 1. Let z(l) = v*a(l) - 4*w(l). Determine h, given that z(h) = 0.
-1/2, 1/3
Let m(k) be the second derivative of -k**7/70 + 3*k**6/20 - k**5/4 - 3*k**4/2 - 36*k**2 + 2*k - 3. Let x(h) be the first derivative of m(h). Factor x(f).
-3*f*(f - 4)*(f - 3)*(f + 1)
Let v be 7/((-168)/16)*-6. Find g such that -4*g**3 - 10*g**2 + 3*g**5 + 9*g**3 - 8*g**5 + 10*g**v = 0.
-1, 0, 1, 2
Let q(f) be the second derivative of 11*f**4/96 - 89*f**3/2 + 97*f**2/4 - 39*f - 70. Let q(n) = 0. What is n?
2/11, 194
Let o be 12/72 - (-5 + 91/18). Let f(u) be the third derivative of 8*u**2 - o*u**3 + 0 - 1/360*u**5 + 0*u + 1/36*u**4. Let f(m) = 0. Calculate m.
2
Factor -286/7 + 1/7*n**2 + 9/7*n.
(n - 13)*(n + 22)/7
Let m = 11074/15 - 10694/15. Suppose -m*a + 4/3*a**2 + 24 = 0. What is a?
1, 18
Let j(n) be the third derivative of 0*n + 1/110*n**5 - 2/33*n**3 - 1/44*n**4 + 1/330*n**6 - 48*n**2 + 0. Factor j(p).
2*(p - 1)*(p + 2)*(2*p + 1)/11
Let t be (-2 - 280/(-135))*(0 + -4 + 10). Let v(y) be the third derivative of t*y**3 + 0*y - 5/36*y**4 + 1/90*y**5 + 0 + 18*y**2. Factor v(d).
2*(d - 4)*(d - 1)/3
Factor -62/3*d - 20*d**2 + 0 + 2/3*d**3.
2*d*(d - 31)*(d + 1)/3
Factor -12995*j - 252 + 25934*j + 3*j**3 + 39*j**2 - 12999*j.
3*(j - 3)*(j + 2)*(j + 14)
Let f = -70 + 364/5. Let l be -1 + 2 + ((-590)/50 - -11). Solve l*j**2 + f*j + 49/5 = 0.
-7
Let p(n) be the second derivative of -1/25*n**6 + 3*n + 16/5*n**2 + 2/25*n**5 - 17 + 1/210*n**7 - 8/5*n**3 + 4/15*n**4. Suppose p(l) = 0. Calculate l.
-2, 2
Suppose 786*s**2 + 791*s**2 - 580 - 1572*s**2 + 178*s + 102*s = 0. Calculate s.
-58, 2
Let f(o) be the second derivative of -o**6/150 - 1014*o**5/25 - 342732*o**4/5 + 3428*o. Factor f(i).
-i**2*(i + 2028)**2/5
Let g = -34 + 2. Let i = g - -36. Factor -2*w + 5*w**3 - 17*w**3 + 11*w + 4*w**4 - 4*w**2 - w + i*w**5.
4*w*(w - 1)**2*(w + 1)*(w + 2)
Suppose 54*b = 58*b - 12*c - 76, 4*b + 2*c = 6. Let n(i) be the second derivative of -40*i + 1/3*i**3 + 0 - 1/30*i**5 + 2/3*i**2 + 0*i**b. Factor n(y).
-2*(y - 2)*(y + 1)**2/3
Let l(s) be the third derivative of -s**5/15 + 210*s**4 - 264600*s**3 - s**2 - 35*s + 13. Let l(t) = 0. What is t?
630
Let n(i) = -i**3 + 186*i**2 + 4245*i - 4415. Let d(x) = -2*x**3 + 558*x**2 + 12730*x - 13246. Let h(f) = 3*d(f) - 8*n(f). Factor h(u).
2*(u - 1)*(u + 47)**2
Let t(o) be the third derivative of 25/4*o**4 + 0*o + o**2 - 5/4*o**6 + 58 + 56/3*o**5 - 375/2*o**3 + 1/42*o**7. Factor t(d).
5*(d - 15)**2*(d - 1)*(d + 1)
Determine i, given that 2124/11 - 1/11*i**2 + 193*i = 0.
-1, 2124
Let w(y) be the first derivative of -238 + 17/6*y**4 + 16/15*y**5 + 20/9*y**3 + 0*y + 1/9*y**6 + 0*y**2. Suppose w(o) = 0. What is o?
-5, -2, -1, 0
Let v(b) be the third derivative of 0*b**4 + 2/1785*b**7 - 1/255*b**5 + 7/1020*b**6 + 0 - 74*b**2 - 1/408*b**8 + 0*b**3 + 0*b. Determine l so that v(l) = 0.
-1, 0, 2/7, 1
Let u(f) be the second derivative of 3*f**5/20 + 9*f**4/4 - 17*f**3 + 36*f**2 - f + 264. Factor u(x).
3*(x - 2)*(x - 1)*(x + 12)
Let r(f) = 2*f**2 - f. Let t be r(-2). Let x(n) = -n**2 + 9*n + 14. Let p be x(t). Factor -2*b**2 + 11*b**3 + 156*b**4 - 4*b**3 - 4*b**5 - 160*b**p.
-b**2*(b + 2)*(2*b - 1)**2
Factor -13/3*w**2 - w + 15 + w**3.
(w - 3)**2*(3*w + 5)/3
Suppose -26226187*o + 26226187*o - 390*o**3 - 5*o**4 - 385*o**2 = 0. Calculate o.
-77, -1, 0
Let a be (-2)/10 - (-766)/5. Determine u so that -4*u + 4*u**3 + 52 + 36*u**2 + 12*u**2 - a*u**2 + 53*u**2 = 0.
-1, 1, 13
Find k, given that 417*k + 322*k**2 + 683*k - 2*k**3 + 180*k - 1600*k**2 = 0.
-640, 0, 1
Let g(s) be the third derivative of -11/6*s**3 + 1/390*s**5 + 0*s + 0 + 1/2340*s**6 - s**2 + 0*s**4. Let r(w) be the first derivative of g(w). Solve r(b) = 0.
-2, 0
Let s(q) be the second derivative of q**5/130 + 7*q**4/78 - 7*q**3/13 - 27*q**2/13 - q + 7799. Factor s(i).
2*(i - 3)*(i + 1)*(i + 9)/13
Let d(b) be the third derivative of -25/3*b**3 + 1/300*b**6 + 5/4*b**4 - 60*b**2 + 0 + 0*b - 1/10*b**5. Let d(w) = 0. Calculate w.
5
Suppose -2*c - 16 = b - 11, -c = 4*b - 8. Solve -32 - 3*w**2 + 21*w**2 - w**3 + 4*w + 7*w + b*w**3 + w = 0.
-8, -2, 1
Let x be (-90)/(-8)*-30*94/(-8460). Determine l, given that 5/2*l**2 - x*l**3 - 1/4*l**5 - 5/2*l**4 + 0 + 4*l = 0.
-8, -2, -1, 0, 1
Suppose 5*z - 2*f = 402 + 229, z = -4*f + 113. Suppose -3*o - z = -131. Factor 2/7 - 4/7*h**o + h.
-(h - 2)*(4*h + 1)/7
Find t such that 15/8*t**2 - 13 - 1/8*t**3 - 9/4*t = 0.
-2, 4, 13
Determine j, given that 13*j**3 + 39*j + 5*j**4 - 75437*j**2 + 41*j + 75557*j**2 + 32*j**3 = 0.
-4, -1, 0
Suppose -9 = -2*f - 3*h + 2*h, f = -3*h + 12. Suppose -13 - 18*k**f + 197 + 544*k - 198*k**2 + 588*k**2 = 0. Calculate k.
-2/3, 23
Suppose 48*t + 14*t = 248. Suppose 3*j - 4*b - 18 = -26