 - 15476. Let p be l(-8). Determine z so that 25/4*z**3 - 27/2 + 125/4*z**p - 315/4*z**2 + 243/4*z = 0.
-2, 3/5
Let o(a) be the first derivative of 9*a**5/40 + 5*a**4 + 11*a**3/4 - 39*a**2/2 - 103*a + 123. Let p(m) be the first derivative of o(m). Factor p(d).
3*(d + 1)*(d + 13)*(3*d - 2)/2
Let n(w) be the third derivative of -w**6/120 + 43*w**5/5 - 3698*w**4 + 2544224*w**3/3 - 278*w**2. Factor n(x).
-(x - 172)**3
Let a = -274 + 551. Let f = -827/3 + a. Let f + 2/3*b**2 + 2*b = 0. What is b?
-2, -1
Suppose -24*t - 72*t + 14*t = -164. Let z(w) be the third derivative of -2/5*w**5 + 0*w + 64/3*w**3 + 0*w**4 + 0 + 7*w**t - 1/30*w**6. Factor z(i).
-4*(i - 2)*(i + 4)**2
Let i(f) be the first derivative of f**5/5 + 43*f**4/2 - 212*f**3 + 693*f**2 - 837*f - 779. Determine r so that i(r) = 0.
-93, 1, 3
Suppose 1/3*r**5 + 2/3*r**2 + 0*r**4 + 0 + 0*r - r**3 = 0. What is r?
-2, 0, 1
Find o such that 255/4*o**4 + 253 - 1/4*o**5 - 763/4*o**2 + 252*o - 503/4*o**3 = 0.
-1, 2, 253
Suppose r - 4*c = -18, -c + 36 = -2*r + 2*c. Let v be ((-14)/10 + 1)/(r/10). Determine j so that -8/9 + v*j**2 - 2/9*j**3 + 8/9*j = 0.
-2, 1, 2
Let l(s) = -6*s**2 + 2 + 3 - 8*s + 2*s**2. Suppose -31*m = -138 - 79. Let z(w) = 4*w**2 + 8*w - 6. Let v(r) = m*z(r) + 6*l(r). Solve v(h) = 0.
-3, 1
Let s = 399 + -780. Let a = s + 771/2. Factor a*i**3 - 3*i**4 + 3/4*i**5 + 3/4*i - 3*i**2 + 0.
3*i*(i - 1)**4/4
Let u = -2129509/45 + 47330. Let i = 49/45 + u. Solve -i*a**3 + 0*a - 4/3*a**2 + 0 - 10*a**5 - 52/3*a**4 = 0.
-1, -2/5, -1/3, 0
Let -4*p**3 - 14164 + 2*p**3 - 15236 - 238*p**2 - 4542*p - 48*p**2 - 6098*p = 0. Calculate p.
-70, -3
Let k(t) be the third derivative of 1/75*t**5 - 31*t + 1/10*t**4 + 0 - 8/15*t**3 - 2*t**2. Factor k(i).
4*(i - 1)*(i + 4)/5
Let j(y) = y**3 + 8*y**2 + 115*y + 622. Let s be j(-6). Solve -3/4*z**5 + 4*z**2 + 0 - 2*z**s + 0*z + 5*z**3 = 0 for z.
-4, -2/3, 0, 2
Factor 52/3*b**2 - 4/3*b**4 + 0 - 20*b + 4*b**3.
-4*b*(b - 5)*(b - 1)*(b + 3)/3
Determine b, given that 78048/5*b - 584/5*b**4 - 20736/5 - 7168/5*b**3 - 17056/5*b**2 - 14/5*b**5 = 0.
-18, -8, 2/7, 2
Let a be 55146/312 - (7 - 2 - -1). Let i = a - 677/4. Factor 6*c**2 - i*c**3 + 0*c + 0.
-3*c**2*(c - 4)/2
Let t = 2/2049691 + 18447211/8198764. Factor 5/4*d**3 + 1/2 + t*d**2 + 7/4*d + 1/4*d**4.
(d + 1)**3*(d + 2)/4
Let n be ((-2757)/(-4595))/((-7)/(-60)). Factor 4 + 64/7*t + n*t**2.
4*(t + 1)*(9*t + 7)/7
Suppose -a - 4*s + 182 = 64, -5*a + 4*s + 542 = 0. Let o = -14 + a. Suppose -15*j**3 + 16 + 4 + 151*j**2 - o*j**2 - 60*j = 0. Calculate j.
2/3, 1, 2
Suppose 5517*i - 5506*i = 0. Let x(t) be the first derivative of -11 - 128/39*t**3 - 24/65*t**5 - 24/13*t**4 + i*t - 1/39*t**6 + 0*t**2. Factor x(w).
-2*w**2*(w + 4)**3/13
Let x(w) be the second derivative of -w**7/2520 - w**6/240 - 143*w**4/12 - 123*w. Let u(i) be the third derivative of x(i). Factor u(z).
-z*(z + 3)
Suppose -5 = 12*m - 13*m. Suppose 4*x + 4 = 3*z, -m*x + 2*z + 1 + 1 = 0. Let 9*r**x + 5*r - 7*r**2 - 3*r**2 + 11*r**2 = 0. Calculate r.
-1/2, 0
Let w(h) be the first derivative of 495*h**4/4 + 1985*h**3/3 + 1000*h**2 + 20*h - 18. Determine s so that w(s) = 0.
-2, -1/99
Let x = 349148 - 349144. Let -18/5*c**3 - 27/5*c**x + 12/5*c - 12/5 + 33/5*c**2 = 0. What is c?
-1, 2/3
Suppose -p = -2*k - 4, 0*k - 4*k - 5*p + 48 = 0. Let b(n) be the first derivative of 4/11*n + 1/11*n**k - 1/22*n**4 - 4/33*n**3 - 40. Factor b(f).
-2*(f - 1)*(f + 1)*(f + 2)/11
Let r be 64/228 - 64/(-1216). Let q(i) be the first derivative of r*i**6 + 0*i**2 + 0*i**4 + 2/5*i**5 + 0*i + 15 + 0*i**3. Let q(j) = 0. What is j?
-1, 0
Let z(v) = -v**2 + 3*v + 11. Let o = -15 + 19. Let d be z(o). Factor -5*i**2 + 4*i**2 - 3*i + d*i.
-i*(i - 4)
Let t(p) be the third derivative of -1/63*p**7 + 41/540*p**6 + 6 - 2*p**2 - 2/9*p**3 + 0*p + 1/756*p**8 + 29/108*p**4 - 17/90*p**5. Find u such that t(u) = 0.
1/2, 1, 2, 3
Let p(z) = -z**3 + 93*z - 229. Let x be p(8). Factor 100/3 + 80/3*y + 1/3*y**x - 19/3*y**2.
(y - 10)**2*(y + 1)/3
Let v(y) = -y**3 + 15*y**2 - 72*y + 162. Let f be v(9). Find a such that -4/3*a**2 + 0*a + f - 2/3*a**3 = 0.
-2, 0
Let s(k) = 15*k**2 + 95*k + 60. Let p(w) = w**2 + w - 1. Let r(h) = -6*h - 95. Let n be r(-16). Let t(c) = n*s(c) - 20*p(c). Let t(b) = 0. Calculate b.
-1, 16
Let g(x) be the third derivative of x**7/525 + 7*x**6/300 + x**5/10 + 13*x**4/60 + 4*x**3/15 - 2098*x**2. Determine p so that g(p) = 0.
-4, -1
Factor -2400*f**2 + 3840000*f - 2048000000 + 1/2*f**3.
(f - 1600)**3/2
Let m be -6 + (-6 - (0 + -541)). Solve -2*z - 3*z + m - 41*z + z**2 = 0.
23
Let f(t) = 3*t**3 - 9*t**2 + 6*t - 5. Let b(q) = q**2 + 10 + 23 - 32 - q. Let r(i) = -15*b(i) - 3*f(i). What is z in r(z) = 0?
0, 1/3, 1
Let n(v) be the first derivative of -12*v**2 - 4/3*v**3 + 58 + 0*v. Factor n(u).
-4*u*(u + 6)
Let w(x) be the second derivative of -x**6/90 + x**5/12 + 43*x**4/36 - 53*x**3/18 - 15*x**2 + 1134*x. Find m such that w(m) = 0.
-5, -1, 2, 9
Let h(m) = 13*m**3 - 1290 + 18*m + 8*m**3 - 39*m**2 + 1284. Let g(o) = -43*o**3 + 78*o**2 - 36*o + 13. Let y(b) = -6*g(b) - 13*h(b). Factor y(v).
-3*v*(v - 2)*(5*v - 3)
Let a(v) be the second derivative of -v**5/20 + 5*v**4/6 - 3*v**3 + 19*v**2/2 + 26*v. Let b be a(8). What is j in 0*j**2 + 2/15*j**b - 2/15*j + 0 = 0?
-1, 0, 1
Find s such that 125*s**2 + 261*s**3 - 377*s**2 + 146*s**2 - 428*s**2 + 1 + 285*s - 13 = 0.
4/87, 1
Let z(i) be the second derivative of i**5/5 - 248*i**4/3 - 166*i**3 - 36*i + 37. Factor z(x).
4*x*(x - 249)*(x + 1)
Let x = 71132 + -426791/6. Factor -g**3 + x*g**2 + 0 - 1/6*g**4 + g.
-g*(g - 1)*(g + 1)*(g + 6)/6
Let q(b) be the first derivative of 0*b**2 - 20 + 2/3*b**3 - b**4 + 1/2*b**5 - 1/12*b**6 + 0*b. Factor q(x).
-x**2*(x - 2)**2*(x - 1)/2
Let f be 7 - (-10 - (-368)/22). Let w(s) be the first derivative of 2/11*s + f*s**2 + 2 + 2/11*s**3 + 1/22*s**4. Factor w(q).
2*(q + 1)**3/11
Let m(f) be the second derivative of -55225*f**7/21 + 33323*f**6/3 - 168499*f**5/10 + 58057*f**4/6 - 952*f**3/3 + 4*f**2 - 95*f. Factor m(y).
-2*(y - 1)**3*(235*y - 2)**2
Let h = 295557/14 + -21111. Let l(j) be the third derivative of 13/20*j**5 + 0*j - 1/4*j**4 + h*j**7 + 0*j**3 + 0 + 33*j**2 - 13/20*j**6. What is s in l(s) = 0?
0, 1/3, 2/5, 1
Let v(r) be the third derivative of -1/630*r**7 - 8*r**2 + 0 - 4*r + 0*r**3 + 1/360*r**6 + 1/90*r**5 + 0*r**4. Factor v(i).
-i**2*(i - 2)*(i + 1)/3
Let l(w) be the second derivative of -6 + 1/5*w**5 + 5*w - 1/3*w**4 + 8*w**2 - 8/3*w**3. What is j in l(j) = 0?
-2, 1, 2
Let u = -701 - -536. Let v be ((-15)/(-25))/(u/(-50)). Factor v*w**4 - 1/11*w**5 + 0*w**3 - 2/11*w**2 + 1/11*w + 0.
-w*(w - 1)**3*(w + 1)/11
Let d(f) be the second derivative of 9*f**5/140 - 5*f**4/4 + 11*f**3/7 - 2*f - 1201. Suppose d(z) = 0. What is z?
0, 2/3, 11
Let a(c) = 9*c**2 - 649*c + 1295. Let x be a(2). Let q(u) be the second derivative of x*u + 0 - 7/40*u**5 - 2/3*u**4 + 3/2*u**2 + 17/12*u**3. Factor q(r).
-(r - 1)*(r + 3)*(7*r + 2)/2
Let u(s) be the first derivative of -2/5*s**2 - 48 - 1/25*s**5 - 1/5*s**3 + 4/5*s + 1/5*s**4. Factor u(f).
-(f - 2)**2*(f - 1)*(f + 1)/5
Suppose 2/5*v**2 + 52/5*v + 176/5 = 0. What is v?
-22, -4
Let h = 28 + -17. Suppose -v + h = 9. Factor 14*x**2 + 7*x**2 + 15*x**v + x - 37*x**2.
-x*(x - 1)
Let t(m) be the third derivative of -2*m**5/15 - 191*m**4/12 - 47*m**3 + 449*m**2. Suppose t(y) = 0. What is y?
-47, -3/4
Let g = 496 + -493. Solve 4*i + 4*i**4 + 12*i**2 + 16*i**3 + 5*i**g - 9*i**3 = 0 for i.
-1, 0
Determine u, given that 13944500 + 5*u**2 - 5798*u - 5460*u - 3827*u + 3880*u - 5495*u = 0.
1670
Let y(o) = -74*o**2 + 640*o + 1198. Let i(b) = -4*b**2 + 3*b + 1. Let q(s) = 36*i(s) - 2*y(s). Determine a, given that q(a) = 0.
-2, 295
Let t be 128/(-40)*(-5)/2. Let r = 237 - 235. Determine k so that t*k**4 - 7*k**4 - 4*k**4 + 3*k**r + 0*k**2 = 0.
-1, 0, 1
Let d(w) be the third derivative of -2/45*w**5 + 35/36*w**4 + 28*w**2 + w**3 + 0*w + 0. Factor d(y).
-2*(y - 9)*(4*y + 1)/3
Let n(g) be the third derivative of g**8/252 + 4*g**7/63 + 7*g**6/90 - 2*g**5/5 - 549*g**2. What is q in n(q) = 0?
-9, -2, 0, 1
Let -1/4*l**3 + 105/4 + 137/4*l + 31/4*l**2 = 0. What is l?
-3, -1, 35
Let w = 906997/5 + -181397. Solve w*a + 9/5*a**2 + 3/5 = 0 for a.
-1, -1/3
Let x(b) be the first derivative of -1/36*b**5 - 23*b**2