o(d). Determine u so that 14 + 0*u + 8 - v*u - 28 + 2*u**2 = 0.
-1, 3
Let r be (-12)/20*(-5320)/504. Suppose 1/3*y**3 - 2/3*y**2 - r*y + 20/3 = 0. Calculate y.
-4, 1, 5
Let p(m) be the first derivative of -1/7*m**3 + 6/7*m**2 - 20 + 15/7*m. Find l, given that p(l) = 0.
-1, 5
Let j = -137159/20 + 6858. Let v(l) be the second derivative of -11/12*l**4 + 35/6*l**3 - 25/2*l**2 + 0 - 41*l + j*l**5. Suppose v(f) = 0. What is f?
1, 5
Suppose 368*u - 4 + 5 - 1 = 0. Factor 0*c - 1/3*c**2 + u - 1/3*c**3 + 1/3*c**4 + 1/3*c**5.
c**2*(c - 1)*(c + 1)**2/3
Let x = 4/25591 + 51154/179137. Factor -32/7*v + 40/7*v**2 + 0 - 16/7*v**3 + x*v**4.
2*v*(v - 4)*(v - 2)**2/7
Let k(x) = -4*x + 10. Let m(t) = t**2 + 8*t - 27. Let l be m(-10). Let o be k(l). Let -4 - 4*w**2 - o*w + 3 + 33*w = 0. What is w?
-1, -1/4
Let x be -1*((-3)/(3/5))/(2/2). Let s(a) be the second derivative of -3/10*a**3 - 1/60*a**6 + 0*a**2 + 0 - 19/40*a**4 - 4/25*a**x - 17*a. Factor s(q).
-q*(q + 3)**2*(5*q + 2)/10
Let r(u) = 5*u**2 + 2*u - 7. Let x(n) = 2*n**2 - n - 1. Let v be (-6)/8 - 684/304. Let y(c) = v*x(c) + r(c). Factor y(l).
-(l - 4)*(l - 1)
Let i(k) be the second derivative of 4*k + 1/18*k**4 + 1/60*k**5 - 19/18*k**3 - 10/3*k**2 - 7. Determine o, given that i(o) = 0.
-5, -1, 4
Let f = 605 - 603. Factor -4*r**f + r**3 - r + 10*r - 4 - 2*r**2.
(r - 4)*(r - 1)**2
Factor 9115*y - 3483*y - 310*y**2 - 500*y**2 - y**4 + 50*y**3 - 8192 - 54*y**2.
-(y - 16)**3*(y - 2)
Let c(m) be the third derivative of 3*m**8/14 - 2*m**7/15 - 23*m**6/15 - 23*m**5/15 - m**4/3 - 2*m**2 - 2*m - 325. Determine n, given that c(n) = 0.
-1, -1/2, -1/9, 0, 2
Let g(h) be the third derivative of -1/560*h**7 + 0 + 1/10*h**5 + 0*h**3 - h**4 - 102*h**2 + 0*h + 1/80*h**6. Factor g(p).
-3*p*(p - 4)**2*(p + 4)/8
Let a = 880690/3 + -293563. Factor 1/3 + 0*h - a*h**2.
-(h - 1)*(h + 1)/3
Let u(l) = l**2 + 2*l - 4. Let d(x) = -2*x**2 - 45*x + 152. Let n(m) = 5*d(m) + 15*u(m). Factor n(k).
5*(k - 35)*(k - 4)
Let l = 663247 + -663243. Factor -2/7*m**l + 0 + 0*m + 6/7*m**3 - 4/7*m**2.
-2*m**2*(m - 2)*(m - 1)/7
Solve 3*m**2 + 196*m + 5058 + 550*m - 376*m + 491*m = 0 for m.
-281, -6
Let g(f) = f**3 - 11*f**2 + 4. Let h be g(11). Suppose -h*u - 29 = -n - 6, u = -5. Factor -9*t**2 - 25*t - n + 23 + 4*t**2 + 10*t**2.
5*(t - 4)*(t - 1)
Let f be -19 - ((-900)/20 + 23). Solve -20/17 + 38/17*c - 16/17*c**2 - 2/17*c**f = 0.
-10, 1
What is d in -18/13*d**3 - 30/13*d**2 + 28/13*d + 0 = 0?
-7/3, 0, 2/3
Let q = -197 + 198. Let y(s) = 26*s**2 + 42*s + 10. Let o(a) = -a**2 + 0 + a + 0*a**2 + 1. Let f(w) = q*y(w) + 6*o(w). Factor f(g).
4*(g + 2)*(5*g + 2)
Let m be 1 - -8 - 312/260*(-15)/(-2). Factor m - 1/9*c**2 + 4/3*c.
-c*(c - 12)/9
Let t be 14/(-91) + (-168)/(-78). Let h(o) be the first derivative of 16*o + 4/3*o**3 + 10*o**t + 17. Solve h(r) = 0 for r.
-4, -1
Let m(b) be the first derivative of b**3/2 - 3*b**2/4 - 9*b - 1068. Solve m(y) = 0 for y.
-2, 3
Let q = -27030 + 27032. Let q - 32/15*a**2 - 28/15*a**3 + 2/15*a**4 + 28/15*a = 0. Calculate a.
-1, 1, 15
Let a(v) be the second derivative of 16*v**2 - 18*v + 1/12*v**4 + 11/2*v**3 + 4. Factor a(q).
(q + 1)*(q + 32)
Suppose -4*p + 9051 = 9051. Let y(f) be the third derivative of 0*f + 1/60*f**5 + p*f**3 + 0 + 1/480*f**6 + 1/24*f**4 + 13*f**2. Factor y(z).
z*(z + 2)**2/4
Let l(v) = v**3 - 4*v**2 + 2*v + 6. Let q be l(3). Solve a**4 + 14*a**3 + 8*a + 12*a + 35*a**2 - q*a + 5*a**3 = 0 for a.
-17, -1, 0
Let w(t) be the first derivative of 15/4*t**4 + 0*t**3 - t**5 + 23 - 10*t**2 + 0*t. Let w(j) = 0. What is j?
-1, 0, 2
Suppose -87*c**2 - 82*c**2 - 663*c + 238*c**2 - 72*c**2 = 0. Calculate c.
-221, 0
Let x = -1001 - -1003. Suppose x*m + 2*s = 2, -5 = 3*m - 5*m - 5*s. Solve -1/3*g**5 - 7/9*g**3 + 0 + 2/9*g**2 + 8/9*g**4 + m*g = 0.
0, 2/3, 1
Let g(s) be the third derivative of s**5/20 - 1603*s**4/4 + 2569609*s**3/2 - s**2 + 30*s - 3. Solve g(v) = 0.
1603
Let k(s) be the second derivative of -s**5/20 + 151*s**4/6 - 22801*s**3/6 - 334*s. Suppose k(h) = 0. Calculate h.
0, 151
Let b = 797 + -794. Let n(g) = g**2 - 6*g - 3. Let l be n(7). Suppose 1174 - 1174 - l*f + f**b = 0. Calculate f.
-2, 0, 2
Let j(g) be the third derivative of g**6/720 - 119*g**5/120 + 707*g**4/144 + 355*g**3/12 + 559*g**2 - 2*g - 2. Suppose j(l) = 0. What is l?
-1, 3, 355
Let j(c) be the third derivative of -c**5/20 - 21*c**4 + 169*c**3/2 - 74*c**2 - 3*c - 1. Solve j(m) = 0 for m.
-169, 1
Factor -976/15 - 2/15*x**2 + 326/5*x.
-2*(x - 488)*(x - 1)/15
Let u = 68 + -103. Let i be 154/6 + u/(-105). Factor -i*y**4 + 40*y**3 - 22*y**4 + 2*y**4 - 4*y**4 - 8*y**2.
-2*y**2*(5*y - 2)**2
Let 152/7*x**2 + 10/7*x**4 + 0 - 68/7*x**3 - 16*x = 0. What is x?
0, 2, 14/5
Let k(i) be the second derivative of i**6 - 147*i**5/10 + 352*i**4/5 - 484*i**3/5 + 6*i + 212. Determine q, given that k(q) = 0.
0, 1, 22/5
Suppose -2*b = -v + 55, -v = v + 4*b - 118. Suppose 2*l + v = 61. Factor 8*s - 31*s**l + 6 + 15*s**2 + 18*s**2.
2*(s + 1)*(s + 3)
Let g(y) be the first derivative of -y**4/2 + 148*y**3 - 872*y**2 - 4989. Factor g(x).
-2*x*(x - 218)*(x - 4)
Factor 29/9*l - 68/9*l**2 + 25/9*l**3 + 14/9.
(l - 2)*(l - 1)*(25*l + 7)/9
Let x(c) = -c**2 + 26*c + 11. Let q(o) = -8*o - 14. Let s be q(-5). Let d be x(s). Solve i**3 - 19*i**2 - 25*i**3 + 14*i**5 + 18*i**4 + d*i**2 = 0 for i.
-2, -2/7, 0, 1
Let s = -3/2630 + 5287/23670. Let u(f) be the second derivative of 0*f**5 + s*f**4 + 0 + 0*f**3 - 10*f - 2/45*f**6 - 2/3*f**2. Let u(g) = 0. What is g?
-1, 1
Let z(x) = x**2 - 18*x - 44. Let k be z(-10). Factor -118 + 48*i**2 - 72 + i**3 + 93*i + k.
(i + 1)**2*(i + 46)
Let q(p) be the second derivative of -1/36*p**4 + 1/252*p**7 + 21*p - 1/30*p**5 + 1/12*p**3 + 1/6*p**2 + 0*p**6 + 0. Suppose q(k) = 0. What is k?
-1, 1, 2
Let s(m) be the third derivative of -m**9/12096 - m**8/504 + m**5/20 + 3*m**3/2 - 15*m**2 + 3. Let l(c) be the third derivative of s(c). Factor l(x).
-5*x**2*(x + 8)
Let p(u) be the first derivative of -u**7/336 - u**6/135 + 5*u**5/144 - u**4/24 + 244*u**3/3 - u**2 + 36. Let r(t) be the third derivative of p(t). Factor r(l).
-(l + 2)*(3*l - 1)*(5*l - 3)/6
Let r be 875/4725*72/15. Let v(i) be the first derivative of 1/6*i**4 - 5/3*i**2 - 4 + 0*i - r*i**3. Suppose v(b) = 0. What is b?
-1, 0, 5
Suppose 100 = 23*s + 376. Let l be (s/8)/((-42)/140). Let 26/11*o + 4*o**2 + 14/11*o**4 + 6/11 + 2/11*o**l + 36/11*o**3 = 0. What is o?
-3, -1
Let o(t) be the second derivative of 25*t**7/7 - 154*t**6/3 - 2579*t**5/10 - 195*t**4 + 668*t**3/3 + 104*t**2 + 37*t + 6. Solve o(l) = 0 for l.
-2, -1, -2/15, 2/5, 13
Let k(w) = -w**2 + 57*w + 38. Let x(p) = 58*p + 38. Let d(o) = -3*k(o) + 2*x(o). Let y be d(19). Factor 0*g - 2/11*g**2 + y.
-2*g**2/11
What is t in 0 + 2*t**2 + 20/11*t + 2/11*t**3 = 0?
-10, -1, 0
Let -440*d + 504*d**2 - 1510*d**2 + 501*d**2 + 509*d**2 = 0. Calculate d.
0, 110
Factor 9/2*l**4 + 0 + 71*l**2 + 1279/2*l**3 + 0*l.
l**2*(l + 142)*(9*l + 1)/2
Let u = 25/43 + -132/301. Factor -4/7*d**2 + 0 + u*d**3 + 1/7*d**4 - 4/7*d.
d*(d - 2)*(d + 1)*(d + 2)/7
Let u(f) be the third derivative of 0 + 0*f - 1/18*f**4 + 1/90*f**5 + 19*f**2 + 0*f**3. What is d in u(d) = 0?
0, 2
Let i be 93/15 + ((-1424)/(-80) - 18). Let d(f) be the third derivative of 1/24*f**4 + 0*f**5 - 31*f**2 + 0*f + 1/9*f**3 - 1/360*f**i + 0. Factor d(m).
-(m - 2)*(m + 1)**2/3
Let g(f) be the third derivative of f**5/570 + 613*f**4/38 + 1127307*f**3/19 - 441*f**2 + 1. Factor g(t).
2*(t + 1839)**2/19
Let k = 1/7023 - -505649/49161. Let q = -51163 - -358153/7. Factor k*s - q - 33/7*s**2.
-3*(s - 2)*(11*s - 2)/7
Let i(x) be the first derivative of -3*x**5/5 + 288*x**3 - 62208*x - 3087. Suppose i(p) = 0. What is p?
-12, 12
Factor -85/4*v**2 - 657 - 1/4*v**3 - 228*v.
-(v + 6)**2*(v + 73)/4
Let d(q) be the first derivative of -q**5/20 + 7*q**4/8 - 55*q**3/12 + 21*q**2/4 + 7047. Factor d(u).
-u*(u - 7)*(u - 6)*(u - 1)/4
Let j(o) be the second derivative of 0 + 7*o**3 + 15/2*o**2 - 3/4*o**4 + 59*o. Factor j(h).
-3*(h - 5)*(3*h + 1)
Let n(h) be the third derivative of -11*h**6/30 - 166*h**5/15 - 137*h**4/2 - 24*h**3 + 573*h**2 + h. Find c, given that n(c) = 0.
-12, -3, -1/11
Let h(j) be the third derivative of -j**5/240 - 19*j**4/32 - 55*j**3/12 - 1434*j**2. Factor h(r).
-(r + 2)*(r + 55)/4
Let b(i) be the 