Determine c, given that 18/7*c - 8/7*c**3 + u + 6/7*c**2 = 0.
-1, -1/4, 2
Let o(l) be the second derivative of -l**7/1260 - l**6/135 - l**3 + 3*l. Let v(c) be the second derivative of o(c). Factor v(p).
-2*p**2*(p + 4)/3
Find g such that -162 - 158 - 134*g**3 + 478 - 2*g**5 - 158 + 70*g**4 + 66*g**2 = 0.
0, 1, 33
Let s(j) be the third derivative of j**7/840 - j**6/480 - 11*j**5/120 - 11*j**4/24 - j**3 - 92*j**2. Factor s(r).
(r - 6)*(r + 1)*(r + 2)**2/4
Solve -1/2*d**5 + 24/5*d - 27/10*d**4 + 4/5*d**2 - 4*d**3 + 8/5 = 0 for d.
-2, -2/5, 1
Let i(x) be the second derivative of 2/15*x**6 + 7/10*x**5 + 3*x + 4*x**2 - x**4 - 7/3*x**3 + 0. Find k such that i(k) = 0.
-4, -1, 1/2, 1
Let w be 5/(-8) - (75 - 76). Let g be (-2)/(-3) + (-48)/(-36). Factor 1/4*s**g + w*s - 1/8*s**3 + 0.
-s*(s - 3)*(s + 1)/8
Let x(d) be the first derivative of 1/6*d**2 + 2/3*d**3 + 17 + 0*d + 5/12*d**4. Determine c, given that x(c) = 0.
-1, -1/5, 0
Suppose -5*a = 12*z - 8*z - 23, 0 = 3*z + 5*a - 21. Let d(f) be the first derivative of 0*f - 8/5*f**5 - 8/3*f**3 + 3*f**4 + 1/3*f**6 - 4 + f**z. Factor d(l).
2*l*(l - 1)**4
Suppose 2*f + 5 = -i, -2*i - 40 = f - 30. Factor f - 8/3*l**2 + 0*l - 4/3*l**3.
-4*l**2*(l + 2)/3
Let a(s) = 10*s**2 - 4*s + 4. Let v be a(4). Factor -v*z + z**2 + 148*z.
z**2
Let n = 8 + -7. Let k(q) = q**2 - 1. Let b(d) = 5*d**3 - 75*d**2 - 5*d + 75. Let l(w) = n*b(w) + 30*k(w). Let l(i) = 0. What is i?
-1, 1, 9
Let n be 0 - 5/(-1) - (-535)/(-102). Let a = 7/17 + n. Factor -1/6*q**3 - a*q**4 + 5/6*q + 1/2*q**2 + 1/3.
-(q - 2)*(q + 1)**3/6
Suppose -2*j**4 - 819*j**2 + 35*j**2 + 90*j**3 - 2*j**4 + 22*j**3 = 0. Calculate j.
0, 14
Solve 3/2*b**3 + 32 - 22*b**2 - 34*b = 0.
-2, 2/3, 16
Suppose 10*g = 27*g + 21*g. Factor -1/3*r**3 + 0*r**2 + 0*r + g*r**4 + 1/3*r**5 + 0.
r**3*(r - 1)*(r + 1)/3
Let t(z) be the third derivative of -z**8/84 + 2*z**7/35 + z**6/30 - 11*z**5/15 + 2*z**4 - 8*z**3/3 - 4*z**2 + 23*z. Factor t(h).
-4*(h - 2)*(h - 1)**3*(h + 2)
Let v(b) = 48*b**4 - 384*b**3 + 687*b**2 + 384*b - 768. Let m(g) = 3*g**4 - 24*g**3 + 43*g**2 + 24*g - 48. Let i(l) = -33*m(l) + 2*v(l). Factor i(z).
-3*(z - 4)**2*(z - 1)*(z + 1)
Let x be (4/(-6))/(8/(-36)). Factor -4*y**4 - y**2 + y**4 + y**5 + x*y**3 + 0*y**4.
y**2*(y - 1)**3
Let c(f) be the first derivative of -9*f**4/2 + 38*f**3 + 41*f**2 + 14*f + 31. Factor c(t).
-2*(t - 7)*(3*t + 1)**2
Let f = 10735667/6518910 - -68196/3683. Let p = f - -1/295. Factor -55/2*z**3 + 0 + 8*z**2 - 2/3*z + p*z**4.
z*(z - 1)*(11*z - 2)**2/6
Let m(x) = -x**3 + 7*x**2 + x + 2. Let f(y) = 2*y**3 - 8*y**2 - 2. Let k(r) = -3*f(r) - 4*m(r). Let v(q) = -q**3 - 1. Let j(z) = k(z) - 6*v(z). Factor j(h).
4*(h - 1)**2*(h + 1)
Suppose -45*z + 42*z + 24 = 0. Find g, given that z*g**3 - 3*g**4 - 24*g - 35*g**2 + 7*g**4 + 15*g**2 = 0.
-3, -1, 0, 2
Let s(t) be the third derivative of 2*t**7/105 - 11*t**6/30 + 13*t**5/5 - 15*t**4/2 - t**2 - 63*t. Factor s(w).
4*w*(w - 5)*(w - 3)**2
Suppose 0 = 4*j, 4*c + 16*j - 8 = 21*j. Solve 1/3 + 16*d**c + 4*d + 64/3*d**3 = 0.
-1/4
Let t = 157753/72 - 2191. Let a(g) be the second derivative of -1/4*g**2 + 0 - 1/9*g**3 - t*g**4 - 12*g. Let a(c) = 0. What is c?
-3, -1
Factor -164/7*t - 64/7 - 10/7*t**2.
-2*(t + 16)*(5*t + 2)/7
Let w(h) be the second derivative of h**5/80 - h**4/12 - 11*h**3/24 - 3*h**2/4 + 39*h + 1. Solve w(n) = 0.
-1, 6
Factor 88/9*q + 4/3*q**3 - 40/9 - 58/9*q**2.
2*(q - 2)**2*(6*q - 5)/9
Let d(r) be the third derivative of -r**10/28080 + r**9/19656 + r**8/21840 + r**4/4 - 36*r**2. Let s(z) be the second derivative of d(z). Factor s(x).
-2*x**3*(x - 1)*(7*x + 2)/13
Let c = -167 + 175. Suppose -w + c = w. What is k in -16/5*k**w - 19/5*k - 57/5*k**2 - 56/5*k**3 - 2/5 = 0?
-2, -1, -1/4
Let b(p) be the second derivative of -p**5/150 - 119*p**4/90 - 3599*p**3/45 - 3481*p**2/15 + 13*p + 4. Factor b(r).
-2*(r + 1)*(r + 59)**2/15
Determine w, given that 121 + 32*w**4 + 6261*w**2 - w**5 - 6403*w**2 - 43*w**3 - 11*w**4 - 55*w**3 + 99*w = 0.
-1, 1, 11
Let y be -10 + 10 + (4 - 1). Determine h so that 0*h**4 - 3*h + 4*h + 3*h**2 - 3*h**3 + 2*h - y*h**4 = 0.
-1, 0, 1
Let h be ((-2)/21)/(5/(-14)). Let c(g) be the third derivative of h*g**6 - 3*g**3 - 4/3*g**5 + 0 + 11/4*g**4 + g**2 + 0*g. Solve c(t) = 0.
3/4, 1
Let r be (-10)/15*15/(-2). Let w = -1240 - -1243. Factor -2*h**2 - h - 1/5*h**r - h**4 - 2*h**w - 1/5.
-(h + 1)**5/5
Factor 24*f - 6 + 15 - 3*f**2 - 18*f.
-3*(f - 3)*(f + 1)
Find b such that 10*b**5 + 37*b - 110*b**2 - 102*b - 90*b**3 - 36*b**4 - 15*b**5 - 15 + b**4 = 0.
-3, -1
Let b(q) be the second derivative of 4/3*q**3 + 0 + 3*q**4 + 0*q**2 - 17*q - 24/5*q**5 - 224/15*q**6. Determine r, given that b(r) = 0.
-1/4, 0, 2/7
Let c be -5 - (4726/(-306) + 1/(-3)). Let l(v) be the first derivative of 11*v**2 - 22/3*v**4 + 16/15*v**5 - 3 + 3*v + c*v**3. Let l(k) = 0. What is k?
-1/4, 3
Let c(y) be the second derivative of 10/7*y**3 + 0 + 20*y - 150/7*y**2 - 1/28*y**4. Suppose c(r) = 0. Calculate r.
10
Let s be 6/(-21) - 1507/(-7). Suppose -70 + s = 5*b. Factor 9*v - 6 - b*v**2 - 3*v**3 + 29*v**2.
-3*(v - 1)**2*(v + 2)
Suppose 4*n + c = -3*c - 40, 0 = 5*c + 20. Let o(h) = 25*h. Let m(s) = -s**2 - 26*s. Let z(r) = n*o(r) - 5*m(r). Factor z(u).
5*u*(u - 4)
Let b be (0 - (-4)/10) + (-131)/655. Factor -b*k**2 + 0 + 0*k + 1/5*k**3.
k**2*(k - 1)/5
Let u = -22666 + 22672. Determine z so that -9/2*z - 3/2*z**5 + u*z**3 - 3*z**2 + 3 + 0*z**4 = 0.
-2, -1, 1
Let n(d) = d**3 + 11*d**2 + 22*d + 38. Let q be n(-9). Let r(o) be the first derivative of -3 + 2/13*o**q - 2/39*o**3 - 1/26*o**4 + 0*o. Factor r(b).
-2*b*(b - 1)*(b + 2)/13
Let f(z) be the third derivative of -5*z**8/168 + 19*z**7/14 - 15*z**6 - 337*z**5/6 - 25*z**4/4 + 375*z**3/2 + 3*z**2 + 3. Suppose f(u) = 0. Calculate u.
-1, 1/2, 15
Let f(o) be the third derivative of -o**6/90 - 2*o**5/15 - 5*o**4/18 - 100*o**2. Factor f(z).
-4*z*(z + 1)*(z + 5)/3
Let g be 11/60 + 6/30 + 61/(-244). Let 0*c + 0 + 22/15*c**4 + 2/3*c**5 + g*c**2 + 14/15*c**3 = 0. What is c?
-1, -1/5, 0
Suppose -16*f**3 + 57*f**3 - 24*f**3 - f - 18*f**3 - 2*f**2 = 0. Calculate f.
-1, 0
Let w = 10 - 5. Determine v so that w*v + 209*v**3 - 8*v - 188*v**3 + 6*v**2 + 12*v**4 = 0.
-1, 0, 1/4
Let c(b) = -4*b**2 + 16*b - 27. Let f(s) = 3*s**2 - 17*s + 24. Let x(v) = -2*c(v) - 3*f(v). Factor x(a).
-(a - 18)*(a - 1)
Let x = -4414/3 - -1474. Determine m, given that x*m**2 - 20/3*m - 4 = 0.
-1/2, 3
Suppose 6*o + 26 - 38 = 0. Let j(n) be the first derivative of -2/21*n**3 - 3 + 0*n**o + 0*n. Factor j(v).
-2*v**2/7
Suppose -8*y + 30 = -3*y. Suppose 4*p = y - 2. Factor -14*k**2 + 4 - 4*k + p - 5.
-2*k*(7*k + 2)
Factor 16 + 20*a**2 + 5*a**3 - 64*a + 3*a**3 + 20*a.
4*(a - 1)*(a + 4)*(2*a - 1)
Let f(i) = 8*i**2 + 3*i + 4. Let z be f(3). Suppose 5*t + 25 = z. Factor 4 - 11*n**4 + 8*n**4 + 4*n**5 - 9*n**4 + 8*n**3 - t*n + 8*n**2.
4*(n - 1)**4*(n + 1)
Let i(r) = 9*r**5 - 26*r**4 + 21*r**3 + 4*r**2 + 8*r. Let q(u) = u**5 + u**4 - u**3 + u**2 + 2*u. Let c(k) = i(k) - 4*q(k). Let c(o) = 0. What is o?
0, 1, 5
Let d(q) be the third derivative of -q**6/540 - 4*q**5/45 - 55*q**4/36 - 242*q**3/27 + 6*q**2 + 8*q. Factor d(k).
-2*(k + 2)*(k + 11)**2/9
What is z in -792*z**2 - 4320 - 34*z**4 - 75*z**3 + 62*z**4 - 32*z**4 - 17*z**3 - 3024*z = 0?
-6, -5
Let y(h) = 6*h**3 + 28*h**2 - 90*h + 88. Let d(z) = 2*z**3 + 10*z**2 - 31*z + 29. Let x(m) = 16*d(m) - 5*y(m). Determine k, given that x(k) = 0.
-12, 1
Let u(s) be the first derivative of -s**6/165 + s**5/55 - s**4/66 - 13*s - 27. Let b(n) be the first derivative of u(n). Determine c, given that b(c) = 0.
0, 1
Let f be (-1)/1*7*18/(-84). Factor x + 1/2*x**3 + 0 + f*x**2.
x*(x + 1)*(x + 2)/2
Factor 108*u + 3*u**5 + 274*u**3 - 47*u**4 + 17*u**4 - 163*u**3 - 180*u**2.
3*u*(u - 3)**2*(u - 2)**2
Let m(o) be the second derivative of 3*o**3 + 1/4*o**4 + 0 + 27/2*o**2 + 6*o. Find g, given that m(g) = 0.
-3
Let t(f) be the second derivative of -2*f**6/15 - 24*f**5/5 - 21*f**4 + 8*f**3/3 + 168*f**2 + 26*f. Let t(d) = 0. Calculate d.
-21, -2, 1
Let v(k) be the second derivative of -1/8*k**4 + 0 + 3*k + 1/10*k**5 + 0*k**3 + 3*k**2. Let a(j) be the first derivative of v(j). Factor a(o).
3*o*(2*o - 1)
Let q(m) be the first derivative of m**5/35 - 3*m**4/28 + 2*m**2/7 - 99. Factor q(n).
n*(n - 