Let w(p) = -14*p**2 - 174*p - 1194. Let h(f) = -39*f**2 - 523*f - 3587. Let g(z) = 6*h(z) - 17*w(z). Find m such that g(m) = 0.
-6, 51
Solve -244/5*s**2 + 4356 - 3036/5*s - 4/5*s**3 = 0 for s.
-33, 5
Let i(x) = x**3 - 64*x**2 + 2*x - 124. Let r be i(64). Determine s, given that -8*s**3 - 4/3*s**2 + 22/3*s + r + 2/3*s**5 - 8/3*s**4 = 0.
-1, 1, 6
Let o(n) be the first derivative of -14/45*n**5 - 8/9*n**2 + 1/2*n**4 - 1/27*n**6 + 14/27*n**3 - 46 + 0*n. Let o(q) = 0. What is q?
-8, -1, 0, 1
Let y(w) be the third derivative of -w**6/1200 - 19*w**5/600 - 19*w**4/48 - 77*w**3/60 - 36*w**2. Determine r, given that y(r) = 0.
-11, -7, -1
Let d(a) = -a**3 - 23*a**2 + 19*a - 70. Let y be d(-23). Let g be (-4)/(-26) - -13*6/y. Factor g - 1/2*i**2 + 0*i - 1/2*i**3.
-i**2*(i + 1)/2
Suppose -10*k - 6*k = -64. Factor -k*m - 2*m**4 - 6*m**2 - m**3 + 3*m**2 + 5*m**2 + 5*m.
-m*(m - 1)*(m + 1)*(2*m + 1)
Suppose -u - 22*z - 17 = -27*z, 7*u - 25 = -z. Let -8 - 32/3*t**2 + 52/3*t + 4/3*t**u = 0. Calculate t.
1, 6
Let k(t) be the first derivative of t**5/150 - t**4/18 - 13*t**3/45 - 7*t**2/15 + 46*t - 49. Let d(u) be the first derivative of k(u). Let d(p) = 0. What is p?
-1, 7
Let s be (-19)/((-1197)/6) + ((-57)/(-63) - -4). Let j(l) be the second derivative of 0*l**4 + 20*l - 2/5*l**2 - 1/5*l**3 + 1/50*l**s + 0. Factor j(r).
2*(r - 2)*(r + 1)**2/5
Suppose -o + w = -34, 5*w - 1 = 2*o - 72. Suppose -2*k - 3*q + 23 = -6*q, -2*k = -5*q - o. Let -2/11*b**3 + 0*b - 2/11*b**2 + 0 + 24/11*b**k = 0. What is b?
-1/4, 0, 1/3
Find s, given that -41*s**4 - 31*s**4 - 121*s**3 + 5*s**5 - 19*s**3 - 31*s**4 + 160*s**2 + 123*s**4 = 0.
-8, 0, 2
Suppose -255*g + 264*g = 3906. Let x be (-1)/2 + g/124. Factor -8/7*s + 0*s**2 + 0 + 6/7*s**x - 2/7*s**4.
-2*s*(s - 2)**2*(s + 1)/7
Solve 150*w**3 - 9 - 24 - 74*w**3 + 5 - 77*w**3 + 28*w**2 + w = 0 for w.
-1, 1, 28
Let l be 7*(-17)/153*9 - ((-20)/4 + -5). Let x be 2/(-10)*(-5)/4. Factor -x*i + 0 + i**l - 3/4*i**2.
i*(i - 1)*(4*i + 1)/4
Let q be 51/187 - 450/(-165). What is r in -2/3*r**2 + 4*r + q + 1/3*r**4 - 4/3*r**3 = 0?
-1, 3
Let z(b) be the second derivative of b**4/12 - 56*b**3/3 + 327*b**2/2 + 783*b. Find v such that z(v) = 0.
3, 109
Let s(f) be the second derivative of -343*f**6/30 + 833*f**5/4 + 6489*f**4/4 + 8829*f**3/2 + 5832*f**2 + 122*f - 5. Factor s(d).
-(d - 16)*(7*d + 9)**3
Let j be (-192424)/(-27872) + 8/(-52). Factor -27/8*n - 15/8*n**2 + j.
-3*(n + 3)*(5*n - 6)/8
Determine w, given that 28*w**3 + 18 - 25*w**3 - 28*w**2 + 164*w + 157*w - 314*w = 0.
-2/3, 1, 9
Let t(p) be the first derivative of p**7/280 + p**6/40 + p**5/80 - 3*p**4/16 - 3*p**2 - 5*p + 96. Let j(h) be the second derivative of t(h). Factor j(s).
3*s*(s - 1)*(s + 2)*(s + 3)/4
Let s(p) be the third derivative of -p**5/70 + 2*p**4/7 - p**3 - 14*p**2 + 79. Factor s(k).
-6*(k - 7)*(k - 1)/7
Factor -624*f - 789*f**2 - 156 - 24 - 75*f**4 - 45172*f**3 + 44749*f**3 + 3*f**5.
3*(f - 30)*(f + 1)**3*(f + 2)
Let j(t) = 2*t**3 - 9*t**2 - t. Let d(g) = -17*g**3 + 90*g**2 + 668*g - 12584. Let h(l) = -d(l) - 8*j(l). Suppose h(i) = 0. Calculate i.
-26, 22
Factor -13*p**3 + 711*p**5 - 710*p**5 + 1 + 5*p**3 - p**4 + 12*p**2 - 1.
p**2*(p - 2)**2*(p + 3)
Let s(b) = 17*b**2 - 17*b. Let t be (-357)/28*(-4)/1. Let w = t - 43. Let x(f) = 6*f**2 - 6*f. Let y(r) = w*x(r) - 3*s(r). Factor y(k).
-3*k*(k - 1)
Let v(y) be the first derivative of 0*y + 223 + 16*y**2 + 4/3*y**3. Factor v(l).
4*l*(l + 8)
Let f(r) be the second derivative of r**4/6 + r**3/3 - r**2/2 - 196*r. Let w(z) = -21*z**2 - 28*z + 20. Let m(t) = 44*f(t) + 4*w(t). Factor m(g).
4*(g - 3)**2
Suppose 54 = 5*i + 4*m, 13*m - 8*m + 185 = 19*i. Factor i*b - 1/2*b**2 - 19/2.
-(b - 19)*(b - 1)/2
Let w(g) be the first derivative of 6*g**5/35 + 9*g**4/2 - 2*g**3/7 - 9*g**2 - 1049. Suppose w(c) = 0. What is c?
-21, -1, 0, 1
Let x(u) be the second derivative of u**7/56 + 83*u**6/40 + 243*u**5/40 - u**4/8 - 163*u**3/8 - 243*u**2/8 - 1174*u - 3. Solve x(i) = 0 for i.
-81, -1, 1
Let q(f) be the third derivative of 4*f**7/1365 + 11*f**6/780 - 19*f**5/195 - 27*f**4/52 - 12*f**3/13 + 53*f**2 - 2*f + 38. Determine b, given that q(b) = 0.
-4, -1, -3/4, 3
Suppose 2346 = 8*m + 15*m. Suppose -m*s - 60 = -132*s. Solve 4/5*p**3 - s*p**2 + 0 + 4/5*p = 0 for p.
0, 1/2, 2
Let q(g) be the third derivative of g**5/30 - 199*g**4/6 + 39601*g**3/3 - 317*g**2. Factor q(f).
2*(f - 199)**2
Let n(f) be the second derivative of f**3 + 7/40*f**5 + 2/3*f**4 + 74*f + 0 + 1/60*f**6 + 0*f**2. Determine s, given that n(s) = 0.
-3, -2, 0
Let l = -600 - 1121. Let f = l + 1723. Factor 9/5*h**f - 4/5 - 6/5*h - 1/2*h**3.
-(h - 2)**2*(5*h + 2)/10
Let j(o) be the third derivative of o**6/48 + 741*o**5/40 + 295*o**4/4 - 443*o**3/3 + 3296*o**2. Factor j(t).
(t + 2)*(t + 443)*(5*t - 2)/2
Let a(g) be the second derivative of 2/25*g**6 - 3/5*g**3 + 0*g**2 - 1/5*g**4 - g + 1/105*g**7 + 4/25*g**5 + 85. Let a(x) = 0. What is x?
-3, -1, 0, 1
Let i = -7 - -6. Let o(r) = -3*r**5 - r**4 + 61*r**3 - 40*r**2 - 240*r + 288. Let g(c) = c**5 - c**4 + c**3. Let k(t) = i*g(t) + o(t). Factor k(w).
-4*(w - 2)**3*(w + 3)**2
Suppose 1/3*w**2 + 14884/3 - 244/3*w = 0. What is w?
122
Let l(h) be the third derivative of -h**8/6720 - h**7/2520 + 43*h**4/24 - h**3/6 + 53*h**2. Let u(p) be the second derivative of l(p). What is z in u(z) = 0?
-1, 0
Let s(g) be the first derivative of -22 - 9*g**2 - 81*g - 1/3*g**3. Suppose s(w) = 0. What is w?
-9
Let w(a) be the third derivative of a**5/300 + 673*a**4/20 + 1358787*a**3/10 + 4007*a**2. Let w(n) = 0. What is n?
-2019
Suppose 184/9*c**2 + 25088/9 - 3976/9*c - 2/9*c**3 = 0. What is c?
14, 64
Let v = 23781/56 + -2970/7. Let j(u) be the first derivative of -v*u**2 - 1/12*u**3 + 3 + u. Factor j(c).
-(c - 1)*(c + 4)/4
Suppose -21*g = -18*g + 6, 5*g = p - 14. Solve 5 + 1050*t**3 - p*t**2 - 1046*t**3 - 1 - 4*t = 0 for t.
-1, 1
Let z(r) = -80*r**2 + 100*r - 20. Let m be (-540)/(-63) + 16/(-28). Let j(h) = -121*h**2 + 151*h - 30. Let f(q) = m*z(q) - 5*j(q). Factor f(w).
-5*(w - 1)*(7*w - 2)
Let a = -52 + 56. Let m be a/6 + (-40)/(-30). Suppose -24*x**3 - 4*x - 2*x**5 + 250*x**2 - m*x**5 - 266*x**2 - 16*x**4 = 0. What is x?
-1, 0
Let b(p) be the first derivative of p**6/10 - 1944*p**5/5 + 629856*p**4 - 544195584*p**3 + 264479053824*p**2 - 342764853755904*p/5 + 2713. Factor b(n).
3*(n - 648)**5/5
Let r(o) be the third derivative of o**6/40 + 229*o**5/60 - 773*o**4/6 - 176*o**3 - 21*o**2 - 18. Find l, given that r(l) = 0.
-88, -1/3, 12
What is f in -1080*f**2 + 2*f**5 + 5*f**5 - 167*f**4 - 1425*f**3 - 419*f**4 + 246*f**4 - 2*f**5 = 0?
-3, -1, 0, 72
Let y(k) be the first derivative of -27/4*k**4 - 4*k**3 - 105 + 0*k - 2/3*k**2. Determine t so that y(t) = 0.
-2/9, 0
Let t(h) = 96*h - 2. Let s be t(-1). Let y = s + 203/2. Solve 11/4*d**3 - y*d**4 + 3*d**2 + 1/2 - 11/4*d = 0 for d.
-1, 2/7, 1/2, 1
Suppose -333*y + 2977 = 2977. Let y + 2/3*n - 2/9*n**2 = 0. Calculate n.
0, 3
Let t be 0 - -4 - (17640/(-1322))/(-10). Let u = t + 2/1983. Factor -10/3*j**2 - 4/3*j - u*j**3 - 2/3*j**4 + 0.
-2*j*(j + 1)**2*(j + 2)/3
Let c be (-3 + 24/20)*5/(-3). Determine g, given that -10*g**3 + c*g**3 + 9 + 31*g**2 + 9*g**3 + 25*g + 19*g - 6*g**3 = 0.
-1, -1/4, 9
Let i(u) be the second derivative of -u**7/126 - 2*u**6/45 + 7*u**4/18 + 17*u**3/18 + u**2 + 164*u - 3. Factor i(w).
-(w - 2)*(w + 1)**3*(w + 3)/3
Suppose -10*r = -8*r + 2, 5*m - 25 = 5*r. Find p, given that 5*p**m + 20*p**3 + 4604*p**2 + 5 - 4574*p**2 + 20*p + 0 = 0.
-1
Let h = 142686 - 576099/4. Let f = h + 1340. Factor 1/4*x**5 + 0 + 3/4*x**3 - x + 5/4*x**4 - f*x**2.
x*(x - 1)*(x + 1)**2*(x + 4)/4
Let x(h) = -13*h + 1. Let c be x(-2). Factor 3 - 67 - c*z**2 - 60*z + 31*z**2.
4*(z - 16)*(z + 1)
Let x(h) be the second derivative of h**7/840 + h**6/160 - h**5/60 - 83*h**2 + 137*h. Let w(f) be the first derivative of x(f). Find v such that w(v) = 0.
-4, 0, 1
Let h(k) be the first derivative of k**5/5 + 75*k**4/4 - 76*k**3/3 - 196. Suppose h(a) = 0. Calculate a.
-76, 0, 1
Find j such that 164/9*j**2 + 0*j + 0 + 2/9*j**4 + 86/9*j**3 = 0.
-41, -2, 0
Let g be ((24/9)/(-8)*-12*(-9)/18)/(-1). What is q in -91/4*q - 3/4*q**g - 15/2 = 0?
-30, -1/3
Let h be 1/7*(3*2/(-51) + 28188/13311). Find x, given that h*x**2 + 90/7 + 92/7*x = 0.
-45, -1
W