*4 - h*u**2 + 0*u + 0 = 0. What is u?
0, 1, 4
Let b = 106 - 104. Factor 735*k**2 - k - 734*k**2 + b*k.
k*(k + 1)
Let h(r) be the second derivative of -11/2*r**3 - 7/16*r**4 + 0 - 77*r - 9/2*r**2. Factor h(i).
-3*(i + 6)*(7*i + 2)/4
Let j(u) be the first derivative of u**3/12 - 3*u**2/2 - 27*u + 1415. Factor j(f).
(f - 18)*(f + 6)/4
Factor 2/13*t**3 - 10/13*t**2 - 8/13*t + 40/13.
2*(t - 5)*(t - 2)*(t + 2)/13
Suppose 0 = -u + 3, 2*p - 9 = 2*u + 25. Let a be (p/(-490)*7)/((-24)/14). Factor a*m**3 - 1/3 + 0*m**2 - 1/2*m.
(m - 2)*(m + 1)**2/6
Suppose 1197*w**3 + 43200 + 20028*w**2 + 4983*w + 30766*w + 26171*w - 125*w**3 + 3*w**5 - 153*w**4 + 80*w**3 = 0. Calculate w.
-4, -1, 30
Let j be 18*((-238)/21 - -1). Let t = j - -188. Factor 0 - 1/4*b**3 - 1/4*b**4 + 1/4*b**t + 1/4*b.
-b*(b - 1)*(b + 1)**2/4
Let s be -8 - ((-2)/6 + (-269600)/31350 + (-3)/19). Factor 0 + s*j + 14/11*j**3 + 26/11*j**2.
2*j*(j + 1)*(7*j + 6)/11
Suppose -70*w - 9 = -73*w. Let l be w/(-10)*(5 + 2 + -9). Factor -9/5*z**4 + 0 - l*z**2 + 0*z + 9/5*z**3 + 3/5*z**5.
3*z**2*(z - 1)**3/5
Suppose -4*w + 8 = 3*i, -5*w - 10*i + 5 = -5*i. Determine y, given that 7*y**2 - 100 - 14159*y + 88*y**2 + w*y**4 - 60*y**3 + 14219*y = 0.
-1, 1, 2, 10
Let y(v) be the third derivative of -v**5/30 - 10*v**4/3 + 176*v**3/3 + 1040*v**2. Factor y(g).
-2*(g - 4)*(g + 44)
Let h(b) be the third derivative of 1/156*b**4 - 46*b - 2*b**2 + 0 - 1/390*b**5 + 1/39*b**3 - 1/780*b**6. Factor h(n).
-2*(n - 1)*(n + 1)**2/13
Let c(k) be the first derivative of -k**6/180 + 4*k**5/15 - 38*k**3 + 12. Let r(j) be the third derivative of c(j). Factor r(x).
-2*x*(x - 16)
Factor 104976 + 216*r + 1/9*r**2.
(r + 972)**2/9
Let x = -14548 + 14590. Let u(v) be the third derivative of 8/3*v**3 - 1/5*v**5 + 0*v - 2/105*v**7 + x*v**2 - 2/15*v**6 + 2/3*v**4 + 0. Factor u(p).
-4*(p - 1)*(p + 1)*(p + 2)**2
Let o = -24/4531 - -22727/13593. Find m such that 0 + o*m**5 + 20*m**2 + 20/3*m + 65/3*m**3 + 10*m**4 = 0.
-2, -1, 0
Factor -3*d**4 - 290*d**3 + 3*d**2 + 12*d + 151*d**3 + 127*d**3.
-3*d*(d - 1)*(d + 1)*(d + 4)
Let a(x) be the second derivative of 1960*x**2 + 5/12*x**4 + 140/3*x**3 + 22 + 2*x. Determine z so that a(z) = 0.
-28
Factor 16*b + 0 + 2/5*b**3 + 26/5*b**2.
2*b*(b + 5)*(b + 8)/5
Let q = 466210/3 - 155401. Determine c, given that -8/3 + q*c**2 + 10/3*c = 0.
-2, 4/7
Suppose -4*x = -5*k + 2965, -3*x - 2048 = -4*k + 175. Let v = x - -750. Factor v*s**2 - 15/2*s - 5.
5*(s - 2)*(2*s + 1)/2
Let q(s) be the third derivative of 5*s**7/112 - s**6/12 + s**5/15 + s**4/24 - 13*s**3/6 - 84*s**2. Let b(z) be the second derivative of q(z). Factor b(k).
(15*k - 4)**2/2
Let g(j) be the second derivative of -13/9*j**3 + 0*j**2 + 0 - 84*j + 1/18*j**4. Factor g(k).
2*k*(k - 13)/3
Let t(f) be the third derivative of -160/3*f**3 + 0 - 1/12*f**5 - 4*f - 10/3*f**4 + 6*f**2. Find b such that t(b) = 0.
-8
Let n(v) = 11*v**3 - 165*v**2 - 2347*v - 2187. Let f(u) = -40*u**3 + 495*u**2 + 7040*u + 6561. Let w(b) = 2*f(b) + 7*n(b). Suppose w(o) = 0. What is o?
-27, -1
Let v be -1*3/((-3)/10). Let n = 92 + -88. Factor -20*d**3 - 10*d**4 - 15*d**n - 8*d**3 - 5*d**5 - v*d - 35*d**2 - 17*d**3.
-5*d*(d + 1)**3*(d + 2)
Factor 859 - 157*f + 4*f**2 + 2*f**2 - 8*f**2 + 473 + 3*f**2.
(f - 148)*(f - 9)
Let l be 3/14 + (-34380)/(-280) + -121. Factor -60/7 + 27/7*a - 3/7*a**l.
-3*(a - 5)*(a - 4)/7
Let w(a) be the third derivative of a**8/1512 + a**7/189 - 2*a**6/45 + 2*a**5/135 + 8*a**4/27 - a**2 - 74. Let w(t) = 0. What is t?
-8, -1, 0, 2
Let i be 99*(-2)/(-42) - 4/(-14). Factor -3*f**2 + 43*f**2 + 46 + i*f**3 - 97 + 51.
5*f**2*(f + 8)
What is h in 101761/5*h + 638/5*h**2 + 1/5*h**3 + 0 = 0?
-319, 0
Let g(c) be the first derivative of 2*c**3/3 - 1318*c**2 + 2634*c - 11516. Determine j, given that g(j) = 0.
1, 1317
Let z = 22783/21906 + 173/2434. Factor -2/9*d**3 + 0 - 8/9*d + z*d**2.
-2*d*(d - 4)*(d - 1)/9
Factor 31/5*y + 2/5*y**4 + y**3 - 11/5 - 27/5*y**2.
(y - 1)**3*(2*y + 11)/5
Let q(v) = v**5 + v**4 - v**3 + 3*v**2 - 2*v. Let p(f) = -3*f**5 - 8*f**4 - 2*f**3 + 24*f**2 - 19*f. Let g(u) = p(u) + 4*q(u). Factor g(o).
o*(o - 3)**2*(o - 1)*(o + 3)
Let s(j) = -57*j**2 + 2088*j - 344757. Let n(a) = -237*a**2 + 8361*a - 1379027. Let z(i) = -6*n(i) + 25*s(i). Solve z(d) = 0.
339
Let y(b) = -b**4 + 57*b**3 - 15*b**2 - 12*b + 21. Let s(x) = x**4 - 63*x**3 + 13*x**2 + 9*x - 20. Let d(o) = 5*s(o) + 6*y(o). Solve d(f) = 0.
-1, 1, 26
Let c(d) be the second derivative of d**5/160 - 405*d**4/32 + 809*d**3/16 - 1213*d**2/16 + 659*d + 4. Factor c(t).
(t - 1213)*(t - 1)**2/8
Let j(b) = 11*b**2 - 12*b + 29. Let d be j(6). Find c, given that -698*c**2 - 5*c + 344*c**2 + d*c**2 + 3*c = 0.
-2, 0
Let s(r) be the third derivative of -4/39*r**3 + 1/390*r**5 + 1/39*r**4 - 6*r + 0 - 5*r**2 - 1/780*r**6. What is b in s(b) = 0?
-2, 1, 2
Let l(x) be the first derivative of -x**5/5 - 13*x**4/3 - 8*x**3 + 326*x + 179. Let z(s) be the first derivative of l(s). Let z(j) = 0. What is j?
-12, -1, 0
Let h(n) = n**3 + 4*n**2 - 14*n - 41. Let b be h(-5). Factor 6*w**b + w**4 - 2*w**4 + 110*w**2 + 0*w**4 + 65*w**3.
5*w**2*(w + 2)*(w + 11)
Let i(l) be the first derivative of 7*l**5/15 + 29*l**4/12 + 25*l**3/9 + l**2/2 + 266. Factor i(d).
d*(d + 1)*(d + 3)*(7*d + 1)/3
Let i(s) = 17*s**4 - 49*s**3 + 41*s**2. Let v(o) = 4*o**4 - 12*o**3 + 10*o**2. Let l(a) = 4*i(a) - 18*v(a). Factor l(w).
-4*w**2*(w - 4)*(w - 1)
Let o(b) be the second derivative of -b**4/60 - 117*b**3/5 + 3837*b + 1. Factor o(d).
-d*(d + 702)/5
Suppose 3*c - 2 = 31. Factor 44*u + c*u**2 - 29*u**2 + 14*u**2.
-4*u*(u - 11)
Let f(o) be the second derivative of -7*o**6/45 - 3*o**5/2 - 4*o**4 + 28*o**3/9 + 32*o**2 + 13587*o. Determine m, given that f(m) = 0.
-24/7, -2, 1
Let h(o) be the second derivative of -39*o - 2 - 5/2*o**2 - 5/24*o**4 - 5/4*o**3. Let h(f) = 0. What is f?
-2, -1
Let w(k) = 5*k - 50. Let i be w(10). Let g be (i + -6)*(-170)/(-570)*-2. Let -2/19*c**2 - g*c**3 + 32/19*c + 8/19 - 42/19*c**4 = 0. What is c?
-1, -2/7, 2/3
Suppose 22 = 7*z + 1. Suppose -14 = b + 4*a, -z*b - 4*a - 6 = -a. Find i such that 21*i**4 + 3*i**3 - b*i - 5*i**5 + 4*i**5 - 20*i**4 - i**2 = 0.
-1, 0, 1, 2
Suppose 4 = 2*r - 3*r. Let i be r + (-1)/(-4) + 245/28. Let -2/9 - 2/9*l**3 - 7/9*l + 2/9*l**4 - 8/9*l**2 + 1/9*l**i = 0. What is l?
-1, 2
Let x(s) = -40*s**3 - 3035*s**2 + 870*s - 5. Let g(z) = z**3 + 1. Let q(f) = 5*g(f) + x(f). Find i, given that q(i) = 0.
-87, 0, 2/7
Let u(a) be the second derivative of 9/10*a**5 - 3*a**4 - 1/10*a**6 + 0 + 0*a**2 - 145*a + 4*a**3. Factor u(o).
-3*o*(o - 2)**3
Let 4913 - 4923 + 72*r**4 - 35*r**2 - 27*r**4 + 55*r**3 - 55*r = 0. Calculate r.
-1, -2/9, 1
Factor 59290*f + 2/15*f**3 - 154*f**2 - 22826650/3.
2*(f - 385)**3/15
Let d(c) be the second derivative of 3/80*c**5 - 3/40*c**6 - 55*c + 0*c**2 + 3/16*c**4 - 1/56*c**7 + 0*c**3 + 2. What is m in d(m) = 0?
-3, -1, 0, 1
Let y = -32 - -218. Let q be y/195 + (-4)/26. Find h such that -16/5 + q*h**2 + 6/5*h**3 - 24/5*h = 0.
-2, -2/3, 2
Find h, given that -72/11 - 210/11*h**2 + 2/11*h**4 - 6*h**3 - 214/11*h = 0.
-1, 36
Find r, given that 21*r**3 - 441/2*r**2 - 1/2*r**4 + 0 + 686*r = 0.
0, 7, 28
Let o(y) be the third derivative of -1/60*y**5 + 0*y - 3/8*y**4 + 23*y**2 + 0 - 4/3*y**3. Factor o(c).
-(c + 1)*(c + 8)
Suppose m + 1 = 5*b, 2*m = -4*b - m - 3. Let j be (0 - b)*(-2)/64*-16. Factor j*z**2 + 0 + 0*z + 3/5*z**5 + 27/5*z**3 + 18/5*z**4.
3*z**3*(z + 3)**2/5
Solve 0 + 143/2*g - 1/2*g**2 = 0 for g.
0, 143
Suppose -4/3 + 68/3*k + 35/3*k**2 = 0. Calculate k.
-2, 2/35
Let p(n) be the first derivative of -n**7/2940 - 17*n**6/420 + 160*n**3/3 + 243. Let m(i) be the third derivative of p(i). Factor m(y).
-2*y**2*(y + 51)/7
Let g(p) be the first derivative of -p**5/25 - p**4/12 + 7*p**3/30 + p**2/5 + 47*p + 37. Let z(n) be the first derivative of g(n). Factor z(q).
-(q - 1)*(q + 2)*(4*q + 1)/5
Factor 1016*z + 102708*z**2 + 279*z - 51137*z**2 - 53016*z**2 + 5*z**4 + 145*z**3.
5*z*(z - 7)*(z - 1)*(z + 37)
Suppose 44*l = 29*l + 45. Factor 7*c**2 - 2*c - 8*c + 981*c**3 - 982*c**l.
-c*(c - 5)*(c - 2)
Suppose -3*x - 8*x = -44. Let l(v) be the third derivative of -1/66*v**x + 10*v**2 + 1/33*v**3 + 1/330*v**5 + 0*v + 0. Factor l(s).
2*(s - 1)**2/11
Let x be 33/(-5) + (-424)/1060. Let m be (1 -