
Let a(x) be the third derivative of x**6/40 - 7*x**4/8 + 3*x**3 + 59*x**2. Factor a(l).
3*(l - 2)*(l - 1)*(l + 3)
Let u(o) be the second derivative of -o**5/180 - 5*o**4/72 + o**3/3 + 20*o**2 + 26*o. Let i(p) be the first derivative of u(p). Factor i(v).
-(v - 1)*(v + 6)/3
Let m = -418 + 420. Let p = 28/3 + -8. Suppose -p*v + 2/3*v**m + 2/3 = 0. Calculate v.
1
Factor 0*z**3 - 3*z**4 - 1/6*z**5 + 0*z**2 + 0*z + 0.
-z**4*(z + 18)/6
Let b be (-126)/168*((-46)/(-27) + -2). Determine f so that -b*f + 0 + 2/9*f**3 + 0*f**2 = 0.
-1, 0, 1
Factor 90*a - 447*a + 10 - 44*a**3 + 272*a**2 - 87*a + 12 + 50.
-4*(a - 3)**2*(11*a - 2)
Let l(s) be the first derivative of -23*s**4/9 + 32*s**3/9 - 2*s**2/9 - 222. Factor l(t).
-4*t*(t - 1)*(23*t - 1)/9
Let u(y) be the first derivative of -9*y**5/5 + 39*y**4/16 - y**3/4 + 205. Determine x, given that u(x) = 0.
0, 1/12, 1
Let -24*h**2 - 9 + 40*h + 6*h**2 + 1 - 32*h**2 = 0. What is h?
2/5
Let b = -883 - -883. Let b + 0*k + 8/3*k**2 - 12*k**3 = 0. Calculate k.
0, 2/9
Suppose -4*s + 18 = -22. Find h such that 64*h - 36*h - 33*h + s + 5*h**3 + 5*h**4 - 15*h**2 = 0.
-2, -1, 1
Let -2/13*r**3 - 480/13*r + 3200/13 - 72/13*r**2 = 0. What is r?
-20, 4
Determine p so that -147456 + 23040*p + 125/6*p**3 - 1200*p**2 = 0.
96/5
Let b(h) = 158*h + 4266. Let s be b(-27). Factor -1/3*c**2 - 2/3*c**3 - 1/3*c**4 + 0*c + s.
-c**2*(c + 1)**2/3
Let v = 32 + -38. Let h(n) = -2*n - 8. Let g be h(v). Suppose 0*k - k**2 + 2 - 11*k**3 - k**2 + g*k**3 + 7*k = 0. What is k?
-1, -2/7, 1
Let n = -45/14 + 309/70. Find v, given that 4/5 - 4/5*v**2 - n*v = 0.
-2, 1/2
Let s(n) be the first derivative of -n**9/1008 - n**8/140 - n**7/56 - n**6/60 + 8*n**3/3 + 12. Let o(i) be the third derivative of s(i). Factor o(w).
-3*w**2*(w + 1)**2*(w + 2)
Let b = 23 + -20. Suppose 0 = b*y + 4*a - 22, -2 = -y + 3*a - 12. Let -j**2 - 4*j**y + 10*j**3 - j**4 - 4*j**4 + 0*j**2 = 0. What is j?
0, 1
Let q(g) be the first derivative of 4*g**3/15 - 14*g**2/5 - 32*g/5 - 537. Factor q(z).
4*(z - 8)*(z + 1)/5
Let x(n) be the first derivative of 0*n**3 + 0*n**5 - 1/2*n**6 + 22 + 0*n + 3/2*n**4 - 3/2*n**2. Factor x(g).
-3*g*(g - 1)**2*(g + 1)**2
Factor 5*h - 3*h**2 + 178*h - 240 + 34*h + 26*h.
-3*(h - 80)*(h - 1)
Suppose 32*w - 64*w = -64. Factor 4/5*t**3 - 8/5 - 8/5*t + 6/5*t**w - 2/5*t**4.
-2*(t - 2)**2*(t + 1)**2/5
Let f(u) be the third derivative of u**6/480 + 7*u**5/240 - 17*u**4/96 + 3*u**3/8 + 76*u**2 + u. Factor f(h).
(h - 1)**2*(h + 9)/4
Suppose -3 - 5 = -2*g. Let c = 7 - g. Find s, given that 3*s**5 + 3*s + 3*s**4 - 6*s**c - 3*s**4 + 0*s**4 = 0.
-1, 0, 1
Factor 9*u**3 + 117*u**2 + u + 177*u + 80 + 3*u**3 + 0*u**4 + 8*u**3 + u**4.
(u + 1)**2*(u + 8)*(u + 10)
Suppose 4*y + 4*z = 4, -2*y - z + 0*z = -1. Let q(r) be the second derivative of -1/4*r**4 + 1/2*r**3 - 8*r + y + 0*r**2. Determine l so that q(l) = 0.
0, 1
Let q(i) be the first derivative of -1/20*i**5 - 3/4*i**3 - 1/2*i + 7/8*i**2 + 5/16*i**4 - 21. Let q(y) = 0. What is y?
1, 2
Suppose 10*q + 9 = 11*q. Let a be -4 - -1 - -5 - q/6. Let -a*c - 1/2 + 1/2*c**2 + 1/2*c**3 = 0. What is c?
-1, 1
Factor 44327 + 3*y**2 + 12267 + 3*y**2 - 3*y**2 - 7442 - 768*y.
3*(y - 128)**2
Let w(z) = 9*z**2 + 17*z + 65. Let p = 60 - 54. Let d(b) = -8*b**2 - 18*b - 66. Let s(l) = p*w(l) + 7*d(l). Find u, given that s(u) = 0.
-6
Suppose 0 = -2*j - 4*u + 20, -4*u - 6 = 28*j - 39*j. Factor -2/3 - 1/6*t**j - 2/3*t.
-(t + 2)**2/6
Let -65/4*q**2 + 2 + 15/4*q**4 - 11*q**3 + 1/2*q = 0. What is q?
-1, -2/5, 1/3, 4
Let t = -1642 - -1645. What is m in -16/15 + 2/15*m**t + 8/5*m - 4/5*m**2 = 0?
2
Suppose 435 = 20*r - 15*r. Let d = 438/5 - r. Find w, given that 0*w + 0 + d*w**4 + 0*w**2 + 2/5*w**3 + 1/5*w**5 = 0.
-2, -1, 0
Let -1/2*q - 7/4*q**2 + 3/4*q**4 - 1/2*q**3 + 0 = 0. Calculate q.
-1, -1/3, 0, 2
Suppose 1/6*k**2 - 43/2 + 64/3*k = 0. Calculate k.
-129, 1
Let n(i) = 5*i**3 + 235*i**2 - 250*i - 480. Let s(f) = -f**3 - 39*f**2 + 42*f + 80. Let c(r) = -4*n(r) - 25*s(r). Suppose c(h) = 0. What is h?
-8, -1, 2
Find j such that 102 + 2*j + 22 + 0*j**3 + j**3 - 124*j**2 + 2*j - 5*j**3 = 0.
-31, -1, 1
Let s(r) = -13*r + 30. Let m be s(2). Let w(o) be the third derivative of 0*o + 0 + 0*o**m + 1/240*o**5 + 0*o**3 - 5*o**2. Factor w(t).
t**2/4
Let p = 14955 - 14955. Determine x so that p - 1/5*x - 2/5*x**2 - 1/5*x**3 = 0.
-1, 0
Let j(w) be the third derivative of -7*w**7/120 + 7*w**6/24 - 5*w**5/12 + 15*w**2 + 6. Suppose j(k) = 0. Calculate k.
0, 10/7
Let k(o) = -o - 2. Suppose -5*p = 5*y + 10, -11 = y - 6*p + 4*p. Let t be k(y). Factor -z - z - 6*z**2 + 3*z**4 + 21*z**3 - 19*z**3 + t*z**4.
2*z*(z - 1)*(z + 1)*(3*z + 1)
Suppose 0 + 0*s**3 + 3/5*s**2 + 0*s - 3/5*s**4 = 0. What is s?
-1, 0, 1
Let r = 40 + -36. Let i = -6 - -6. Determine s, given that 2 - 5 - r*s**2 + 7*s**2 + i = 0.
-1, 1
Suppose 5*m + 2*x - 20 = 0, 3*m + 7*x = 4*x + 12. Factor 4*r**3 + 4*r**2 + 1 - 4*r**5 + 41*r**m - 1 - 45*r**4.
-4*r**2*(r - 1)*(r + 1)**2
Let q(j) be the third derivative of j**8/1176 + j**7/735 - j**6/140 - j**5/210 + j**4/42 - 59*j**2. Determine c, given that q(c) = 0.
-2, -1, 0, 1
Solve -23/3*k - 4/3*k**2 + 2 = 0 for k.
-6, 1/4
Let p = 3945 - 11959/3. Let x = 42 + p. Solve 6 + x*r**2 - 4*r = 0.
3
Suppose -1 + 21 = 4*m - 2*h, -8 = -4*m - 4*h. Determine j so that -39*j**2 + m*j - 2*j**4 - 2*j**3 + 45*j**2 + 6*j + 4 = 0.
-1, 2
Suppose -48*q - 62*q = 0. Factor -2/3*v**2 + 2*v + q.
-2*v*(v - 3)/3
Let z(u) = -2*u**3 - 2*u**2 + 4*u + 2. Let s be (-6 + 2 + 3)/(2/4). Let h be z(s). Determine a, given that -2/7*a + 1/7*a**h + 0 = 0.
0, 2
Let v(k) = -k**2 - 10*k - 14. Let b be v(-8). What is s in -19*s - 14*s**3 - 35*s**2 - 27*s + 4*s**3 - 12 - 9*s**b = 0?
-3, -1, -2/5
Let k(w) be the third derivative of 0*w**6 + 19*w**2 + 0*w**3 + 1/588*w**8 - 1/42*w**4 - 4/735*w**7 + 0 + 2/105*w**5 + 0*w. Factor k(c).
4*c*(c - 1)**3*(c + 1)/7
Let o(i) = -i + 6. Let v be o(3). Factor 8*r - 4 + 4*r**3 + 4 - 8*r**2 - 10*r**v.
-2*r*(r + 2)*(3*r - 2)
Let p(k) be the third derivative of 9*k**2 + 0*k**3 - 1/336*k**8 + 0*k**7 + 0*k**4 + 0 + 1/40*k**6 + 0*k - 1/30*k**5. Factor p(i).
-i**2*(i - 1)**2*(i + 2)
Factor 3*k**3 - 4*k + k**4 + k + 0*k**4 + 5*k**2 + 4*k - 2*k**2.
k*(k + 1)**3
Let a(j) be the third derivative of j**8/1344 - 13*j**7/420 + 13*j**6/30 - 229*j**5/120 - 209*j**4/96 + 121*j**3/6 - 475*j**2. Suppose a(k) = 0. Calculate k.
-1, 1, 4, 11
Let h(c) = 2*c - 1. Let n(k) = 3*k**2 + 10*k - 11. Let w(x) = -18*h(x) - 2*n(x). What is r in w(r) = 0?
-10, 2/3
Let s be 7 - (-6 + 3 + 4). Factor 12*k + 2*k**2 + s - 5*k + 3*k + 2.
2*(k + 1)*(k + 4)
Suppose 97*c = 107*c. Factor c*y + 5/8*y**5 + 0 - y**4 + 1/8*y**3 + 1/4*y**2.
y**2*(y - 1)**2*(5*y + 2)/8
Let f(h) be the second derivative of -25/6*h**3 + 0 - 5/6*h**4 - 4*h + 5/4*h**5 + 5*h**2. Factor f(v).
5*(v - 1)*(v + 1)*(5*v - 2)
Let m = 472/7 - 11327/168. Let g(z) be the third derivative of 7*z**2 + 1/1470*z**7 + 1/140*z**5 + 0*z - m*z**4 - 1/280*z**6 + 0 + 0*z**3. Factor g(y).
y*(y - 1)**3/7
Let u(v) be the first derivative of 10*v**2 + 12*v - 3 + 4/3*v**3 - v**4. Factor u(l).
-4*(l - 3)*(l + 1)**2
Let u(y) be the first derivative of y**5/90 - y**4/36 - 2*y**3/9 - 19*y**2/2 - 7. Let c(p) be the second derivative of u(p). Factor c(b).
2*(b - 2)*(b + 1)/3
Let g be (-9 + 13)/(1 - (-2)/(-4)). Suppose n + z - g = 0, 8 + 7 = 3*z. Suppose 8/3*u**n - 8/3*u**4 - 2*u**5 + 0 + 0*u**2 + 0*u = 0. What is u?
-2, 0, 2/3
Let u be -2*(-18)/24*2. Let i(x) be the second derivative of -3/4*x**4 + 2*x + u*x**2 + 0 - 3/20*x**5 + 1/10*x**6 + 1/2*x**3. Determine g so that i(g) = 0.
-1, 1, 2
Let n = 27 + -25. Suppose 3*j - 4*t = 21, -5*j + 7 + 28 = -n*t. Factor -8*d**3 + 0*d**5 + 9*d**4 - j*d**3 + 3*d**2 + 6*d**3 - 3*d**5.
-3*d**2*(d - 1)**3
Suppose -6*n = 2*s - 46 + 76, -4*n - 20 = -5*s. Suppose s*u + 2/5*u**2 + 0 + 2/15*u**3 = 0. Calculate u.
-3, 0
Let z be ((-279)/155)/((-33)/5)*11. Solve -1/4*n**4 - 5/4*n**z + 0 - 3/4*n - 7/4*n**2 = 0.
-3, -1, 0
Let o = 175 - 171. Let n(u) be the first derivative of -5 - 1/3*u**3 - 7/20*u**o + 1/5*u**2 + 0*u. Factor n(v).
-v*(v + 1)*(7*v - 2)/5
Let t(s) be the first derivative of 0*s + 1/150*s**5 + 4*s**2 - 3 + 2/15*s**3 - 1/20*s**4. Let k(a) be the second derivative of t(a). Factor k(p).
2*(p - 2)*(p - 1)/5
Let l be (10 - 15)*40/(-