c + 1)**3*(c + 2)
Let f(w) be the second derivative of -w**5/70 - 4*w**4/21 - 5*w**3/21 + 2*w**2 - 459*w. Determine c, given that f(c) = 0.
-7, -2, 1
Let k(w) be the third derivative of 1/12*w**5 + 0*w + 55/12*w**4 + 16*w**2 + 0 + 605/6*w**3. Factor k(n).
5*(n + 11)**2
Let f = 132 + -130. Let s(b) be the second derivative of -1/8*b**4 + b**2 - f*b + 1/3*b**3 + 0. Suppose s(u) = 0. Calculate u.
-2/3, 2
Let a(u) = 9*u**2 - 82*u - 1352. Let q(o) = o**2 + 2*o. Let s(j) = -2*a(j) + 22*q(j). Let s(c) = 0. Calculate c.
-26
Let y = 549/226 + -105/113. Factor y*a**2 - 3 - 7/2*a.
(a - 3)*(3*a + 2)/2
Let f(k) be the second derivative of k**7/294 - 3*k**6/70 + k**5/28 + 29*k**4/84 - k**3 + 8*k**2/7 - 15*k - 1. Suppose f(h) = 0. What is h?
-2, 1, 8
Let l(q) be the first derivative of -49*q**3/3 + 140*q**2 - 400*q + 64. Factor l(m).
-(7*m - 20)**2
Let c be (-60)/(-18) + (-2)/(-3). Let t be (0 - 1)/(2/(-8)). What is p in 7*p**3 + 8*p**t + 5*p**3 - 15*p**5 - 4*p**c + 2*p**2 - 3*p**3 = 0?
-2/5, -1/3, 0, 1
Factor 189/2*a**2 + 9*a**3 - 3/2*a**4 + 162*a + 0.
-3*a*(a - 12)*(a + 3)**2/2
Suppose -4*n + 60 = -5*n. Let d = n + 301/5. Let 0 - d*j**2 + 0*j + 1/5*j**3 = 0. Calculate j.
0, 1
Let k = 311/7 - 919/21. Factor 4/3 + 2*c - k*c**3 + 0*c**2.
-2*(c - 2)*(c + 1)**2/3
Factor 0 + 4/9*b**4 + 0*b + 2/9*b**2 - 1/9*b**5 - 5/9*b**3.
-b**2*(b - 2)*(b - 1)**2/9
Let p(v) be the third derivative of -v**6/24 - 3*v**5/2 - 20*v**4 - 400*v**3/3 - 72*v**2. Factor p(k).
-5*(k + 4)**2*(k + 10)
Let u(w) be the third derivative of 0*w**3 - 1/270*w**5 + 0 + 0*w + 1/54*w**4 - 1/540*w**6 + 7*w**2. Factor u(y).
-2*y*(y - 1)*(y + 2)/9
Let z(w) be the second derivative of -w**7/525 - w**6/60 - 7*w**5/150 - w**4/20 + w**2 + 43*w. Let p(f) be the first derivative of z(f). Solve p(y) = 0.
-3, -1, 0
Let u(g) be the second derivative of 0*g**4 - 1/150*g**5 + 11*g + 0 + 1/45*g**3 + 0*g**2. Factor u(z).
-2*z*(z - 1)*(z + 1)/15
Solve 86/9*n - 164/9 - 2/9*n**2 = 0.
2, 41
Let u(o) be the second derivative of 0*o**2 - 7/8*o**4 + 0 - 5*o - 1/2*o**3. Factor u(y).
-3*y*(7*y + 2)/2
Let l be (-2)/(1/2 - 1) - 13. Let c be ((-4)/(-10))/(-1)*5/l. Factor -2/3*n**2 + 2/3*n - c + 2/9*n**3.
2*(n - 1)**3/9
Suppose -3*b + 3*o = 9, 3*b + 3*o + 4 = 1. Let k(s) = 2*s**3 + 5*s**2 + 3*s + 2. Let v be k(b). Factor 0 + v*u + 2/7*u**3 - 4/7*u**2.
2*u**2*(u - 2)/7
Let f(p) = -p**3 - p. Let h(o) = 2*o + 17. Let y be h(-8). Let j(z) = 18*z**3 + 12*z. Let i(a) = y*j(a) + 15*f(a). Factor i(r).
3*r*(r - 1)*(r + 1)
Let s = 56 + 24. Suppose 440*j**3 - 80 + 520*j**2 - j**5 + 10*j**5 + 80*j + s*j + 155*j**4 + 11*j**5 = 0. Calculate j.
-2, 1/4
Factor 8*z + 5*z - 5*z**2 - 205*z + 29*z - 87*z.
-5*z*(z + 50)
Let j(a) = -3*a**4 + 8*a**3 + a**2 - 6*a - 4. Let v(c) = -8*c**4 + 23*c**3 + c**2 - 19*c - 11. Let h(t) = 11*j(t) - 4*v(t). Factor h(x).
-x*(x - 2)*(x + 1)*(x + 5)
Let f = -15763/14 - -1126. Let a(w) be the second derivative of 0*w**2 - 3/28*w**4 + 7*w + 0 - 1/70*w**6 - f*w**3 - 9/140*w**5. Factor a(v).
-3*v*(v + 1)**3/7
Let x(j) be the first derivative of j**3/18 + 29*j**2/6 + 841*j/6 + 496. Factor x(u).
(u + 29)**2/6
Let 9/4*s**2 + 7/2*s + 1/4*s**3 + 0 = 0. Calculate s.
-7, -2, 0
Suppose -r - 2*n - 4 = 0, -5 = 2*r + 5*n + 6. Suppose 3*o + 7 = r*x + 2*o, -2*x - 2 = -4*o. Determine g, given that -5 + 3*g**2 + 3 + 1 + 3*g - x = 0.
-2, 1
Let q(o) be the second derivative of 0*o**2 + 0 - 14*o - 1/6*o**3 - 1/4*o**4 - 1/30*o**6 - 3/20*o**5. Factor q(l).
-l*(l + 1)**3
Let h(o) be the second derivative of 1/5*o**2 + 4/15*o**4 + 3/5*o**3 + 0 + 18*o. Determine s so that h(s) = 0.
-1, -1/8
Let a(s) be the second derivative of -s**9/13608 - s**8/2520 - s**7/1890 + s**3/3 + 3*s. Let q(t) be the second derivative of a(t). Suppose q(y) = 0. What is y?
-2, -1, 0
Let r(c) be the third derivative of c**7/210 - c**6/6 + 19*c**5/10 - 9*c**4/2 - 81*c**3/2 - 2*c**2 + 19*c. Solve r(d) = 0.
-1, 3, 9
Let r(f) = -7*f**3 + 10*f**2 + f + 4. Let n = -204 - -205. Suppose -w - 4 = -0. Let i(p) = -p**3 + p**2 + p + 1. Let v(q) = n*r(q) + w*i(q). Factor v(o).
-3*o*(o - 1)**2
Factor -z**3 - 4/3*z**2 + 1/3*z**4 + 0 + 0*z.
z**2*(z - 4)*(z + 1)/3
Suppose 0 + 4*g - 16/3*g**2 + 1/3*g**5 - g**3 + 2*g**4 = 0. Calculate g.
-6, -2, 0, 1
Let p(a) = -4*a - 87. Let j be p(22). Let g be ((-6)/(-5))/((-70)/j). Factor 4/3*t + 2/3*t**2 - 2/3*t**g + 0.
-2*t*(t - 2)*(t + 1)/3
Let x be (-14 - -15)*(5 + -5). Determine m, given that 2/9*m - 2/9*m**3 - 2/9*m**2 + x + 2/9*m**4 = 0.
-1, 0, 1
Suppose 125 = 858*p - 1104*p + 617. Suppose -5*g = -2*g. Solve 2/3*x**2 + g - p*x = 0 for x.
0, 3
Factor -5*y**5 - 188*y + 15*y**3 + 378*y - 10*y**2 - 190*y.
-5*y**2*(y - 1)**2*(y + 2)
Let b = 236 + -234. Let h(o) be the second derivative of 0 + 1/21*o**6 - 5/21*o**3 - 1/147*o**7 - 7*o + 5/21*o**4 - 1/7*o**5 + 1/7*o**b. Factor h(u).
-2*(u - 1)**5/7
Let g = -12725/14 - -909. Let w(y) be the first derivative of 0*y + g*y**4 + 8/21*y**3 + 11 + 4/7*y**2. Solve w(v) = 0 for v.
-2, 0
Determine m, given that 1/5*m**4 - 14/5*m - 3/5*m**2 - 8/5 + 4/5*m**3 = 0.
-4, -1, 2
Let i(x) be the third derivative of x**5/165 - x**4/44 - 2*x**3/33 + 66*x**2. Solve i(v) = 0 for v.
-1/2, 2
Let u(w) be the first derivative of -w**4 - 20*w**3/3 + 66*w**2 - 108*w - 203. Suppose u(d) = 0. What is d?
-9, 1, 3
Let p(v) be the third derivative of -v**8/840 + 4*v**7/525 - v**6/60 + v**5/75 + 5*v**2 + 14. Factor p(x).
-2*x**2*(x - 2)*(x - 1)**2/5
Let m be (567/72 - 8)*(-2 - -1). Factor -1/4*d + 0 + 3/8*d**2 - m*d**4 + 0*d**3.
-d*(d - 1)**2*(d + 2)/8
Let n = -135 - -138. Let d(z) be the third derivative of 0*z**4 - 1/175*z**7 + n*z**2 + 0*z**5 + 0*z**3 - 1/200*z**6 + 0 + 0*z - 1/560*z**8. Solve d(w) = 0.
-1, 0
Let b = -148 + 153. Let d(r) be the third derivative of -b*r**2 + 0*r - 3/80*r**5 + 1/2*r**3 + 0 + 1/160*r**6 + 0*r**4. Factor d(y).
3*(y - 2)**2*(y + 1)/4
What is a in -25*a - 3*a**3 - 8*a - 42*a - 30*a**2 = 0?
-5, 0
Let q = 2085 - 2082. Find w such that 0 + w**5 - 1/2*w - 1/2*w**q + 9/4*w**2 - 9/4*w**4 = 0.
-1, 0, 1/4, 1, 2
Let o(n) = 20*n + 562. Let p be o(-28). Factor -2*x**3 + 7/2*x**p - 1/2 - x.
-(x - 1)**2*(4*x + 1)/2
Let b(y) = -y**3 + 11*y**2 + 12*y - 6. Let z be b(10). Factor -1125 - 3*o**2 - 4*o**2 + 2*o**2 - z*o + 64*o.
-5*(o + 15)**2
Let y(x) be the second derivative of x**5/40 - x**4/6 - 7*x**3/4 + 2*x - 254. Solve y(l) = 0.
-3, 0, 7
Let f = -21 - -11. Let g be f/25 + (-12)/(-5). Find k, given that -8*k**2 + 12*k**g - k**3 - 3*k**3 = 0.
0, 1
Let w(j) be the first derivative of -3*j**4/8 - j**3 - 65. Factor w(s).
-3*s**2*(s + 2)/2
Let f be -1 - 12/(-9) - ((-564)/36 + 16). Let -44/9*q**2 + f - 8/9*q = 0. What is q?
-2/11, 0
Suppose -9 - 20 = q. Let n be q/(-9) + 18/(-81). Suppose 3 + 15*z - 9 - 8*z**n - 7*z**3 + 6*z**2 = 0. Calculate z.
-1, 2/5, 1
Let g(d) be the second derivative of -1/30*d**5 + 0 + 1/2*d**2 - 2/3*d**3 - 3*d - 1/4*d**4. Let z(c) be the first derivative of g(c). Solve z(a) = 0 for a.
-2, -1
Let j = -42 - -39. Let c(m) = -4*m**2 + 20. Let y(w) = -4*w**2 + 19. Let u(v) = j*c(v) + 4*y(v). Determine d, given that u(d) = 0.
-2, 2
Let r(c) = c**2 - 13*c + 10. Let p be r(11). Let m = p + 15. Factor -6*x**3 - 4*x**2 + 5*x**3 + 5*x**m + 12*x**3.
4*x**2*(4*x - 1)
Let x(y) be the second derivative of -2*y**7/7 - 63*y**6/10 - 6*y**5 + 39*y**4/2 + 22*y**3 - 45*y**2/2 + 33*y. Find b such that x(b) = 0.
-15, -1, 1/4, 1
Let w(d) be the first derivative of -d**6/270 - 2*d**5/45 - d**4/6 - 29*d**3/3 + 24. Let o(h) be the third derivative of w(h). Factor o(a).
-4*(a + 1)*(a + 3)/3
Let h(s) be the second derivative of -s**8/2184 + s**7/1365 + s**6/780 - s**5/390 + 9*s**2/2 - 4*s. Let z(i) be the first derivative of h(i). Factor z(c).
-2*c**2*(c - 1)**2*(c + 1)/13
Let u(m) be the second derivative of 1/20*m**5 - m + 0*m**2 - 1/3*m**4 + 1/2*m**3 + 0. Let g(c) = c - 1. Let z(r) = 6*g(r) + 3*u(r). Factor z(b).
3*(b - 2)*(b - 1)**2
Let c(v) = -2*v**3 - 14*v**2 - 42*v - 32. Let w(z) = z**2 - z. Suppose -5*y - t = 0, -3 = -4*y - t - 2. Let d(q) = y*c(q) + 2*w(q). Let d(x) = 0. What is x?
-4, -2
Let y(d) be the first derivative of 4*d**3 + 14*d**2 + 16*d - 38. Factor y(t).
4*(t + 1)*(3*t + 4)
Factor 2 + 3/11*w**2 - 35/11*w.
(w - 11)*(3*w - 2)/11
Let x be (4 + -8)*(10 + 21/(-2)). Factor 4/5*y**3 + 8/5 - 4/5*y - 8/5*y**x.
4