et m be 2/31 - (-1836)/372. Let g(a) be the second derivative of 0*a**2 - 3*a - 1/32*a**4 + 3/40*a**m + 0*a**3 + 0. Factor g(w).
3*w**2*(4*w - 1)/8
Find m such that -48/5*m**4 - 162/5*m - 8 - 2/5*m**5 - 172/5*m**3 - 248/5*m**2 = 0.
-20, -1
Let g(o) = -o - 1. Suppose 4*a = -3*b + 46, a = -0*a - 2. Let t(w) = -126*w**2 + 13*w - 5. Let s(l) = b*g(l) - 2*t(l). Factor s(y).
4*(7*y - 2)*(9*y + 1)
Let j = 51 - 36. Factor -3*u**5 - j*u**3 - 2*u**4 - 3*u**2 + 9*u**2 + 14*u**4.
-3*u**2*(u - 2)*(u - 1)**2
Let j(y) be the first derivative of y**3/12 - y**2 + 3*y + 332. Factor j(r).
(r - 6)*(r - 2)/4
Let x be ((-5138)/(-182) - 28)*13. Factor x*b - 10/3 + 1/3*b**2.
(b - 1)*(b + 10)/3
Let w(q) = 4*q - 3 + 4*q**3 - 4*q - q**2 + 1 + 2*q. Let h be w(1). Determine k, given that 6*k**2 + 6*k**5 + 27*k**h - 17*k**5 - 34*k**5 + 0*k**3 + 12*k**4 = 0.
-2/5, -1/3, 0, 1
Let u = -1841/738 - 2/369. Let s = 4 + u. Find b, given that -s + 3*b - 3/2*b**2 = 0.
1
Let r(k) be the second derivative of k**4/72 - 5*k**3/18 - 11*k**2/12 - k + 18. Find z, given that r(z) = 0.
-1, 11
Suppose -2*n + 27*a - 25*a = 6, 0 = 3*n - a - 1. Factor 16/21*t**3 + 0*t + 0 + 10/21*t**4 + 2/21*t**5 + 8/21*t**n.
2*t**2*(t + 1)*(t + 2)**2/21
Let z(t) be the first derivative of -4*t**5/35 + 55*t**4/14 - 102*t**3/7 + 149*t**2/7 - 14*t + 125. Let z(j) = 0. Calculate j.
1, 49/2
Let h(u) = 2*u**2 + 6*u - 8. Let s(b) = 3*b**2 + 5*b - 8. Let o(i) = -2*h(i) + 3*s(i). Factor o(l).
(l - 1)*(5*l + 8)
Let x(m) be the third derivative of m**6/360 - m**5/15 + 25*m**2 - 13. Factor x(v).
v**2*(v - 12)/3
Let b(h) be the third derivative of h**5/15 + 13*h**4/3 - 188*h**2 + 1. Let b(a) = 0. Calculate a.
-26, 0
Let m(q) be the first derivative of 1/2*q**4 + 9 - 2*q - 2*q**3 + 3*q**2. Factor m(b).
2*(b - 1)**3
Let n(u) be the second derivative of -u**8/33600 - u**7/4200 + u**6/900 + 3*u**4/4 - 10*u. Let r(t) be the third derivative of n(t). Factor r(k).
-k*(k - 1)*(k + 4)/5
Suppose 15*g - 1205 = -1175. Determine c, given that -40/3*c**g + 10 - 5*c**3 + 25/3*c = 0.
-3, -2/3, 1
Let z = 9870 + -9868. Factor -1/6*n**z - 2/3 + 2/3*n.
-(n - 2)**2/6
Suppose -3*b = -k + 4, -5*k - 4*b = -5*b - 20. Factor 6*m**5 - 2*m**k - 4*m**3 + 18*m**4 + 18*m**3 + 4*m**2.
2*m**2*(m + 1)**2*(3*m + 2)
Suppose -3*x = -2*p + 18, 4*p + x - 11 = -p. Let v = -21 - -48. What is h in -v*h + 3*h**2 + p*h + 4*h**2 + 12 + 2*h**2 = 0?
2/3, 2
Let c(g) be the second derivative of g**6/60 - 9*g**5/20 + 10*g**4/3 + 3*g**3/2 - 81*g**2/4 - g - 21. Solve c(m) = 0 for m.
-1, 1, 9
What is s in 0*s**3 + 0*s + 6*s**2 - 3/4*s**4 - 12 = 0?
-2, 2
Let d(k) be the first derivative of 0*k**2 + 1/20*k**5 + 0*k - 1/3*k**3 - 1/8*k**4 - 1/120*k**6 - 3. Let j(i) be the third derivative of d(i). Factor j(y).
-3*(y - 1)**2
Let a(b) = -2*b**3 + 8*b**2 + 14*b + 4. Let s = -50 - -58. Let f(h) = h**2 + h + 1. Let x(m) = s*f(m) - a(m). Factor x(l).
2*(l - 1)**2*(l + 2)
Suppose 5*j = 18 + 82. Let q be j/3*(-14)/(-70). Solve 1/3*k - 4/3*k**2 + 1/3*k**5 + 2*k**3 + 0 - q*k**4 = 0.
0, 1
Let m(p) be the first derivative of 8*p**3/45 - 23*p**2/15 - 4*p/5 - 248. Find g, given that m(g) = 0.
-1/4, 6
Let v be 4/18 - 452/(-774). Let m = -6/43 + v. Factor -2*g + 0 + m*g**2.
2*g*(g - 3)/3
Let f(o) be the second derivative of 2/3*o**2 + 0*o**3 - 1/60*o**5 - 1/12*o**4 - 2*o + 0. Factor f(q).
-(q - 1)*(q + 2)**2/3
Factor 2*a**2 + 3*a**3 + 199 + 25*a**2 + 45*a - 178.
3*(a + 1)**2*(a + 7)
Let n(d) = 18*d**5 - 33*d**4 - 21*d**3 + 30*d**2 - 15*d - 15. Let y(k) = -k**5 + k**4 + 2*k**3 + k + 1. Let c(u) = -n(u) - 15*y(u). What is z in c(z) = 0?
-1, 0, 2, 5
Let z(a) be the third derivative of a**5/60 - 19*a**4/24 + 44*a**3/3 - 92*a**2. Factor z(x).
(x - 11)*(x - 8)
Let j(a) be the second derivative of 3/4*a**5 + 0 + 1/6*a**6 + 0*a**3 + 0*a**2 + 5/6*a**4 + 11*a. Determine z, given that j(z) = 0.
-2, -1, 0
Factor -5*w**4 - 53412 + 220*w**3 - 2630*w**2 + 51207 + 6889*w - 2269*w.
-5*(w - 21)**2*(w - 1)**2
Let g(d) = -d**2 + d + 56. Let p be g(-7). Suppose -h - 2*j + 8 = -0*h, h - j + 1 = p. Find x, given that -3/4*x**3 + 1/2*x**h + 0 + 1/4*x = 0.
-1/3, 0, 1
Let j(k) be the first derivative of -2/21*k**3 + 10/7*k + 27 + 4/7*k**2. Factor j(a).
-2*(a - 5)*(a + 1)/7
Suppose 2/15*r**3 - 2/3*r**2 - 8/15 + 16/15*r = 0. Calculate r.
1, 2
Let d(o) be the third derivative of 1/22*o**4 - 1/330*o**5 + 2*o**2 + 0*o + 0 - 3/11*o**3. Factor d(r).
-2*(r - 3)**2/11
Let r(u) be the second derivative of -2*u**6/135 + 122*u**5/45 - 560*u**4/3 + 147200*u**3/27 - 256000*u**2/9 + 386*u. Let r(m) = 0. Calculate m.
2, 40
Let u = 484 - 19359/40. Let o(z) be the second derivative of 0*z**2 + u*z**5 + 9*z - 1/24*z**4 + 0 + 0*z**3. Find m such that o(m) = 0.
0, 1
Let h = 238 + -234. Let d(a) be the first derivative of -4/15*a + 1/30*a**h - 2/75*a**5 + 2/15*a**3 - 1/15*a**2 + 3. Suppose d(m) = 0. What is m?
-1, 1, 2
Let b(n) = -4*n**3 + 26*n - 3 - 11 - 31*n**2 - 9*n**2. Let q(m) = -m**3 - 8*m**2 + 5*m - 3. Let l(t) = -3*b(t) + 14*q(t). Factor l(g).
-2*g*(g - 2)**2
Let s(f) = f**5 - 25*f**4 - 48*f**3 - 32*f**2 - 4*f - 4. Let d(y) = 2*y**5 - 26*y**4 - 48*y**3 - 31*y**2 - 5*y - 5. Let x(j) = 4*d(j) - 5*s(j). Factor x(r).
3*r**2*(r + 2)**2*(r + 3)
Find m such that -9/2 - 3/4*m**2 - 21/4*m = 0.
-6, -1
Factor 1/9*q - 11/9*q**2 - 1/9*q**3 + 11/9.
-(q - 1)*(q + 1)*(q + 11)/9
Let f(c) be the second derivative of c**5/20 - 7*c**4/6 + 49*c**3/6 - 72*c. Let f(n) = 0. Calculate n.
0, 7
Let t be 4/(-10)*(-40)/12*3. Suppose 2*b - b - 2*h - 13 = 0, -t*b + 28 = 4*h. Factor -1/3*l**4 - b*l**2 - 3*l**3 - 9*l + 0.
-l*(l + 3)**3/3
Let c(j) be the second derivative of -5/12*j**4 + 0 + 0*j**2 + 1/8*j**5 + 5/12*j**3 - 10*j. Let c(n) = 0. Calculate n.
0, 1
Let b(w) be the second derivative of 5/12*w**4 + 8*w + 0 - 1/6*w**6 + 5/6*w**3 - 1/4*w**5 + 0*w**2. Factor b(o).
-5*o*(o - 1)*(o + 1)**2
Let h = 24 - 24. Suppose 3*z = o - 2*o + 12, h = -4*z + 4*o. Factor 45 - 5*y**z - 45.
-5*y**3
Suppose -40 = 6*i + 2*i. Let z be (-2 + 2)/2 + (-2)/i. Find a such that z + 0*a**3 + 8/5*a**4 - 2*a**2 - 3/5*a + 3/5*a**5 = 0.
-2, -1, 1/3, 1
Determine y so that 358*y**2 - 75 - 351*y**3 - 43*y**2 + 331*y**3 - 220*y = 0.
-1/4, 1, 15
Let n(v) be the second derivative of -11*v**5/15 - 13*v**4/9 - 4*v**3/9 - 505*v. Factor n(m).
-4*m*(m + 1)*(11*m + 2)/3
Let b be -2*(-2)/4*-15. Let t = -11 - b. Factor -6*u**2 - t*u**2 + 11*u - u - 4 + 2*u**2 + 2*u**3.
2*(u - 2)*(u - 1)**2
Let m(v) be the second derivative of v**6/360 + v**5/120 - v**4/12 - 2*v**3/3 + 8*v. Let b(c) be the second derivative of m(c). Find z such that b(z) = 0.
-2, 1
Let z(u) be the third derivative of u**8/420 + 11*u**7/1050 - u**6/200 - 4*u**5/75 + u**4/30 + 4*u**2 - 4*u. Let z(f) = 0. Calculate f.
-2, 0, 1/4, 1
Find o, given that 75*o - 235*o**3 + 85*o**3 + 5*o**5 - 130*o - 40*o**4 - 160*o**2 = 0.
-1, 0, 11
Let b be ((-5)/(-15))/(1/6). Solve -6*l - l**2 - b*l + 3*l + 2*l = 0.
-3, 0
Let y(l) be the third derivative of 13*l**2 - 1/160*l**6 + 0 - 11/32*l**4 - 5/8*l**3 - 7/80*l**5 + 0*l. Factor y(j).
-3*(j + 1)**2*(j + 5)/4
Let v = 2 + 8. Suppose -1 - 13*k - v*k - 13*k + 13 - 21*k**2 = 0. Calculate k.
-2, 2/7
Let t(w) = 5*w**2 + 1. Let s(h) = -4*h**2 - 1. Let r = 53 - 58. Let u(l) = r*t(l) - 6*s(l). Factor u(a).
-(a - 1)*(a + 1)
Let y be (-2 - -2) + (-1)/100*-3. Let w(j) be the second derivative of 0 + 0*j**2 + 1/5*j**3 - 6*j + y*j**5 + 3/20*j**4. Factor w(p).
3*p*(p + 1)*(p + 2)/5
Let y = -1529/7 + 219. Let q = -1/245 + 71/245. Factor 6/7*m**3 - y*m + 0 - q*m**2.
2*m*(m - 1)*(3*m + 2)/7
Suppose 4*m - 558 = 642. Factor 2*s**2 + m*s + 4*s**3 - 33*s**2 + 4*s**2 - 33*s**2 - 500.
4*(s - 5)**3
Let m(g) = -3*g**3 + 7*g**2 + 10*g + 3. Let w be m(-4). Let p = 2939/11 - w. Factor -2/11*x + 0 - 4/11*x**2 - p*x**3.
-2*x*(x + 1)**2/11
Let a(p) be the first derivative of -3*p**5/10 - 51*p**4/8 - 22*p**3 - 21*p**2 - 14. Let a(l) = 0. What is l?
-14, -2, -1, 0
Let a(w) be the first derivative of -2*w**5/55 + 17*w**4/22 - 62*w**3/33 + 15*w**2/11 + 149. Determine u so that a(u) = 0.
0, 1, 15
Let k(b) = -7*b**2 + 92*b + 99. Let v(n) = 36*n**2 - 459*n - 495. Let z(f) = 21*k(f) + 4*v(f). Solve z(l) = 0.
-1, 33
Suppose -7*n - 20 = -2*n. Let c be n/5*(-6 + 1). Factor 24 - 12*g**3 - 46 + 22 + 4*g**c + 16*g.
4*g*(g - 2)**2*(g + 1)
Let k(r) = 3*r 