. Factor a(g).
g*(g + 1)/2
Let a(l) be the second derivative of l**8/4200 - l**7/2100 - l**6/900 + l**5/300 + 8*l**3/3 - 22*l. Let r(w) be the second derivative of a(w). Factor r(b).
2*b*(b - 1)**2*(b + 1)/5
Suppose c + 51 = 18*c. Find j, given that 20*j + 14*j**2 + j**2 + 5*j**c - 10*j = 0.
-2, -1, 0
Let l = 2360 + -7079/3. Let 5/3*u**2 + 0 + l*u = 0. Calculate u.
-1/5, 0
Let c = 2/105 + 1132/105. Factor -2/5*k**3 + 18/5*k**2 - c*k + 54/5.
-2*(k - 3)**3/5
Let w(i) be the first derivative of i**5/25 + i**4/2 + 4*i**3/5 - 36*i**2/5 - 34. Find q, given that w(q) = 0.
-6, 0, 2
Let 150*z - 8*z**2 - 140*z - 4*z**3 + z**2 + z**4 = 0. Calculate z.
-2, 0, 1, 5
Let m(z) be the first derivative of -4*z**3/21 - 8*z**2 - 112*z - 63. Factor m(r).
-4*(r + 14)**2/7
Let f(i) be the second derivative of 0*i**4 + 9*i + 0*i**3 + 1/30*i**5 + 0 - i**2 - 1/60*i**6. Let b(p) be the first derivative of f(p). Factor b(c).
-2*c**2*(c - 1)
Let o be 1 + -2 + (21 + 6)/(-3). Let z be (-8)/(-4)*(-4)/o. Solve -8/5*w + 4/5 + z*w**2 = 0 for w.
1
Let z(u) be the first derivative of -5*u**4/12 + 10*u**2 + 6*u - 21. Let s(l) be the first derivative of z(l). Factor s(f).
-5*(f - 2)*(f + 2)
Suppose 4*v = 3*n + 14, -n - 84*v = -87*v + 13. Factor -2 + 1/2*z + 1/4*z**n.
(z - 2)*(z + 4)/4
Let j be (-22)/(-18) + 22/(-99). Suppose 1 - 9*k - 2*k**3 + 3*k - j - 8*k**2 = 0. Calculate k.
-3, -1, 0
Let b(p) be the third derivative of 1/120*p**5 + 0*p + 1/48*p**4 + 0 + 0*p**3 - 4*p**2. Factor b(i).
i*(i + 1)/2
Let t = -95 - -101. Factor -t*q - 4*q - 138*q**2 + 69*q**2 + 64*q**2.
-5*q*(q + 2)
Let j be -1 + (4/(-22))/(4/(-22)). Let a be (-1)/(-4) + 3/(-12). Find s, given that j*s**2 + 2/7*s**4 + a*s + 4/7*s**3 - 2/7*s**5 + 0 = 0.
-1, 0, 2
Let j(t) be the second derivative of t**8/1344 + t**7/504 - t**6/144 - t**5/24 + t**4 + 19*t. Let p(w) be the third derivative of j(w). Solve p(x) = 0.
-1, 1
Factor -32/5 - 38/15*b - 2/15*b**2.
-2*(b + 3)*(b + 16)/15
Let f(b) be the first derivative of b**6/75 + 3*b**5/25 + 2*b**4/15 - 2*b**3/5 - b**2 - 3*b + 28. Let h(v) be the first derivative of f(v). Factor h(y).
2*(y - 1)*(y + 1)**2*(y + 5)/5
Factor 294*j**2 + 7*j**3 + 368*j + 13*j**3 + 120 - 2*j**3.
2*(j + 15)*(3*j + 2)**2
Let b(z) be the third derivative of -z**6/120 + z**5/6 + z**4/2 - 3*z**3/2 - 5*z**2. Let w be b(11). Factor 6*t**3 + t**4 + 4*t**5 + 5*t**4 - 2*t**5 + 2*t**w.
2*t**2*(t + 1)**3
Let d(t) be the third derivative of -t**8/50400 + t**7/2100 - t**6/360 + 4*t**5/15 + 13*t**2. Let c(x) be the third derivative of d(x). Factor c(o).
-2*(o - 5)*(o - 1)/5
Suppose -4*n - 10 = -2*y + 32, 0 = 2*y + 3*n - 14. Let u = y - 11. Factor u + 2*c**4 - c + c**3 + 3*c**4 - 2*c**4 - 3*c**2 - 2*c**4.
(c - 1)**2*(c + 1)*(c + 2)
Factor 6*j**3 - 210*j - 58*j + 1000 - 2*j**3 - 32*j.
4*(j - 5)**2*(j + 10)
Let b(z) be the third derivative of -1/525*z**7 + 0*z**3 + 0 + 0*z**4 - 1/50*z**5 + 37*z**2 + 0*z + 1/75*z**6. Determine m so that b(m) = 0.
0, 1, 3
Let z(b) be the first derivative of 1/24*b**4 + b - 1/12*b**3 + 1/40*b**5 - 1/4*b**2 + 5. Let k(w) be the first derivative of z(w). Solve k(u) = 0 for u.
-1, 1
Let u(n) = -n**3 + 68*n**2 + 72*n. Let b(f) = -f**3. Let p(q) = -3*b(q) - u(q). Factor p(t).
4*t*(t - 18)*(t + 1)
Suppose 13*s - 7 = 32. Let h be ((-1)/s)/(5/(210/(-7))). Factor 1/6*i + 1/3 - 1/6*i**h.
-(i - 2)*(i + 1)/6
Suppose -3*b**4 - 15*b**3 - 7*b + 3*b**2 + 55*b + 4*b**3 + 36 - b**3 = 0. Calculate b.
-3, -2, -1, 2
Suppose -5*k + k + 6 = 2*d, 5*k + 4*d - 6 = 0. Suppose 682*q - 677*q - 20 = 0. Solve q*h**2 - 2*h**4 - 3*h**5 - 2*h**3 - 9*h**k + 6*h**3 + 7*h**2 - h = 0 for h.
-1, 0, 1/3, 1
Let g(h) = 14*h**2 - 6*h**2 - 16*h**3 - 22*h + 1 + 22*h**2 + 1. Let x(z) = z**3 + z**2 + 1. Let k(m) = -g(m) - 2*x(m). Factor k(j).
2*(j - 1)**2*(7*j - 2)
Let a = 15056/13 - 1158. Suppose -a*g**2 + 0 + 6/13*g = 0. Calculate g.
0, 3
Let t(z) be the first derivative of -5*z**8/672 + z**7/42 + z**6/48 - z**5/12 - 7*z**2/2 + 7. Let p(b) be the second derivative of t(b). Solve p(x) = 0 for x.
-1, 0, 1, 2
Let j(v) = v**3 + 10*v**2 - 25*v + 4. Let d be j(-12). Let y = 2 - 0. Factor b**3 - 11 + b**4 - 5 - 2*b**y + d.
b**2*(b - 1)*(b + 2)
Factor 64 - 2240/9*s**3 + 1280/3*s + 5728/9*s**2 + 196/9*s**4.
4*(s - 6)**2*(7*s + 2)**2/9
Let l(x) = x**2 - 27*x + 56*x - 28*x. Let p be l(0). Let p - 2/5*n**2 + 0*n + 9/5*n**3 = 0. What is n?
0, 2/9
Suppose -9*y + 4 = -8*y. Factor 7*d**5 - 5*d**3 - 5*d**5 + 3*d**5 + d**2 + 10*d**y - 11*d**2.
5*d**2*(d - 1)*(d + 1)*(d + 2)
Let w(q) be the first derivative of q**6/42 + q**5/7 + q**4/4 - q**3/21 - 4*q**2/7 - 4*q/7 + 274. Determine c, given that w(c) = 0.
-2, -1, 1
Let v(q) be the second derivative of q**7/273 + 3*q**6/65 + 7*q**5/65 - q - 52. Factor v(p).
2*p**3*(p + 2)*(p + 7)/13
Let u be (7/20)/1 + 6/(-30). Let o(q) be the first derivative of 0*q - 6 - 1/5*q**3 - u*q**4 + 0*q**2. Let o(z) = 0. What is z?
-1, 0
Suppose -5*f = t - 30, 4*f - f - 3*t = 36. Determine z so that f*z + z - z**2 + 7*z**2 - 2*z**2 = 0.
-2, 0
Let z(c) be the third derivative of 0*c + 21*c**2 - 7/20*c**5 + 0 + 3/8*c**4 + 0*c**3. Find k, given that z(k) = 0.
0, 3/7
Let f be 4/(-6) - 85/(-15). Suppose 3*j - j**2 - 1 - f + 4 = 0. What is j?
1, 2
Let m(v) = -9*v - 14. Let b be m(0). Let u be (b/(-714))/(2/24). Find d such that u - 22/17*d**2 + 18/17*d = 0.
-2/11, 1
Let 15 + 7 + 78 + 10*c**2 + 205*c = 0. Calculate c.
-20, -1/2
Find v such that 6*v**5 - 39 + 126*v**2 - 64*v**4 + 37*v**4 - 3*v**3 - 84*v - 33 = 0.
-2, -1/2, 2, 3
Let v = -480 - -485. Let o = 5/26 - -17/182. Factor 0 + 2/7*d**4 + 0*d - o*d**3 - 2/7*d**2 + 2/7*d**v.
2*d**2*(d - 1)*(d + 1)**2/7
Find q, given that -82/5*q - 32/5*q**2 - 52/5 - 2/5*q**3 = 0.
-13, -2, -1
Factor 2/3*w**2 - 62/3*w + 20.
2*(w - 30)*(w - 1)/3
Factor -2/17*c**5 + 0*c**2 + 0*c + 0 + 0*c**4 + 8/17*c**3.
-2*c**3*(c - 2)*(c + 2)/17
Let s be -5 - -3 - (-2 - 2). Suppose 4 = -s*b + 14. Factor -6*a**4 + 8*a**2 + 3*a**5 + a**b + 14*a**3 + 4 - 6*a**4 - 6*a**3 - 12*a.
4*(a - 1)**4*(a + 1)
Solve -12*s**3 + 50054 - 50054 + s**4 = 0 for s.
0, 12
Let s(l) be the third derivative of -l**6/720 + 11*l**5/120 - 2*l**4 + 64*l**3/9 + 103*l**2. What is q in s(q) = 0?
1, 16
Suppose 3 = -x + 6. Factor -22*a - 2*a**3 - 15*a**2 + 5*a**x + 27 + 31*a.
3*(a - 3)**2*(a + 1)
Let h(m) = 6*m + 58. Let s be h(-9). Suppose s*d - 10 = -0*n - 2*n, -n = 4*d - 9. Solve 0*p**d - 1/4*p**5 + 0*p + 0*p**3 + 0*p**4 + 0 = 0 for p.
0
Let a(h) be the first derivative of -24 + 3/5*h**2 + 9/5*h + 1/15*h**3. Determine f so that a(f) = 0.
-3
Let r = 78 - 9. Let g = r - 69. Factor 0*l + 2/11*l**5 + 2/11*l**4 + g - 2/11*l**2 - 2/11*l**3.
2*l**2*(l - 1)*(l + 1)**2/11
Let d(c) = c**4 - 2*c**3 + c - 1. Let u(k) = 3*k**5 - 6*k**4 + 39*k**3 - 15*k**2 - 21*k + 21. Let t(w) = 21*d(w) + u(w). Factor t(f).
3*f**2*(f - 1)*(f + 1)*(f + 5)
Suppose 0 = -15*y - 14 + 59. Let b(r) be the third derivative of -3/80*r**6 + 0 - 1/40*r**5 + 0*r**y + 0*r**4 + 3*r**2 + 0*r. Factor b(j).
-3*j**2*(3*j + 1)/2
Let v(h) be the third derivative of 2*h**7/105 - h**6/10 - h**5 - 17*h**4/6 - 4*h**3 - 92*h**2. Factor v(g).
4*(g - 6)*(g + 1)**3
Find n such that 1/7*n**3 + 8/7 + 6/7*n**2 + 12/7*n = 0.
-2
Determine a so that -a**4 + 31*a - 63*a**2 - 9*a**2 + 115*a + 15*a**3 - 38*a = 0.
0, 3, 6
Let i = -1113/4 + 14541/52. Factor -24/13*b**2 - 4/13 + 10/13*b**3 + i*b.
2*(b - 1)**2*(5*b - 2)/13
Let c be (-14)/(-77) + (-16)/(-154). Let r be (5*72/(-210))/(-3). Factor r*n**2 + 0*n - c*n**4 + 0 - 2/7*n**3.
-2*n**2*(n - 1)*(n + 2)/7
Let i(n) be the second derivative of n**6/1440 + n**5/96 - n**4/16 - 7*n**3/2 + 11*n. Let h(d) be the second derivative of i(d). Factor h(x).
(x - 1)*(x + 6)/4
Suppose 9 = o + 7. Solve -240*u**2 + 85*u**4 - 299*u**3 - 2560*u + 757*u**o - 5*u**5 + 1243*u**2 - 261*u**3 + 1280 = 0 for u.
1, 4
Let v(r) be the first derivative of r**4/10 - 8*r**3/15 - r**2/5 + 8*r/5 - 77. Factor v(n).
2*(n - 4)*(n - 1)*(n + 1)/5
Let x(y) = y**3 - 5*y**2 - 7*y + 9. Let j be x(6). Determine m, given that 4*m**2 - m**2 + 6*m**j - 456*m**4 + 459*m**4 = 0.
-1, 0
Let b = -223005/4 - -55752. Factor 21/4*w + b*w**2 + 15/2.
3*(w + 2)*(w + 5)/4
Let s(w) be the first derivative of -w**5/90 + w**4/12 - 2*w**3/9 - 8*w**2 - 12. Let f(g) be the second derivative of s(g). Factor f(k).
-2*(k - 2)*