et d(a) be the second derivative of -a**4/24 + 3*a**3/4 - 9*a**2/2 + a + 31. Find o such that d(o) = 0.
3, 6
Let t be -1 + -1 - (4 - (-124)/(-16)). Suppose 14*h - 11*h - 15 = 0. Factor -3/2*w**2 + 3/4*w**h + w**3 + 2*w**4 - 1/2 - t*w.
(w - 1)*(w + 1)**3*(3*w + 2)/4
Suppose 8 = 3*k + k. Suppose -2*f**2 - 6*f**2 - 2*f**3 - f**5 - k + 2*f**4 - 7*f + 2*f**5 = 0. What is f?
-1, 2
Let s(f) be the third derivative of -f**8/1680 - 2*f**7/525 - f**6/600 + f**5/30 + f**4/30 - 4*f**3/15 - 15*f**2. Solve s(h) = 0 for h.
-2, 1
Factor 0 - 5/4*m**2 + 1/4*m**3 + 0*m.
m**2*(m - 5)/4
Let f(b) = -215*b - 212. Let m be f(-1). Suppose 0 - 1/3*l - 1/3*l**m - 2/3*l**2 = 0. Calculate l.
-1, 0
Let y be (9/((-1215)/(-6)))/((-3)/(-18)). Let t be (-11)/30 + (-4 + 0)/(-8). Suppose -y + 4/15*l**2 + t*l - 2/15*l**3 = 0. What is l?
-1, 1, 2
Let g(x) be the second derivative of x**5/5 + 5*x**4/3 - 25*x + 3. Factor g(m).
4*m**2*(m + 5)
Let o(w) be the first derivative of -1/120*w**5 + 7 + 7/2*w**2 + 0*w**3 + 0*w + 1/16*w**4. Let t(j) be the second derivative of o(j). Factor t(k).
-k*(k - 3)/2
Let q(k) be the second derivative of -3*k**5/160 + 23*k**4/32 + k**3/16 - 69*k**2/16 + 4*k - 25. Suppose q(g) = 0. Calculate g.
-1, 1, 23
Let t be -4 + 2 - (-5 - 0). Suppose t*y - 40 = y. Factor 15*u + 145 + y*u**2 + 5*u**3 - 145.
5*u*(u + 1)*(u + 3)
Let a(k) be the second derivative of k**7/105 - 7*k**5/50 + k**4/5 + 2*k. Find f such that a(f) = 0.
-3, 0, 1, 2
Factor -2*r - 2/9*r**2 + 44/9.
-2*(r - 2)*(r + 11)/9
Suppose -3*x - 50 = -8*x. Let q be (x/40)/((-1)/(-4)). Solve 5 - 20*c**4 - q - 4 - 8*c**5 - 16*c**3 - 4*c**2 = 0 for c.
-1, -1/2, 0
Let x(n) be the second derivative of -n**5/15 + n**4/12 + n**3/18 + 4*n + 7. Determine v, given that x(v) = 0.
-1/4, 0, 1
Suppose 0*x + 60 = x - 4*h, 3*x - h - 180 = 0. Let g be (-530)/x + 9 + (-2)/12. Factor g + 3*r**4 - 2/3*r**3 + 2/3*r - 3*r**2.
r*(r - 1)*(r + 1)*(9*r - 2)/3
Let a(f) be the second derivative of -f**4/42 - 2*f**3/21 + 8*f**2/7 - 2*f + 35. Factor a(p).
-2*(p - 2)*(p + 4)/7
Let m = 13348/11997 + -2/1333. Let a(c) be the first derivative of 2/3*c**2 + 2/15*c**5 + m*c**3 + 0*c + 2 + 2/3*c**4. Factor a(i).
2*i*(i + 1)**2*(i + 2)/3
Let w = -17 + 21. Factor -w*n + 16*n**2 - n**3 + n**3 - 2*n**3 - 10*n.
-2*n*(n - 7)*(n - 1)
Solve -20 + 793*u**2 - 788*u**2 + 26*u - 11*u = 0.
-4, 1
Let o = -61084 - -61087. Factor -1/2*n**2 + 0*n + 2/3 - 1/6*n**o.
-(n - 1)*(n + 2)**2/6
Let m(b) = 12*b**3 + 9*b**2 - 21*b + 45. Let p(f) = f**3 + f**2 - f + 5. Let v(k) = m(k) - 9*p(k). What is l in v(l) = 0?
-2, 0, 2
Let r(o) = -7*o**2 + 18*o - 50. Let m(h) = 4*h**2 - 9*h + 26. Let b(v) = -5*m(v) - 3*r(v). Suppose b(l) = 0. Calculate l.
4, 5
Let p(w) = 9*w**4 - 12*w**3 + 45*w**2 - 42*w + 18. Let v(a) = -10*a**4 + 11*a**3 - 46*a**2 + 43*a - 19. Let f(i) = 7*p(i) + 6*v(i). Factor f(n).
3*(n - 2)**2*(n - 1)**2
Let m be ((-322)/(-35))/((-4)/(-10)). Let l = m + -20. Find g such that -12*g**2 - g**3 - l - g**3 - g**4 + 8*g**3 + 10*g = 0.
1, 3
Let h(t) = -15*t**4 - 496*t**3 - 4748*t**2 - 6240*t + 11520. Let k(i) = -5*i**4 - 166*i**3 - 1583*i**2 - 2080*i + 3840. Let q(v) = 2*h(v) - 7*k(v). Factor q(x).
5*(x - 1)*(x + 3)*(x + 16)**2
Factor 37 + g**4 - 2*g**4 + 13 - 13*g**2 + 24*g + 21*g - 9*g**3.
-(g - 2)*(g + 1)*(g + 5)**2
Let f = -2/1697 + 6794/5091. Factor -2/3*x + 4/3*x**3 + 2/3 - 2/3*x**5 - f*x**2 + 2/3*x**4.
-2*(x - 1)**3*(x + 1)**2/3
Let o(t) be the first derivative of -5/12*t**4 + 11 + 2/3*t**2 + 1/18*t**6 - 4/3*t + 5/9*t**3 - 1/15*t**5. What is v in o(v) = 0?
-2, -1, 1, 2
Suppose 23*w - 48 = 21*w. Suppose 2*v - 4*k - 24 = 0, -5*k - w = -2*v + 4. Let -1/6*z**v + 1/6*z**2 - 1/6*z**3 + 1/6*z + 0 = 0. Calculate z.
-1, 0, 1
Let p be (-1472)/(-768) + (-2)/(-24). Let 6/5 - 3*m - 3/5*m**3 + 12/5*m**p = 0. Calculate m.
1, 2
Let g be -2*(12/(-16))/((-9)/(-30)). Suppose -20*t - g + 16*t + t**2 + 0 = 0. Calculate t.
-1, 5
Let l be (2 - 2) + -4 + 16. Suppose l = -3*t, -2*t + 1 + 7 = 2*g. Find j such that -8*j**4 - 12*j + 5*j + 4*j**3 + 3*j + g*j**2 = 0.
-1, 0, 1/2, 1
Let c be ((-9)/(-6))/(1/2). Solve -7*t**2 - 4*t**c + 8*t**2 - 4*t + 7*t**2 = 0.
0, 1
Solve -24 - 2*j**4 - 24*j**3 - 28*j**5 + 23*j**2 - 102*j**4 + 57*j - 5*j + 105*j**2 = 0 for j.
-3, -1, 2/7, 1
Let q(h) = 3*h**2 - h - 2*h**2 - h**3 + 2*h**3 - 71 + 72. Let s(k) = 9*k**3 - 36*k**2 - 99*k - 46. Let g(m) = -4*q(m) + s(m). Factor g(c).
5*(c - 10)*(c + 1)**2
Let f be -1*25*(-20)/55. Let o = f + -389/44. Factor -9/4*z**2 + 7/4*z - 1/2 - o*z**4 + 5/4*z**3.
-(z - 2)*(z - 1)**3/4
Let g(k) be the first derivative of 5*k**5 - 15*k**4/4 - 35*k**3/3 + 15*k**2/2 + 10*k - 124. Let g(v) = 0. What is v?
-1, -2/5, 1
Let g(y) be the third derivative of y**6/30 - 14*y**5/5 + 98*y**4 - 5488*y**3/3 + 4*y**2 - 5. Factor g(w).
4*(w - 14)**3
Determine w, given that 32*w**2 - 11*w**2 + 28*w**2 - 4*w**3 + 96*w + 43*w**2 = 0.
-1, 0, 24
What is a in -302/5*a**3 + 306/5*a + 152/5*a**2 - 4/5*a**5 - 81/5 - 71/5*a**4 = 0?
-9, -1, 1/4, 1
Let f(h) be the second derivative of -h**7/84 - h**6/12 + 3*h**5/20 - 105*h. Factor f(u).
-u**3*(u - 1)*(u + 6)/2
Let m(q) = -3*q - 3. Let a be m(-1). Let n = a + 2. What is w in 2*w + 6*w + 5*w**2 - 6*w**n + 3*w**2 + 6 = 0?
-3, -1
Solve 10/3*r**2 + 2/3*r**3 + 14/3*r + 2 = 0.
-3, -1
Let n be 2*4/(-5)*25/(-10). Let r(c) be the first derivative of 0*c**3 + 2/3*c**6 + 0*c + 2*c**4 - 12/5*c**5 + 0*c**2 - n. Find o such that r(o) = 0.
0, 1, 2
Let g be (3 - 0)/(27/360). Let t = g - 79/2. Find b, given that 1/4*b - t + 1/4*b**2 = 0.
-2, 1
Let a be (-136)/(-105) - 882/735. Factor -2/21*l**2 + 2/21 - 2/21*l + a*l**3.
2*(l - 1)**2*(l + 1)/21
Let n(k) be the third derivative of 0*k**5 + 1/105*k**7 + 1/3*k**4 + 0*k - 1/20*k**6 - 11*k**2 + 0 + 0*k**3. Suppose n(d) = 0. What is d?
-1, 0, 2
Let u(h) be the first derivative of 2*h**5/65 + h**4/26 - 16*h**3/39 - 12*h**2/13 + 46. Factor u(b).
2*b*(b - 3)*(b + 2)**2/13
Let t(c) be the second derivative of -1/21*c**4 + 13*c + 4/21*c**3 + 0 + 6/7*c**2. Factor t(b).
-4*(b - 3)*(b + 1)/7
Suppose 0 = -3*g + r, r - 3 + 5 = 4*g. Let p be 4/(-6) + 4/6. Solve 0*y + p - 1/2*y**g = 0.
0
Let n be (6/(-8))/(5 - 305/60). Let d be (-3 + 9)/(n/6). Determine v, given that 0 - 7/4*v**5 + 0*v - v**3 - 4*v**d + 0*v**2 = 0.
-2, -2/7, 0
Let w(r) = -14*r**3 - 68*r**2 + 118*r - 78. Let u(x) = -2*x**3 - x**2 - 2*x - 2. Let i(m) = -6*u(m) + w(m). Factor i(d).
-2*(d - 1)**2*(d + 33)
Factor 15*g**3 + g**4 + 21*g**3 - 40*g + 104*g + 3*g**4 + 96*g**2.
4*g*(g + 1)*(g + 4)**2
Let a(o) be the second derivative of o**4/12 + 5*o**3/2 - 5*o - 17. Factor a(t).
t*(t + 15)
Suppose -2*h**4 - 2/9*h**2 - 10/3*h**3 + 14/9*h + 4/9 = 0. What is h?
-1, -1/3, 2/3
Let q(m) = -m**2 + m + 3. Let a(j) = -13*j**2 - 33*j - 209. Let g(c) = -2*a(c) + 22*q(c). Factor g(w).
4*(w + 11)**2
Let 3/2 - 7/2*l**5 + 25/4*l**3 - 11/4*l - 45/4*l**2 + 39/4*l**4 = 0. What is l?
-1, -1/2, 2/7, 1, 3
Suppose 23/5*q**2 - 136/5*q - 67/5*q**4 + q**5 + 131/5*q**3 + 44/5 = 0. What is q?
-1, 2/5, 1, 2, 11
Suppose 15/2*s**2 - 6*s**3 + 0 + 3/2*s**4 - 3*s = 0. Calculate s.
0, 1, 2
Let r(b) be the first derivative of 4*b**3/3 + 5*b**2/2 + b + 7. Let l(a) = 2*a**2 + 2*a. Let w(f) = -5*l(f) + 2*r(f). Suppose w(i) = 0. What is i?
-1, 1
Let o = 403 - 400. Let m(q) be the first derivative of 0*q - 40/27*q**o - 25/18*q**4 - 4 - 4/9*q**2. Factor m(x).
-2*x*(5*x + 2)**2/9
Let s(o) = o**2 - 16*o - 5. Let k(n) = 3*n**2 - 2*n**2 - 79 + 0*n**2 + 78. Let f(d) = 5*k(d) - s(d). Factor f(b).
4*b*(b + 4)
Let x(l) be the second derivative of 13*l**7/21 + 23*l**6/3 + 177*l**5/10 - 355*l**4/6 + 50*l**3/3 - 329*l. Find r such that x(r) = 0.
-5, 0, 2/13, 1
Let i(d) be the third derivative of d**8/1344 - d**6/40 - d**5/120 + 9*d**4/32 + 3*d**3/4 + 594*d**2 + d. Determine v, given that i(v) = 0.
-3, -1, 2, 3
Let d(z) be the second derivative of -49*z**4/15 + 94*z**3/15 + 4*z**2/5 - 102*z. Suppose d(f) = 0. Calculate f.
-2/49, 1
Let d = -975 - -980. Let t(q) be the first derivative of -d - 4*q - 4/3*q**3 - 4*q**2. Suppose t(v) = 0. What is v?
-1
Let s(y) be the third derivative of y**5/480 + 7*y**4/96 - 130*y**2. Factor s(p).
p*(p + 14)/8
Let i(x) be the third derivative of -x**6/720 + x**5/120 - 8*x**3/3 + 24*x**2. Let d(c) be the first derivative of i(c). Factor d(v).
-v*(v - 2)