56*x + 84. Let s = 34 + -66. Let t(b) = 37*b**2 - 24*b - 13. Let o(z) = s*t(z) - 5*u(z). What is i in o(i) = 0?
-1/4, 1
Let f(p) be the second derivative of p**6/135 + p**5/18 + 25*p - 1. Factor f(w).
2*w**3*(w + 5)/9
Find s such that -59*s**2 - 41 - 99*s - 20 + s**3 - 82*s + 60*s = 0.
-1, 61
Let r(d) = -2*d**3 + 14*d**2 - 22*d + 62. Let c be r(6). Factor -2 + 1/2*b**c - 3/2*b.
(b - 4)*(b + 1)/2
Let y(d) = 2*d - 8. Let i be y(6). Let c = -75 + 77. Solve 6/7*m**c - 9/7*m**5 + 0 + 9/7*m**3 + 0*m - 6/7*m**i = 0.
-1, -2/3, 0, 1
Let k = 5441 - 5437. Suppose 9/7 + 3/7*b**k + 18/7*b**3 + 36/7*b**2 + 30/7*b = 0. What is b?
-3, -1
Let s(l) be the third derivative of -4/51*l**3 + 0*l + 0 + 1/1020*l**6 + 2/255*l**5 + 24*l**2 - 1/204*l**4. Find k such that s(k) = 0.
-4, -1, 1
Let b(n) be the first derivative of -2*n**3/15 + n**2 - 8*n/5 + 84. Solve b(c) = 0 for c.
1, 4
Let k(p) be the third derivative of 1/420*p**6 - 1/210*p**5 + 0*p**3 - 1/84*p**4 + 2*p**2 + 1/735*p**7 + 0 - 4*p. Factor k(i).
2*i*(i - 1)*(i + 1)**2/7
Let r = 131013 - 919630/7. Let f = 365 + r. Factor f*g**3 + 0*g + 2/7*g**2 + 32/7*g**4 + 0.
2*g**2*(4*g + 1)**2/7
What is r in 12*r - 2*r**2 - 290 + 8*r + 0*r + 242 = 0?
4, 6
Factor 44/7 - 87/7*q + 6*q**2 + 1/7*q**3.
(q - 1)**2*(q + 44)/7
Suppose -3*b = -8*b + 15. Determine i so that 4*i**2 + 3 - 8*i**2 - b + 8*i**3 = 0.
0, 1/2
Let z(i) be the second derivative of -15*i**7/28 - 16*i**6/5 + 51*i**5/10 + 27*i**4/4 - 53*i**3/4 + 15*i**2/2 - 182*i. Determine w so that z(w) = 0.
-5, -1, 1/3, 2/5, 1
Find r such that -9*r + 4*r**4 - 7*r + 4*r**3 + 18 + 14 - 24*r**2 = 0.
-2, 1, 2
Let d(r) be the first derivative of -35/3*r**3 - 5/4*r**4 - 75/2*r**2 + 40 - 45*r. Determine f, given that d(f) = 0.
-3, -1
Let n(v) be the first derivative of 2*v**3/3 - 25*v**2 + 132*v + 100. Factor n(r).
2*(r - 22)*(r - 3)
Let c(y) = -y + 3. Let n be c(0). Solve 8*i**2 - 10*i**2 + 4*i - i + 2*i + n = 0 for i.
-1/2, 3
Let n(x) = -x**2 + 71*x + 5. Let j(k) = 36*k + 2. Let m(y) = -5*j(y) + 2*n(y). Find g such that m(g) = 0.
-19, 0
Let f be 121/55 + -11 - -11. Factor -f*i + 1 + 2/5*i**2.
(i - 5)*(2*i - 1)/5
Let c = 2156 - 90551/42. Let q(v) be the second derivative of -16/7*v**2 + 9*v - 8/21*v**3 + 0 - c*v**4. Factor q(x).
-2*(x + 4)**2/7
Suppose -l - 2*d = -5, -3*l + 3*d = 3 - 9. Factor 15*b**2 + 9 - 11*b - l*b**3 - 5*b - 5*b.
-3*(b - 3)*(b - 1)**2
Let j(p) = 4*p + 1. Let n be j(1). Suppose 0*q - n*z - 13 = -4*q, -4 = -4*q - 4*z. Factor 14*d**3 - 4*d**q - 5*d**3 - 5*d**2 + 3*d + 2*d**4 - 5*d**4.
-3*d*(d - 1)**3
Let v(r) be the third derivative of r**7/630 + r**6/72 - r**5/180 - 5*r**4/72 + 685*r**2. Factor v(x).
x*(x - 1)*(x + 1)*(x + 5)/3
Determine n so that 26 + 3*n**3 + 35*n**2 + 129*n + 20 + 14*n**2 + 20*n**2 + 17 = 0.
-21, -1
Let g = -58 + 61. Let l be (g + (-21)/(-2))/6 - -1. Factor 1/2*o**2 + l*o**3 + 0*o + 5*o**4 + 0 + 9/4*o**5.
o**2*(o + 1)**2*(9*o + 2)/4
Let h(x) = -x**3 - 7*x**2 - 8*x + 9. Let a be h(-5). Let z be a + (22/9 - 1). Determine l so that -z*l + 2/9*l**2 + 2/9 = 0.
1
Let m be -5 + 5/(-3)*(-14)/(-210)*-57. Factor -8*t + m*t**2 + 20/3.
4*(t - 5)*(t - 1)/3
Find s, given that -1001*s**3 - 8*s + 1003*s**3 + 26*s**2 + 32*s = 0.
-12, -1, 0
Suppose 4*v + 10*h = 7*h + 32, 2*v - 4*h + 6 = 0. Let n(t) be the third derivative of 2/3*t**3 - 1/12*t**4 - 1/30*t**v - 2*t**2 + 0 + 0*t. Factor n(i).
-2*(i - 1)*(i + 2)
Let u(z) be the second derivative of -z**5/5 - z**4 + 44*z**3/3 + 48*z**2 + 148*z + 3. Suppose u(k) = 0. What is k?
-6, -1, 4
Let v(i) = -i**2 + 13*i - 36. Let z be v(8). Factor 16*t**2 - 2*t**5 + 357*t**3 - 349*t**3 - 7*t**z + 3*t**5.
t**2*(t - 4)**2*(t + 1)
Factor -22202 - 4*h**2 - 996*h + 94*h - 562*h - 111754.
-4*(h + 183)**2
Let r(q) be the third derivative of 0 + 5/7*q**3 + 0*q - 19*q**2 + 1/420*q**6 - 29/84*q**4 + 13/210*q**5. Determine o so that r(o) = 0.
-15, 1
Suppose 3*v - 8*a + 3*a = 20, v - 16 = 4*a. Suppose 2/3*z**2 + 8/3*z - 2/3*z**4 + v - 8/3*z**3 = 0. What is z?
-4, -1, 0, 1
Let u be -3 - (-1 + -9 + 5). Suppose -2*s + 14 = 5*n, u*n + 9*s - 5*s - 12 = 0. Factor 2/5*m + 1/5*m**n - 1/5*m**3 + 0.
-m*(m - 2)*(m + 1)/5
Let f(u) be the first derivative of u**6/30 - 3*u**5/25 + u**4/10 + 571. Solve f(k) = 0.
0, 1, 2
Let r(o) be the first derivative of -o**3 + 33*o**2/2 + 78*o + 9. Factor r(l).
-3*(l - 13)*(l + 2)
Let w = -122 + 122. Let j(o) be the third derivative of 0 + 1/30*o**5 - 5*o**2 + w*o - 1/60*o**6 + 0*o**4 + 0*o**3. Let j(a) = 0. Calculate a.
0, 1
Suppose -4*x - 2*k - 2*k - 4 = 0, -7 = -2*x + k. Let l(r) be the first derivative of 1/16*r**4 + 0*r**3 - 3/8*r**2 - 1/2*r + x. Factor l(s).
(s - 2)*(s + 1)**2/4
Let i(h) be the first derivative of h**6/24 + h**5/2 + 9*h**4/16 + 113. Factor i(u).
u**3*(u + 1)*(u + 9)/4
Let y = -5 - 5. Let k be (-15)/(-2) - (-5)/y. Factor 9*s - 3*s**5 - s**2 - k*s**3 + 4*s**4 + s**3 - 5*s**2 + 5*s**4 - 3.
-3*(s - 1)**4*(s + 1)
Suppose 3*w - 5*c = -13 + 139, -3*c = -5*w + 210. Let m be 3*((-64)/w)/(-4). Factor -1/7*s**5 + 4/7*s**4 - 1/7*s**3 + m + 4/7*s - 10/7*s**2.
-(s - 2)**3*(s + 1)**2/7
Let k(r) be the second derivative of -r**6/8 + 7*r**5/12 - 5*r**4/12 - 17*r**2 + 3*r. Let z(p) be the first derivative of k(p). Suppose z(c) = 0. Calculate c.
0, 1/3, 2
Let r = -17 - -19. Factor -5*x**r + 3*x**2 - 4*x**4 + 6*x**2.
-4*x**2*(x - 1)*(x + 1)
Let b(j) be the first derivative of j**3/8 - 21*j**2/16 + 9*j/2 - 519. Factor b(l).
3*(l - 4)*(l - 3)/8
Let x(m) = 3*m + 17. Let d be x(-6). Let y be d + (-13 - -4)*8/(-42). Factor w**3 - 2/7*w + 0 - y*w**2.
w*(w - 1)*(7*w + 2)/7
Let u = 219 + -217. Let f(p) be the first derivative of -3/10*p**5 - 3/2*p + 0*p**4 + 3 + p**3 + 0*p**u. What is z in f(z) = 0?
-1, 1
Suppose -y - 2*d + 8 = 0, 5*y + 4*d = 7*y. Suppose 2*f + 9 = 3*q, 4*q + 4*f - 5*f = 12. What is i in 4/3*i**q + 8/3 + 4/3*i**y - 4*i**2 - 4/3*i = 0?
-2, -1, 1
Let s be (-72)/(-45) - (-114)/(-90). Let q(u) be the first derivative of 10 - s*u**2 - 2/15*u**5 + 1/6*u**4 + 2/9*u**3 + 0*u. Factor q(v).
-2*v*(v - 1)**2*(v + 1)/3
Let r(c) be the third derivative of -c**7/168 - c**6/96 + c**5/48 + 5*c**4/96 - 41*c**2. Factor r(f).
-5*f*(f - 1)*(f + 1)**2/4
Let d = 21 - 17. What is b in 7*b + 12 - 15*b**3 - 15*b**5 + 17*b + 3*b**2 - 11*b**5 - 3*b**d + 29*b**5 = 0?
-1, 2
Let g(x) be the first derivative of 5*x**4/3 + 26*x**3/3 - 12*x**2 + 3*x + 10. Let y(t) be the first derivative of g(t). Factor y(q).
4*(q + 3)*(5*q - 2)
Let g(p) be the first derivative of 0*p - 3 - 4*p**3 + 3/2*p**2. Let g(q) = 0. Calculate q.
0, 1/4
Let b(y) = -y**2 - 7*y - 6. Let m(v) = -91*v + v**2 + 0*v**2 + 92*v. Let s(i) = -b(i) - 4*m(i). Determine j, given that s(j) = 0.
-1, 2
Suppose w = -5*t - 1, -23*w + 19*w = 4*t - 12. Factor 1/4*f**3 + 0*f**2 - 1/4*f**w + 0*f + 0.
-f**3*(f - 1)/4
Let t = -47/366 - -18/61. Let o(b) be the third derivative of 4*b**2 + t*b**4 + 0*b - 1/30*b**6 - 4/3*b**3 - 2/105*b**7 + 0 + 1/5*b**5. Solve o(d) = 0.
-2, -1, 1
Let p = 786/23 - 24071/736. Let a = 1/32 + p. Determine u, given that -3/2*u + 3 - a*u**2 = 0.
-2, 1
Let k(i) = 2*i - 8. Let l be k(11). Find g, given that -l*g - 14*g + 3*g**2 + 30*g - 2*g**2 = 0.
-2, 0
Let h(a) = -a**3 - 9*a**2 - 8*a + 18. Let i be h(-8). Let w be 5/3 + -2 - (-33)/i. Factor -w*o**4 - 3/4*o + 0 + 3/2*o**2 + 0*o**3 + 3/4*o**5.
3*o*(o - 1)**3*(o + 1)/4
Let q(h) be the first derivative of -h**3 + 12*h - 250. Suppose q(y) = 0. What is y?
-2, 2
Let a(j) be the first derivative of -j**4/3 - 32*j**3/3 - 128*j**2 - 2048*j/3 + 147. Factor a(y).
-4*(y + 8)**3/3
Suppose -2*y - 4*w - 4 = 0, -6*y + 3*y + 2*w + 18 = 0. Suppose 7*a - 17 = y. Factor 218/7*x**2 - 72/7*x - 36*x**a + 14*x**4 + 8/7.
2*(x - 1)**2*(7*x - 2)**2/7
Let c(g) = 4*g**3 - g + 1. Let p(y) = 7*y**3 + 3*y**2 - 5*y + 3. Let a(n) = -2*c(n) + p(n). Determine v so that a(v) = 0.
1
Suppose 5*m + i - 24 = 0, 4*m = -3*i - 6 + 34. Let f(u) be the third derivative of -1/28*u**m - 2/21*u**3 + 0 - 1/210*u**5 - u**2 + 0*u. Factor f(q).
-2*(q + 1)*(q + 2)/7
Let l(d) be the first derivative of 169*d**4/24 + 13*d**3/9 + d**2/12 - 32. Factor l(t).
t*(13*t + 1)**2/6
Let k(d) be the first derivative of 2*d**3/9 - 13*d**2/3 + 8*d - 65. Determine h, given that k(h) = 0.
1, 12
Let m be (-63)/(-6) + (32 - 38). Factor -m*x**2 + 15/2*x**3 + 0 - 3*x.
3*x*(x - 1)*(5