Let z(c) be the first derivative of 29*c**2 - 62*c**2 - 12 + 6*c**3 + 26*c**2 - 4*c. Suppose z(i) = 0. What is i?
-2/9, 1
Solve 20/7 - 2/7*k**2 - 18/7*k = 0.
-10, 1
Let l(m) = 11*m**3 - 111*m**2 + 594*m + 721. Let u(f) = -16*f**3 + 168*f**2 - 891*f - 1082. Let j(o) = -7*l(o) - 5*u(o). Determine k, given that j(k) = 0.
-1, 11
Let p be (8 - 1)*4/(112/20). Let i(x) be the first derivative of 0*x + 10/13*x**4 + 4 + 8/39*x**3 + 10/13*x**p + 0*x**2. Solve i(s) = 0 for s.
-2/5, 0
Let h(r) be the second derivative of 49*r**4/22 - 140*r**3/11 + 300*r**2/11 - 13*r - 1. Suppose h(n) = 0. Calculate n.
10/7
Let q be (2/(-5))/(1/(-5)). Suppose 27 - 3 = 12*n. Find x, given that 2*x**3 + q*x**5 - 5*x**2 + 6*x**4 + 0*x**3 - x**n - 4*x = 0.
-2, -1, 0, 1
Factor -192*b**3 + 42*b**2 + 147*b + 102*b**3 + 93*b**3.
3*b*(b + 7)**2
Let v(u) = -74*u**2 - 93*u + 163. Let m(i) = -27*i**2 - 31*i + 54. Let j(y) = 11*m(y) - 4*v(y). Let j(c) = 0. What is c?
2, 29
Let o(q) be the second derivative of 0 + 0*q**2 - 2/9*q**3 - 1/36*q**4 - 5*q. What is d in o(d) = 0?
-4, 0
Let r(n) be the third derivative of 0 - 72/5*n**7 + 31*n**2 + 361/15*n**5 + 8/3*n**3 + 0*n + 34/3*n**4 + 15*n**6 + 18/7*n**8. What is d in r(d) = 0?
-1/6, 2
Let 88*q**2 - 53*q - 72*q**3 + 28*q + 82 - 70 - 4*q**5 - 27*q + 28*q**4 = 0. What is q?
1, 3
Determine k, given that 56/9*k - 4/9*k**2 + 0 = 0.
0, 14
Let l(k) be the third derivative of 0*k**4 - 1/30*k**5 - 18*k**2 - 1/105*k**7 - 1/30*k**6 + 0*k + 0 + 0*k**3. Determine r, given that l(r) = 0.
-1, 0
Let o(w) be the first derivative of -w**5/30 + w**4/3 - 11*w**3/9 + 2*w**2 - 8*w + 12. Let k(t) be the first derivative of o(t). Suppose k(c) = 0. Calculate c.
1, 2, 3
Factor 6*b + 41*b**2 + b - 2*b + 4*b**2.
5*b*(9*b + 1)
Suppose -5*t - 1 = -4*l, -4*t = -4*l - 92 + 96. Factor -1/4*r + 1/4*r**2 + 0 + 3/2*r**t.
r*(2*r + 1)*(3*r - 1)/4
Let t(b) = 7*b + 3. Let s be t(11). Let r = s - 77. Suppose 0*l**r + 0 + 1/2*l - 1/2*l**5 - l**2 + l**4 = 0. What is l?
-1, 0, 1
Solve -2*u**5 + 512400*u + 5305*u**3 + 40697*u**2 + 5*u**5 - 1176000 - 222*u**4 + 962*u**3 - 123917*u**2 = 0.
7, 20
Let v be 690/(-75) - -10 - (-16)/5. Factor -4/7*k - 6/7*k**3 + 0 - 10/7*k**2 + 2/7*k**v + 2/7*k**5.
2*k*(k - 2)*(k + 1)**3/7
Let m be 1/2 + (-10)/(-4). Let f be -2 + (2 + 25)/3. Factor -11*b**4 + 2*b**m - b**3 + f*b**3 - b**4.
-4*b**3*(3*b - 2)
Let a(q) be the third derivative of -q**5/100 + 41*q**4/120 + 7*q**3/15 + 70*q**2. Factor a(w).
-(w - 14)*(3*w + 1)/5
Let n = -59818 + 59820. Factor 0 + 0*y - 1/4*y**n + 1/12*y**3.
y**2*(y - 3)/12
Let q(w) be the third derivative of -w**5/2 - 55*w**4/24 - 25*w**3/6 - 219*w**2. Solve q(h) = 0 for h.
-1, -5/6
Let g = 4/37 - -54/185. Suppose 143*c + 50 = 50. Let 2/5 + 0*h + g*h**4 + c*h**3 - 4/5*h**2 = 0. What is h?
-1, 1
Let y(z) be the first derivative of z**4/20 - 4*z**3/5 + 24*z**2/5 + 11*z + 15. Let q(v) be the first derivative of y(v). Factor q(b).
3*(b - 4)**2/5
Factor 36*d**4 + 37*d**4 - 33*d**3 - 75*d - 103*d**4 + 33*d**4 + 105*d**2.
3*d*(d - 5)**2*(d - 1)
Let j(r) = r**2 - 3*r - 14. Let o be j(-3). Find i, given that 0*i + 1/6*i**5 - 1/6*i**3 - 1/6*i**2 + 0 + 1/6*i**o = 0.
-1, 0, 1
Let s(y) = -17*y**2 + 24*y - 36. Let x(g) = -56 - 12*g - 57 + 8*g**2 + 131. Let t = 7 + -13. Let r(d) = t*s(d) - 13*x(d). Determine a, given that r(a) = 0.
3
Let s(h) = 4*h - 16. Let k be s(5). Factor 9*f**3 + 4*f + 2*f - 15*f**3 + 3*f**2 - 3*f**k.
-3*f*(f - 1)*(f + 1)*(f + 2)
Let f(p) be the first derivative of -p**6/45 - p**5/30 + 7*p**3/3 - 19. Let n(b) be the third derivative of f(b). Let n(x) = 0. Calculate x.
-1/2, 0
Suppose -3*q = -14*q + 22. Let c(h) be the third derivative of -1/75*h**5 + 1/15*h**3 + 0*h**4 + 0*h + 3*h**q + 0 + 1/525*h**7 + 0*h**6. Factor c(a).
2*(a - 1)**2*(a + 1)**2/5
Let j(s) be the second derivative of -2*s**7/63 + 74*s**6/45 - 322*s**5/15 - 398*s**4/9 + 646*s**3/9 + 722*s**2/3 + 56*s. Determine h so that j(h) = 0.
-1, 1, 19
Let i(p) = p**5 + p**4 + p**3 + p**2 + 2*p - 1. Let x(c) = -c**5 + 79*c**4 - 1071*c**3 + 5761*c**2 - 6910*c - 13825. Let z(m) = i(m) - x(m). Factor z(w).
2*(w - 12)**3*(w - 4)*(w + 1)
Factor -21*v + 90 - 12*v**2 + 19*v - 49*v - 12*v**2 - 18*v**2 + 3*v**3.
3*(v - 15)*(v - 1)*(v + 2)
Let b(a) be the second derivative of a**4/132 + a**3/11 - 7*a**2/22 + 12*a. Factor b(j).
(j - 1)*(j + 7)/11
Let c(f) be the second derivative of -3*f + 1/3*f**3 + 1/30*f**5 - 1/6*f**4 - 1/3*f**2 + 0. Let c(q) = 0. Calculate q.
1
Let f be (8/(-18))/2 - (-87)/27. Let i be f/(-18)*-3 + (-12)/(-8). Factor 7*n**i + 2/3 + 5/3*n**4 + 17/3*n**3 + 11/3*n.
(n + 1)**3*(5*n + 2)/3
Suppose -2*r = 2*o + 4, 3*o + 16 = -4*r + 7*o. Let p be (63/(-24))/(r/2). Factor 0 - 15/4*m**3 + p*m**2 + 9/4*m**4 - 1/4*m.
m*(m - 1)*(3*m - 1)**2/4
Let o(m) be the first derivative of 3*m**4/5 + 8*m**3/15 - 24*m**2/5 - 32*m/5 - 380. What is p in o(p) = 0?
-2, -2/3, 2
Suppose -l + 1 + 6 = 0. Let z = l + -4. What is b in -5*b**2 + b + 2 - b + z*b**2 = 0?
-1, 1
Let l(x) = -x. Let r(d) = -4*d + 8. Let s(p) = -3*l(p) + r(p). Let j be s(6). Factor 0*z + 3/2*z**3 + 9/2*z**4 - 3*z**j + 0.
3*z**2*(z + 1)*(3*z - 2)/2
Let z(k) be the first derivative of 6*k**3 + 15*k**2/2 - 3*k - 310. Find s, given that z(s) = 0.
-1, 1/6
Let j(g) be the second derivative of g**5 + g**4 - g - 135. Factor j(w).
4*w**2*(5*w + 3)
Let s(b) be the third derivative of b**5/510 - 33*b**4/68 + 98*b**3/51 + 2*b**2 + 19. Factor s(i).
2*(i - 98)*(i - 1)/17
Suppose 0 = -3*m - 185 + 209. Suppose 0 = -6*d - m*d. Suppose -1/4*i**3 + d + 0*i + 0*i**2 = 0. What is i?
0
Let m(s) be the third derivative of -s**6/480 + 7*s**5/240 + 5*s**4/16 - 198*s**2. Suppose m(i) = 0. What is i?
-3, 0, 10
Let z = 5/759 + 6/253. Let u(i) be the second derivative of i + 0*i**2 + z*i**3 - 1/66*i**4 + 0. Factor u(j).
-2*j*(j - 1)/11
Let n(v) be the first derivative of -2/3*v**3 + 12*v - 5*v**2 - 31. Factor n(q).
-2*(q - 1)*(q + 6)
Let w(o) be the second derivative of 8*o + 9/4*o**2 + 2/3*o**4 + 0 - 2*o**3. Solve w(m) = 0 for m.
3/4
Let d be 1 - (-8 + (-205)/(-20) + -2). What is y in -9/2*y - d*y**2 - 27/4 = 0?
-3
Factor 459*f**2 - 476*f**2 + 47*f - 31*f + f**3.
f*(f - 16)*(f - 1)
Let w(d) = -d**2 - 2*d - 4. Let z be w(-2). Let y(t) = -t**2 - 3*t + 6. Let f be y(z). Factor 6/11*v**f + 2/11*v + 0.
2*v*(3*v + 1)/11
Let i be (-2 - -1)/(3 - (-560)/(-185)). Let v = 41 - i. Suppose -36/7*o**2 - 16/7 - 2/7*o**v + 40/7*o + 2*o**3 = 0. Calculate o.
1, 2
Let x(m) be the third derivative of 9*m**8/40 - 166*m**7/175 + 59*m**6/100 + 4*m**5/5 + m**4/5 + 129*m**2. Suppose x(f) = 0. Calculate f.
-2/9, -1/7, 0, 1, 2
Let j be (-52)/(-48)*(-16)/6 + 3. Let u(m) be the first derivative of 1/6*m**4 + 2 - 1/15*m**5 - j*m**3 + 0*m + 0*m**2. Factor u(h).
-h**2*(h - 1)**2/3
Suppose 4*p + 5*v + 5 = 0, 21*v + 4 = p + 17*v. Let s(o) be the first derivative of 1/3*o**6 + 0*o - 9 + 0*o**4 + 0*o**3 + 2/5*o**5 + p*o**2. Factor s(n).
2*n**4*(n + 1)
Let x(l) be the third derivative of l**6/12 + 11*l**5/10 + 4*l**4/3 - 4*l**3 - 211*l**2. Factor x(v).
2*(v + 1)*(v + 6)*(5*v - 2)
Let n(b) be the first derivative of b**7/105 - b**6/60 - 11*b**2/2 - 4. Let q(j) be the second derivative of n(j). Let q(p) = 0. What is p?
0, 1
Let u be 199/6 - (5 + 145/(-30)). Suppose 5 - 1 - 16*m - u*m**2 + 0*m = 0. What is m?
-2/3, 2/11
Factor 1176 - 56*x + 2/3*x**2.
2*(x - 42)**2/3
Let y(j) be the second derivative of -9/5*j**5 + 0 + 64/7*j**4 + 0*j**2 - 47/35*j**6 - 1/7*j**7 - 4*j - 32/7*j**3. Solve y(o) = 0 for o.
-4, 0, 2/7, 1
Suppose -26 = -4*f + 3*z, z = f - 0*f - 6. Let t(r) be the third derivative of 1/16*r**5 + 0 - 1/96*r**6 + 0*r + 0*r**4 - f*r**2 - 5/6*r**3. Factor t(h).
-5*(h - 2)**2*(h + 1)/4
Solve -128 + 29 - 78 - 102*b + 4 - 694 - 3*b**2 = 0.
-17
Let w(y) be the second derivative of y**5/4 - 5*y**4/6 - 10*y**3/3 + 20*y**2 - 137*y. Factor w(a).
5*(a - 2)**2*(a + 2)
Factor 2/19*t**3 - 82/19*t + 2*t**2 + 42/19.
2*(t - 1)**2*(t + 21)/19
Let g(o) be the second derivative of -o**7/63 - 11*o**6/90 - 17*o**5/60 + o**4/18 + 10*o**3/9 + 4*o**2/3 + 3*o - 6. What is q in g(q) = 0?
-2, -1/2, 1
Let o(m) = m**3 + 19*m**2 + 18*m + 2. Let q be o(-18). Factor -3*b**3 + b**q + 175*b**4 - 178*b**4 - b**2.
-3*b**3*(b + 1)
Let m(d) be the first derivative of -2*d**5/5 + 22*d**3/3 + 18*d**2 + 16*d + 51.