-f*u - 27. Factor 2/13*q**u + 2/13*q - 12/13.
2*(q - 2)*(q + 3)/13
Let a = -405 + 408. Suppose -5*o + a*z - 8 + 6 = 0, o = -2*z + 10. Factor -7/4*m + 1/2 + 3/4*m**o.
(m - 2)*(3*m - 1)/4
Let r = -4/702953 + 475901185/352179453. Let z = r + -3/167. What is f in -4/9*f**5 - z*f**4 + 0 + 8/9*f + 4/3*f**2 - 4/9*f**3 = 0?
-2, -1, 0, 1
Let v(d) be the first derivative of -27*d**6/10 + 1449*d**5/25 - 115*d**4/2 - 1298*d**3/15 + 131*d**2/2 + 85*d - 9473. Solve v(f) = 0 for f.
-5/9, 1, 17
Let j(s) be the second derivative of 1/6*s**4 + 0*s**2 + 0 + 11/20*s**5 + 0*s**3 + 29*s. Factor j(v).
v**2*(11*v + 2)
Let l(u) = 39*u**2 + 393*u - 780. Let k(o) = -3*o**2 - 30*o + 60. Let j(a) = 27*k(a) + 2*l(a). Factor j(q).
-3*(q - 2)*(q + 10)
Let q(b) be the second derivative of b**7/5460 + b**6/390 - 4*b**5/195 + b**3 - 15*b**2/2 + 6*b + 4. Let n(c) be the second derivative of q(c). Factor n(p).
2*p*(p - 2)*(p + 8)/13
Let i(z) be the third derivative of -z**6/40 + 59*z**5/20 - 144*z**4 + 3726*z**3 + 3*z**2 + 22*z + 1. Solve i(a) = 0 for a.
18, 23
Let y(w) be the second derivative of -5/4*w**5 - 1 - 59/12*w**4 - 3*w - 47/6*w**3 - 1/10*w**6 - 5*w**2. Find q such that y(q) = 0.
-5, -2, -1, -1/3
Suppose -145*t**2 - 524*t**3 - 160*t - 5*t**4 - 528*t**3 + 1002*t**3 - 60 = 0. What is t?
-6, -2, -1
Let t be 5 - (3 + -4 - 0). Let m = 30 - t. Factor m*z**2 + 100*z + 7 + 16*z**3 + 88*z**2 + 22 - 5.
4*(z + 6)*(2*z + 1)**2
Let m(z) be the first derivative of z**5/15 + 35*z**4/6 + 467*z**3/3 + 2848*z**2/3 - 7168*z/3 + 2475. Factor m(u).
(u - 1)*(u + 7)*(u + 32)**2/3
Let s be (-33)/(-12) - (11/4 - 3). Factor -4*c**3 + 33*c**2 + 16*c + 4*c**4 + 3*c**s - 49*c**2 - 3*c**3.
4*c*(c - 2)*(c - 1)*(c + 2)
Factor 18 - 9*c**3 + 0*c - c**3 + 7*c**3 - 3*c - 74*c**2 + 62*c**2.
-3*(c - 1)*(c + 2)*(c + 3)
Let r(q) be the second derivative of -7*q**5/10 + 596*q**4/3 + 857*q**3/3 - 342*q**2 - 99*q + 2. Factor r(y).
-2*(y - 171)*(y + 1)*(7*y - 2)
Suppose -54 = -13*s - 2. Suppose 6*g**3 + 0*g**3 + 5*g**5 + 4*g**3 - 7*g**s + 22*g**4 = 0. What is g?
-2, -1, 0
Let c = -83473 - -417389/5. Find p such that c*p - 3/5*p**2 - 36/5 = 0.
2, 6
Let s(r) = -27*r + 5. Let o be s(-1). Factor 433*j + 3*j**3 + o - 4*j**3 - 9*j**2 - 429*j - 3*j**3 - 23*j**2.
-4*(j - 1)*(j + 1)*(j + 8)
Suppose -20 = -4*z + 24*z. Let p(q) = 2*q**3 - 15*q**2 - 13*q - 15. Let g(j) = 2*j**2 - 2*j + 1. Let m(x) = z*p(x) - 5*g(x). Determine f so that m(f) = 0.
-2, -1/2, 5
Let b(s) be the third derivative of -1/6*s**6 + 0 - 3*s**2 - 1/2*s**4 + 0*s**3 + 7/15*s**5 + s + 2/105*s**7. Solve b(l) = 0.
0, 1, 3
Determine y so that -1476*y**3 + 24537 - 8316*y + 25740 + 5622*y**2 - 47010 + 135*y**4 = 0.
3/5, 3, 11/3
Let j(a) = -a**3 + 19*a**2 - 36*a + 22. Let r be j(17). Let o = -8 - r. What is g in -o*g + 4*g**4 - 7*g**5 - 6*g**2 + 2*g**3 + 2*g**4 + 9*g**5 = 0?
-2, -1, 0, 1
Determine p, given that -142/3*p**3 + 143/3*p + 73 - 1/3*p**5 + 25*p**4 - 98*p**2 = 0.
-1, 1, 3, 73
Suppose 587 = -f - 5*u, 0 = 4*f + 4*u + 374 + 2022. Let p be (-516)/f*(-1 - (-6)/4). Factor 0*j**3 + 0 - p*j**4 + 9/7*j**2 + 6/7*j.
-3*j*(j - 2)*(j + 1)**2/7
Let y = -829 + 1167. Factor d**4 - 338 + 20*d**3 + 63*d**2 + 10*d + 39*d - 5*d**3 + y.
d*(d + 1)*(d + 7)**2
Let u(z) = z**2 + 24*z + 126. Let o be u(-12). Let w be (84/o - -4) + 104/138. Factor w*p**2 + 8/23 - 8/23*p.
2*(p - 2)**2/23
Let f be (-470)/(-658) + ((-40)/(-35))/(-2). Suppose -4/7*h - 12/7 + f*h**2 = 0. What is h?
-2, 6
Let y(j) be the second derivative of j**5/4 - 2005*j**4/4 + j - 974. Factor y(s).
5*s**2*(s - 1203)
Let v(r) = -r**2 - 441*r + 522. Let g(w) = 43*w - 3. Let d(c) = -4*g(c) + 2*v(c). Solve d(y) = 0 for y.
-528, 1
Suppose 2*f + 1138 = -4*l, 7*l - 2*l - 3*f = -1439. Let m = l - -286. Find o, given that m + 2/25*o + 2/25*o**2 = 0.
-1, 0
Factor 0 + 1/4*t**2 + 337/4*t.
t*(t + 337)/4
Let j(z) be the first derivative of -z**3 - 930*z**2 - 288300*z - 1665. Factor j(w).
-3*(w + 310)**2
Let z(t) be the first derivative of -15 - 23/4*t**4 - 11/10*t**5 - 81/4*t**2 - 1/12*t**6 - 15*t**3 - 27/2*t. Let z(u) = 0. What is u?
-3, -1
Factor 2/17*f**2 + 48/17 + 22/17*f.
2*(f + 3)*(f + 8)/17
Let z(k) be the third derivative of 1/660*k**6 + 1/165*k**5 - 41*k**2 - 2/11*k**3 + 0*k + 0 - 5/132*k**4. Factor z(d).
2*(d - 2)*(d + 1)*(d + 3)/11
Suppose 6 - 4 = -2*j - c, -2*j + 2*c - 8 = 0. Let n be ((-57)/6 - j)*8/(-80). Determine y so that n*y + 1/4*y**2 + 0 = 0.
-3, 0
Let f(y) be the first derivative of -310/3*y**3 + 5/6*y**6 - 18*y**5 - 105/2*y**2 + 0*y - 75*y**4 + 208. Let f(h) = 0. Calculate h.
-1, 0, 21
Factor 10/3*c + 0 - 16*c**2 + 3/2*c**4 + 25/6*c**3.
c*(c - 2)*(c + 5)*(9*c - 2)/6
Let y be (2/(-4))/(22/(-8)*(-6888)/(-12628)). Determine z so that y*z**4 - z**3 - 2/3*z**2 + 4*z - 8/3 = 0.
-2, 1, 2
Let i(l) be the second derivative of -l**8/4200 - 11*l**7/1050 - 121*l**6/900 - 57*l**3/2 - 157*l. Let p(c) be the second derivative of i(c). Factor p(f).
-2*f**2*(f + 11)**2/5
Let f = -565609 - -565611. Suppose 17/8 - 1/8*x**f + 2*x = 0. Calculate x.
-1, 17
Let h(f) be the first derivative of -f**5/30 + 25*f**4/24 - 34*f**3/3 + 51*f**2 - 72*f + 939. Factor h(j).
-(j - 12)*(j - 6)**2*(j - 1)/6
Let v be 2*(-1)/(-4)*6. What is b in 4*b**4 - 9*b**2 - 3*b + 6*b**2 + 15*b**2 - 13*b + 16*b**v - 16 = 0?
-2, -1, 1
Let f = 5783 + -5780. Let h(x) be the first derivative of 3/5*x**2 + 1/15*x**f + 0*x + 1/25*x**5 + 7 - 1/5*x**4. Determine l so that h(l) = 0.
-1, 0, 2, 3
Suppose 0 = k + 2, 0*k + 2 = 5*p + 4*k. Factor 3*m**2 + 6*m + 11*m**2 + 8*m**p - 37 - 20*m**2 + 17.
2*(m - 2)*(m + 5)
Factor -3139*h**4 + 69200*h**3 - 5903*h**5 - 5927*h**5 + 309*h**4 + 38*h**4 + 20000*h**2 + 11858*h**5.
4*h**2*(h - 50)**2*(7*h + 2)
Let z(j) = -204*j + 15098. Let l be z(74). Determine r so that 8 + 28/5*r + 4/5*r**l = 0.
-5, -2
Let l = -185 + 187. Suppose l*k - 9 = 3*b, 0 = -k - 5*b - 15. Suppose -1/3*o**2 + 1/6*o**3 + k*o + 1/6*o**4 + 0 = 0. What is o?
-2, 0, 1
Let z be 18/15 + (-16)/5. Let q be (z/(-10) + 0)/(51/408). Factor -8/5*a + 2/5*a**4 - q*a**3 + 12/5*a**2 + 2/5.
2*(a - 1)**4/5
Let d(m) be the third derivative of -m**7/3780 - m**6/360 - 7*m**4/3 + 49*m**2. Let f(y) be the second derivative of d(y). Factor f(j).
-2*j*(j + 3)/3
Let n(w) be the first derivative of 57/4*w**2 + 15*w + 32 - 3/8*w**4 + 4*w**3. Factor n(h).
-3*(h - 10)*(h + 1)**2/2
Let b(f) be the first derivative of f**6/45 - 11*f**5/120 + f**4/8 - f**3/36 - f**2/12 - 65*f + 44. Let y(n) be the first derivative of b(n). Factor y(v).
(v - 1)**3*(4*v + 1)/6
Let i be -3*(-186575060)/33187440 - (-2)/(-8). Let z = -2/10637 + i. Suppose -2/13*k**3 - 432/13 - 36/13*k**2 - z*k = 0. Calculate k.
-6
Suppose 0*r + 4*r - 2*s + 1146 = 0, 0 = r - 2*s + 291. Let j = r - -863/3. Factor -2/3*f**3 + 0 + j*f**2 + 0*f.
-2*f**2*(f - 4)/3
Let r(v) be the third derivative of -2/21*v**4 + 20/21*v**3 - 1/420*v**6 + 4*v**2 + 0 + 14*v - 11/210*v**5. Solve r(p) = 0 for p.
-10, -2, 1
Let c(t) = -19*t + 122. Let g be c(7). Let h be 51/g - (0 - 5). Factor -2/11*q**2 - h + 6/11*q.
-2*(q - 2)*(q - 1)/11
Determine f so that -f**2 - 108*f + 2*f**2 + 0*f**2 + 56*f - 3*f**2 = 0.
-26, 0
Let n be 43 + 3450/125 + -51. Let 1152/5*m + n*m**3 + 1248/5*m**2 + 0 + 2/5*m**4 = 0. Calculate m.
-24, -1, 0
Suppose -22*p + 7110 = 7022. Factor -2/9*a**5 + 0*a**2 + 0*a + 0 - 2/9*a**3 - 4/9*a**p.
-2*a**3*(a + 1)**2/9
Factor -38/3*i - 56/3 + 17/3*i**2 - 1/3*i**3.
-(i - 14)*(i - 4)*(i + 1)/3
Let f(u) be the third derivative of -u**6/600 - 21*u**5/200 + 11*u**4/20 + 73*u**3/6 - 47*u**2. Let o(c) be the first derivative of f(c). Factor o(l).
-3*(l - 1)*(l + 22)/5
Solve -2*l**5 - 8052 + 94*l**3 + 7876 + 107*l**2 - 184*l + 17*l**2 - 40*l**4 = 0.
-22, -1, 2
Let y be 5 - (1287/77 + (-2)/(-7)). Let k be ((-189)/(-18) + y)*(-1)/6. Solve 1/2*x**2 + x - k*x**3 - 2 = 0.
-2, 2
Let t(h) be the second derivative of -1/30*h**6 - 16/3*h**3 + 1/5*h**5 + 53 - 32*h**2 - h + h**4. What is a in t(a) = 0?
-2, 4
Let f = 118365 - 118365. Factor 4/13*p**2 - 6/13*p + f + 2/13*p**3.
2*p*(p - 1)*(p + 3)/13
Let j(h) be the second derivative of -3*h**5/20 - 31*h**4/3 + 251*h**3/18 - 7*h**2 - h - 3053. Factor j(q).
-(q + 42)*(3*q - 1)**2/3
Let r(n) be the first derivative of n**4/18 + 616*n**3/27 + 23716*n**2/9 - 1210. Factor r(g).
2*g*(g + 154)**2/9
Let x = -4 + 6. Suppo