7. Let r be j(6). Let u(k) be the first derivative of -2 - 2*k**3 - 1/2*k**4 - r*k**2 - 2*k. Factor u(b).
-2*(b + 1)**3
Let m = -30 - -39. Factor 8*d + 7*d**2 - 2*d**3 + m + 2 - 9*d**2 - 3.
-2*(d - 2)*(d + 1)*(d + 2)
Let a(o) be the first derivative of o**7/840 + o**6/180 - o**5/120 - o**4/12 + 4*o**3 + 4. Let b(r) be the third derivative of a(r). Solve b(s) = 0 for s.
-2, -1, 1
Let b be 265 + ((-4)/4 - 2). Factor 2 - 2*y + 4*y**2 + 6*y - b*y**3 + 258*y**3 - 6.
-4*(y - 1)**2*(y + 1)
Let y be 3/18 - (-315)/54. Suppose y*o - 6 = 6. What is c in 0*c - 2/7*c**o + 0 = 0?
0
Let y(x) be the first derivative of 3/4*x**4 + 1 + 81*x + 81/2*x**2 + 9*x**3. Suppose y(o) = 0. Calculate o.
-3
Let s(q) be the third derivative of -q**6/600 - q**5/75 + 11*q**4/120 - q**3/5 + 93*q**2. What is l in s(l) = 0?
-6, 1
Let x(y) = 7*y**3 - 118*y**2 - 131*y + 262. Let w(f) = 20*f**3 - 356*f**2 - 394*f + 785. Let j(k) = -4*w(k) + 11*x(k). Factor j(l).
-3*(l - 43)*(l - 1)*(l + 2)
Let j(s) = -s**3 + 6*s**2 - 8*s + 18. Let b be j(5). Factor -55*a**2 - b*a**3 + 64*a**2 - 5 - 7.
-3*(a - 2)**2*(a + 1)
Let o(c) be the first derivative of -3*c**2 + 2*c - 8/3*c**3 - 20. Factor o(g).
-2*(g + 1)*(4*g - 1)
Let i = 245 + -241. Let s(p) be the first derivative of -3/4*p**i + 0*p**3 + 0*p**2 - 3 + 0*p - 3/5*p**5. Factor s(q).
-3*q**3*(q + 1)
Factor 5*x**3 + 463854*x**2 + 0*x**3 - 463989*x**2.
5*x**2*(x - 27)
Let s = -89 + 91. Let x be s + (12/8 - 3). Factor 2*u**3 + 2*u - 3*u**2 - 1/2*u**4 - x.
-(u - 1)**4/2
Let l = -32/3795 - -1/69. Let r(j) be the third derivative of 9*j**2 - 1/660*j**6 + 0 + 1/132*j**4 + 2/33*j**3 + 0*j - l*j**5. Find i such that r(i) = 0.
-2, -1, 1
Let d(i) = -i - 11. Let s be d(-13). Let x be (0*(1 + 0))/(-1). Suppose 1/2*m + 1/2*m**3 - m**s + x = 0. What is m?
0, 1
Let v = 6 + -4. Suppose 5*a - 3*x = 134, 3*a - 4*a - 5*x = -10. Factor -44*g**5 + 191*g**5 + 152*g**4 - g**2 - 156*g**3 + 58*g**4 + a*g**v.
3*g**2*(g + 2)*(7*g - 2)**2
Let n(k) be the third derivative of 11*k**2 - 1/180*k**5 + 0 + 0*k**3 + 1/36*k**4 + 0*k. Suppose n(h) = 0. What is h?
0, 2
Let a(b) be the first derivative of -b**4/8 + 3*b**3/2 - 27*b**2/4 + 27*b/2 + 171. Find j, given that a(j) = 0.
3
Let m(o) = o**3 + 22*o**2 + 85*o + 4. Let l(g) = -g**3 - 23*g**2 - 86*g - 5. Let q(z) = -4*l(z) - 5*m(z). Factor q(j).
-j*(j + 9)**2
Let a be -5*6/(-15) - -1. Suppose 5*z + z + a*z = 0. Suppose z + 2/9*p**3 + 2/9*p**2 - 2/9*p - 2/9*p**4 = 0. What is p?
-1, 0, 1
Let m be (-11 + -8 - -13) + 48/7. Find h, given that -3/7*h**4 + 6/7*h**5 + 6/7*h + m*h**2 - 12/7*h**3 - 3/7 = 0.
-1, 1/2, 1
Let s be (-8)/(-2) + (14 - 13). Solve -34*y**3 + 0*y**3 + s*y**5 + 19*y**3 + 10*y**2 = 0.
-2, 0, 1
Let p(i) = i. Let h(r) = r**2 - 11*r. Let c(u) = -5*h(u) + 5*p(u). Solve c(o) = 0 for o.
0, 12
Suppose 5*d = -n + 22, -2*n - 16 = -3*d - 4*n. Let q(z) be the first derivative of 1/25*z**5 - 1/10*z**4 - d + 0*z**3 + 1/5*z**2 - 1/5*z. Solve q(h) = 0.
-1, 1
Let k(o) = o**3 - 5*o**2 - 5*o. Let n be k(6). Suppose 5*g + 2*b - 15 - 1 = 0, 3*b = 9. Factor 13*v**3 + n*v**4 + 12*v**g + 2 + 4*v + v**5 - 2.
v*(v + 1)**2*(v + 2)**2
Determine k so that 1922/9*k**2 + 2 - 124/3*k = 0.
3/31
Determine b, given that -25*b**4 - 15*b**5 - 10*b + 25*b**3 - 365 + 25*b**2 + 365 = 0.
-2, -1, 0, 1/3, 1
Factor 1/6*o - 1/6*o**3 + 0 + 0*o**2.
-o*(o - 1)*(o + 1)/6
Let m = -530 + 1063/2. Let w(n) be the first derivative of -3 + 1/3*n**3 + m*n**2 + 2*n. Factor w(x).
(x + 1)*(x + 2)
Determine p so that p**2 + 1/5*p**3 - 24/5 - 2/5*p = 0.
-4, -3, 2
Suppose -3*v + 3*k = 4*k - 269, -v + 93 = -3*k. Let r = v + -179/2. Solve 1/4*n**3 + r - 11/4*n + 3*n**2 - n**4 = 0 for n.
-2, 1/4, 1
Let h = -57 + 59. Suppose -24 + 24*t + 12*t + 18*t**h - 49*t**4 + 40*t**4 - 21*t**3 = 0. What is t?
-2, 2/3, 1
Let t be (4/(-18))/(16 - 792/48). Factor -2/9*l**2 + 2/3 + t*l.
-2*(l - 3)*(l + 1)/9
Determine z, given that -4/7*z**2 - 6/7*z**5 + 2/21*z + 16/21*z**3 + 4/7*z**4 + 0 = 0.
-1, 0, 1/3, 1
Solve 6/5*o + 4/5*o**2 + 2/5 = 0.
-1, -1/2
Factor 19*d**2 - 4*d**2 - 157*d**3 + 148*d**3.
-3*d**2*(3*d - 5)
Suppose 60 = 4*y - 36. Let v be 22/12 + 4/y. Find q, given that -3*q**5 - q**5 + 2*q**2 + q**5 + q**v + 9*q**4 - 9*q**3 = 0.
0, 1
Let a(f) be the third derivative of -f**8/9240 + f**6/660 + f**5/330 + 5*f**3/2 + 10*f**2. Let q(r) be the first derivative of a(r). Factor q(t).
-2*t*(t - 2)*(t + 1)**2/11
Determine y, given that -165*y**2 + 594*y - 66*y**3 + 1755*y - 2187 - 49*y**3 + 118*y**3 = 0.
1, 27
Suppose 4*m - d = -0*d + 21, 0 = -5*m - 3*d + 5. Find n such that 219*n**4 + n + 2*n**5 - 4*n**3 - 213*n**m + n + 6 - 12*n**2 = 0.
-3, -1, 1
Let i(s) be the second derivative of 7*s**7/24 + 77*s**6/120 + 2*s**5/5 + s**4/12 - s. Factor i(k).
k**2*(k + 1)*(7*k + 2)**2/4
Determine q so that 0*q**2 + 17*q**5 + 4*q**3 - 8*q**5 - 4*q**2 + 4*q**4 - 5*q**5 - 16*q**3 + 8*q = 0.
-2, -1, 0, 1
Let j(v) = v**3 + v**2 - v + 1. Suppose -12*f + 54 = -15*f. Let l(g) = 15*g**3 + 36*g**2 - 45*g + 18. Let p(b) = f*j(b) + l(b). Let p(m) = 0. Calculate m.
0, 3
Factor -3/5*b**3 - 9/5*b**2 + 3/5*b + 9/5.
-3*(b - 1)*(b + 1)*(b + 3)/5
Let n = 103 - 72. Suppose -5*v - 3*d + n = 0, 0*d - 8 = -4*d. Determine h so that 2/3*h**v + 0*h + 0 - 2/3*h**4 + 0*h**3 + 0*h**2 = 0.
0, 1
Let -164/5*m - 2/5*m**2 - 3362/5 = 0. Calculate m.
-41
Factor -17/3*l - 17/3*l**2 - 2 - 7/3*l**3 - 1/3*l**4.
-(l + 1)**2*(l + 2)*(l + 3)/3
Factor 0 - 8/3*v**2 - 2/3*v**3 + 0*v + 1/3*v**4.
v**2*(v - 4)*(v + 2)/3
Let o = 91 - -8. Let i = -95 + o. Let -14*d**5 - 8/7 + 106/7*d**3 + 106/7*d**2 - 14*d**i - 8/7*d = 0. What is d?
-1, -2/7, 2/7, 1
Let g = -143281/21 + 6823. Factor g*l**2 + 8/21*l + 8/21.
2*(l + 2)**2/21
Factor 207/5*j**3 + 0*j + 3/5*j**5 + 48/5*j**4 + 54*j**2 + 0.
3*j**2*(j + 3)**2*(j + 10)/5
Let i(z) = -20*z**5 + 55*z**4 + 55*z**3 - 5*z**2 - 125*z - 80. Let n(j) = -j**5 - j**3 - j - 1. Let q(y) = i(y) - 30*n(y). Find g, given that q(g) = 0.
-5/2, -2, -1, 1
Let w(g) be the first derivative of -g**5/180 - g**4/72 + 4*g**2 + 9. Let k(i) be the second derivative of w(i). Determine z so that k(z) = 0.
-1, 0
Let q be 4/6*36/8. Suppose 1 = 2*t - q. Let -5*d + t*d + 9*d - 2*d - 4*d**2 = 0. What is d?
0, 1
Let t(v) = 22*v**3 - 12*v**2 - 22*v + 2. Let o(q) = 7*q**3 - 4*q**2 + 139*q + 1 + 0*q**3 - 146*q. Let c(a) = 10*o(a) - 3*t(a). Factor c(s).
4*(s - 1)**2*(s + 1)
Let o(b) = 3*b**4 - 6*b**3 + 8*b**2 - 2*b + 3. Let v(g) = 7*g**4 - 13*g**3 + 17*g**2 - 3*g + 7. Let p(w) = 15*o(w) - 6*v(w). Factor p(j).
3*(j - 1)**4
Let h(r) = -r**2 + 10*r - 14. Let u be h(8). Factor 8*s**4 - 6*s + 4*s**5 + 6*s**2 - 12*s**3 + 4*s - 6*s**5 + 2*s**u.
-2*s*(s - 1)**4
Suppose 4/7*r**4 + 12/7*r**3 - 4/7*r**2 - 12/7*r + 0 = 0. What is r?
-3, -1, 0, 1
Let z = -305 + 309. Let k(i) be the second derivative of -i + 1/36*i**z + 1/9*i**3 + 1/6*i**2 + 0. Suppose k(p) = 0. Calculate p.
-1
Suppose 0 = 4*f + 12, -8*t - 282 = -4*t + 2*f. Let m be ((-8)/3)/(46/t). Let 5*s + 2*s**3 + 0 - 4*s**4 + 18*s**2 + 8 + 2*s**m + 17*s = 0. Calculate s.
-1, 4
Let r(b) be the second derivative of -b**4/48 + 19*b**3/24 - 837*b. Factor r(p).
-p*(p - 19)/4
Let a(h) be the third derivative of -h**7/210 - 19*h**6/120 - 4*h**5/3 + 25*h**4/6 - 78*h**2. Factor a(l).
-l*(l - 1)*(l + 10)**2
Let c be 1105/1428 + (-2)/(-24). Let k(w) = -w**2 - 5*w - 4. Let t be k(-4). Factor 4/7*f + t + c*f**2 + 2/7*f**3.
2*f*(f + 1)*(f + 2)/7
Let i be 3 + 104/18 + (-4)/(-18). Let v = 11 - i. Determine u, given that 10/7*u + 6/7 + 2/7*u**v - 2/7*u**3 = 0.
-1, 3
Suppose -s - 3*d + 5*d - 2 = 0, 2*s - d = -1. Let k(n) be the second derivative of 6*n - 4/3*n**3 + 0 - 2*n**4 + s*n**2 - 9/10*n**5. Factor k(o).
-2*o*(3*o + 2)**2
Let z = -174 + 174. Let i(j) be the third derivative of 14*j**2 + 0*j + 0*j**3 + z + 0*j**4 + 1/40*j**5. Factor i(u).
3*u**2/2
Suppose -171500/3 - 171*b**4 + 166600*b - 170695/3*b**2 - 5/3*b**5 - 17119/3*b**3 = 0. What is b?
-35, 2/5, 2
Suppose 0 = -3*h - r + 5, 5*r = 2*r - 3. Let d be 0/((-2)/4*-2). Factor 0*g + 3/4*g**3 - 3/4*g**4 + d + 0*g**h.
-3*g**3*(g - 1)/4
Let m be (0/(-2 - 1))/1 + 2. Let s(u) be the second derivative of 1/6*u**4 - 1/3*u**3 + 0 + 0*u**m - u. Factor s(v).
2*v*(v - 1)
Let m(x) = -11*x**3 + 38*x**2 - 6*x - 48. Let t(g) = 10*g**3 - 37*g**2 + 7*g + 48. Let b(z) = -3*m(z) - 2*t(z). Suppose b