2)
Let c(d) be the first derivative of -2/9*d**2 - 2/27*d**3 + 2/3*d + 16. Suppose c(q) = 0. What is q?
-3, 1
Let s = 62 + -60. Suppose -2*c + 4*c + s*c = 0. Find d, given that 1/3*d**3 + 1/3*d**2 + c*d + 0 - 1/3*d**4 - 1/3*d**5 = 0.
-1, 0, 1
Let w(s) = 2*s**4 - 2*s**3 + 3*s - 1. Let q(x) = x**4 + x. Let j(o) = -o**2 - 7*o + 11. Let a be j(-8). Let b = a - 6. Let p(l) = b*q(l) + 3*w(l). Factor p(z).
3*(z - 1)**3*(z + 1)
Let f(q) = -23*q**3 + 183*q**2 - 40*q - 155. Let l(d) = 12*d**3 - 92*d**2 + 20*d + 75. Let j(g) = 3*f(g) + 7*l(g). Factor j(s).
5*(s - 6)*(s - 1)*(3*s + 2)
Let o(b) = 3464*b - 20779. Let d be o(6). Factor -5*p**2 - 5*p**4 - 15/2*p**3 - 5/4*p - 5/4*p**d + 0.
-5*p*(p + 1)**4/4
Suppose 5*s - 22 = -3*m, 76*s - 72*s + m - 12 = 0. Factor 4/7*j**s - 12/7*j + 8/7.
4*(j - 2)*(j - 1)/7
Suppose -3*o**3 + 16*o**2 + 3 + 4 - 39*o + 6 + 5 + 8*o**2 = 0. Calculate o.
1, 6
Let t(f) = 10 - 4*f**2 - 12 + 16 + 10. Let c(p) = -7. Let m(j) = 20. Let s(r) = -17*c(r) - 6*m(r). Let w(z) = 20*s(z) + t(z). Let w(o) = 0. What is o?
-1, 1
Let v(o) = 11*o**2 + 16*o + 63. Let i(u) = -49*u**2 - 63*u - 251. Let z(y) = -4*i(y) - 18*v(y). Find t, given that z(t) = 0.
-13, -5
Let q = -34 - -85. Let a = q - 49. Determine u so that 3 + 1/3*u**2 + a*u = 0.
-3
Let u(z) = 2*z**3 + 4*z**2 - 3*z + 5. Let m be (-12)/8*16*-1. Let t = -29 + m. Let i(a) = a**3 + 2*a**2 - a + 2. Let h(y) = t*i(y) + 2*u(y). Solve h(v) = 0.
-1, 0
Let k(u) be the third derivative of -2*u**7/945 + u**6/270 + 11*u**5/135 - u**4/6 - 4*u**3/3 + u**2 - 2. Suppose k(p) = 0. What is p?
-3, -1, 2, 3
Let 2/13*b**3 + 90/13*b + 24/13*b**2 + 100/13 = 0. What is b?
-5, -2
Suppose 4*n - 4*k = 12, 0 = 7*n - 5*n + 4*k. Factor 1/2*h + 0 - 1/4*h**n.
-h*(h - 2)/4
Let j be 868/308 + (-2)/(-11). Let c be 0/(-2) - (-4 - -2). Factor 4*q**3 - c*q**2 - 24*q + 28*q**2 + 2*q**4 + 8 - 12*q**3 - 4*q**j.
2*(q - 2)**2*(q - 1)**2
Find j, given that 12/7*j**2 + 8/7*j - 16/7 - 2/7*j**4 - 2/7*j**3 = 0.
-2, 1, 2
Suppose 0 = 19*z - 17*z - 4. Suppose 7*o + z = 2. Factor 5/2*v**2 + o + 3/2*v**3 + v.
v*(v + 1)*(3*v + 2)/2
Let r = 158 + -141. Suppose 22*a**3 + r*a**5 - 13*a**5 - 6*a**5 + 1 - 58*a**2 + 2*a**4 + 52*a - 17 = 0. What is a?
-4, 1, 2
Let b = 37 - 18. Let s = 23 - b. Factor 3*y**3 + 4*y**4 + 0*y**3 + 5*y**4 + 6*y**s + 12*y**5.
3*y**3*(y + 1)*(4*y + 1)
Let v be (5/10)/((-1)/6). Let x = v - -5. Suppose 8/3*n + 2/3*n**x + 2 = 0. Calculate n.
-3, -1
Let i(y) be the first derivative of y**3/15 - y**2 - 39*y/5 + 179. Factor i(v).
(v - 13)*(v + 3)/5
Let j(b) = b**2 + 238*b + 233. Let z(q) = 240*q + 235. Let t(m) = 5*j(m) - 4*z(m). Solve t(k) = 0.
-45, -1
Suppose 0 = -y - 2*y - 3*w - 9, 3*y - 11 = w. Let k(c) be the second derivative of 0 - 15/14*c**5 + 4/3*c**3 - 8/7*c**y - c + 5/21*c**4. Factor k(g).
-2*(3*g + 2)*(5*g - 2)**2/7
Let l(u) be the first derivative of u**5/120 - u**4/12 + 8*u**2/3 + 33*u - 19. Let n(f) be the first derivative of l(f). Let n(z) = 0. What is z?
-2, 4
Let h(d) be the second derivative of -d**4/6 + 31*d**3/3 + 32*d**2 - 304*d - 1. Factor h(q).
-2*(q - 32)*(q + 1)
Let b(z) be the first derivative of -z**4/18 + 8*z**3/27 - z**2/9 - 4*z/3 + 93. Factor b(l).
-2*(l - 3)*(l - 2)*(l + 1)/9
Suppose 2*p - 18 = 22. Let -p*q**2 + 17 + q + 7*q - 37 + 32 = 0. Calculate q.
-3/5, 1
Let l(m) be the third derivative of m**7/175 + 3*m**6/50 + 9*m**5/50 - 264*m**2. Suppose l(u) = 0. What is u?
-3, 0
Determine o, given that -1/4*o**3 + 0 + o**4 + 1/4*o - o**2 = 0.
-1, 0, 1/4, 1
Solve -50 - 5*u**2 + 93 - 43 + 40*u = 0.
0, 8
Let j(h) be the second derivative of h**6/30 + h**5/4 + h**4/12 - 7*h**3/2 - 9*h**2 + 7*h + 1. Factor j(m).
(m - 2)*(m + 1)*(m + 3)**2
Let j(n) = -n - 5*n**4 - 4*n - 4*n**3 + 12*n + 2. Let m = -573 + 567. Let p(d) = 24*d**4 + 20*d**3 - 34*d - 10. Let a(q) = m*p(q) - 28*j(q). Factor a(z).
-4*(z - 1)*(z + 1)**3
Let u(d) be the first derivative of -6*d - 1/100*d**5 + 1/12*d**4 - 2 - 4/15*d**3 + 2/5*d**2. Let q(n) be the first derivative of u(n). Solve q(x) = 0.
1, 2
Let k be (-1)/(-3) - (-5)/(-30). Let i(y) be the third derivative of -1/30*y**5 + 0 + k*y**4 - 1/3*y**3 + 0*y + 6*y**2. Factor i(q).
-2*(q - 1)**2
Let z = 1067 - 1065. Let j(x) be the second derivative of 3/2*x**4 + 6*x**3 + 9*x + 0 + 3/20*x**5 + 12*x**z. Let j(f) = 0. Calculate f.
-2
Suppose 0 = 38*t - 91 + 15. Let y = -34 - -103/3. Find s such that -1/2*s**t + 1/6*s**3 + 0 + y*s = 0.
0, 1, 2
Let k = 4 - 7. Let w(m) = -m**2 - 5*m - 4. Let s be w(k). Factor -6*y**s + 10*y**3 - 15*y + 0*y**2 + 6 + 5*y**3.
3*(y - 1)*(y + 1)*(5*y - 2)
Let p(y) = -2*y**4 - 22*y**3 + 14*y**2 + 78*y + 2. Let l(j) = -3*j**4 - 45*j**3 + 27*j**2 + 155*j + 5. Let h(k) = -2*l(k) + 5*p(k). Let h(z) = 0. Calculate z.
-5, -2, 0, 2
Factor -12/11 + 12/11*n**2 + 70/11*n.
2*(n + 6)*(6*n - 1)/11
Let h be 18/4 - (-5)/(-10). Let x be ((-40)/16)/(2/(-8)) + -3. Solve -14*l - 13*l**3 - 2*l**5 - 10*l**h - x*l**3 - 2 + 10*l - 20*l**2 - 6*l = 0 for l.
-1
Let j(i) = 7*i**4 + 11*i**3 + 48*i**2 + 69*i + 32. Let y(v) = -v**4 + v**3 - v. Let p(b) = -2*j(b) - 10*y(b). Factor p(k).
-4*(k + 2)**4
Let f(i) be the first derivative of -6/7*i**3 - 3/28*i**4 - 24/7*i - 2 + 45/14*i**2. Factor f(g).
-3*(g - 1)**2*(g + 8)/7
Let y(b) be the third derivative of -4*b**2 + 0*b + 0*b**3 + 0 - 1/160*b**6 + 0*b**4 + 0*b**5. Factor y(j).
-3*j**3/4
Let b(i) be the first derivative of -4/9*i + 3 - 2/27*i**3 + 1/3*i**2. Factor b(a).
-2*(a - 2)*(a - 1)/9
Suppose -50 - 472*s - 2*s**2 + s**2 + 420*s - s**2 = 0. Calculate s.
-25, -1
Solve 2899 + 2*v**2 + 0*v**2 - 11 + 8*v + 0*v - 160*v = 0.
38
Let u(b) be the first derivative of 4 - 3/2*b**2 + 0*b + 1/2*b**3. Factor u(w).
3*w*(w - 2)/2
Let v be (1 - 3) + (-36)/(-17). Let h = 40/51 - v. What is k in 0 + 0*k**2 + 2/3*k**3 - h*k = 0?
-1, 0, 1
Let y = -4 + -8. Let m(r) = -r**3 - 11*r**2 + 11*r - 10. Let s be m(y). Solve 1/3*u + 1/6*u**s + 1/6 = 0.
-1
Let n = -2587 - -1158977/448. Let u(v) be the third derivative of 1/280*v**7 + 12*v**2 - n*v**8 + 0*v**3 + 0*v + 0*v**6 + 0*v**5 + 0*v**4 + 0. Factor u(r).
-3*r**4*(r - 1)/4
Let n(s) = 2*s**2 - 35*s + 12. Let j(g) = -3*g**2 + 34*g - 12. Let v(r) = r - 7. Let k be v(4). Let t(m) = k*j(m) - 2*n(m). Factor t(p).
(p - 6)*(5*p - 2)
Let l(f) be the second derivative of -f**4/9 + 16*f**3/9 + 6*f**2 - 86*f. Factor l(r).
-4*(r - 9)*(r + 1)/3
Let m(h) = -2*h**2 - 32*h + 59. Let c(r) = -3*r**2 - 63*r + 117. Let y(t) = -5*c(t) + 9*m(t). Suppose y(x) = 0. What is x?
3, 6
Let n(y) be the first derivative of -3*y**6/4 - 7*y**5/10 + 83*y**4/8 - 39*y**3/2 + 29*y**2/2 - 4*y + 63. Suppose n(q) = 0. What is q?
-4, 2/9, 1
Let r(g) be the first derivative of -g**4/26 + 16*g**3/13 - 45*g**2/13 + 44*g/13 - 89. Suppose r(q) = 0. What is q?
1, 22
Let x(l) = -24*l**3 - 60*l**2 + 168*l + 123. Let m(p) = 6*p**3 + 15*p**2 - 42*p - 30. Let t(w) = -9*m(w) - 2*x(w). Factor t(g).
-3*(g - 2)*(g + 4)*(2*g + 1)
Suppose -4*a = 3*v - 26, -2*v + 21 = 5*a - 8. Suppose -1/4*j + 1/4*j**a + 0 - 1/2*j**4 + 0*j**3 + 1/2*j**2 = 0. What is j?
-1, 0, 1
Let q(x) be the first derivative of -32*x - 8*x**2 + 15 - 2/3*x**3. Factor q(v).
-2*(v + 4)**2
Suppose -f = -5*f + 32. Factor -f*l**2 + 293*l - 293*l - 2*l**4 - 10*l**3.
-2*l**2*(l + 1)*(l + 4)
Let m(h) be the third derivative of h**5/50 - 11*h**4/12 + 52*h**3/15 + 694*h**2. What is q in m(q) = 0?
1, 52/3
Suppose -16*q + 795 = 219. Suppose q*d + 6*d**2 + 72 + 1/3*d**3 = 0. What is d?
-6
Suppose 0 = -7*f + 3*f + 16. Factor 1 - 6 + 13 - 12*r + f*r**2.
4*(r - 2)*(r - 1)
Find a, given that -146/7*a - 72/7 - 2/7*a**3 - 76/7*a**2 = 0.
-36, -1
Let q(c) = -6*c**3 + 158*c**2 - 408*c + 256. Let p(o) = -2*o**3 + 53*o**2 - 136*o + 85. Let z(m) = 8*p(m) - 3*q(m). Factor z(n).
2*(n - 22)*(n - 2)*(n - 1)
Let j(o) = o**3 + o**2 - 1. Let r(v) = -2*v**3 - 6*v**2 - 9*v + 44. Let n(g) = 3*j(g) + r(g). Let m(u) be the first derivative of n(u). Let m(h) = 0. What is h?
-1, 3
Let t(y) = y**3 - 7*y**2 + 4*y + 14. Let r be t(6). Suppose -12*j + r - 2 = 0. Factor 1/3 + j*h - 1/3*h**2.
-(h - 1)*(h + 1)/3
Let u(r) = -240*r**2 + 4550*r - 4395. Let x(m) = -17*m**2 + 325*m - 314. Let i(y) = -6*u(y) + 85*x(y). What is t in i(t) = 0?
1, 64
Let q = -4724 + 23623/5. What is l in 3/5*l**5 + q*l**4 - 3/5*l**3 - 3/5*l**2 + 0*l + 0 = 0?
-1, 0, 1
Let s(u) be the fi