Let g**4 + 4*g**3 + 2*g**2 - v*g**4 - 4*g**3 - 2*g + 2*g**3 = 0. Calculate g.
-1, 0, 1
Suppose 0 = 4*k - 23 - 21. Let v(y) = -36*y**3 - 86*y**2 + 14*y + 75. Let a(h) = -7*h**3 - 17*h**2 + 3*h + 15. Let s(r) = k*a(r) - 2*v(r). Factor s(z).
-5*(z - 1)*(z + 1)*(z + 3)
Let p be (-22)/33 + (-24)/(-9). Factor 3/4*v**3 - 3/2*v + 3/4*v**p + 0.
3*v*(v - 1)*(v + 2)/4
Determine j so that -6*j**5 - 36*j**3 + 125*j**2 + 2*j**5 + 10*j**4 + 14*j**4 - 109*j**2 = 0.
0, 1, 4
Let t be -21 - -43 - (5 + -1). Suppose -2*q + t*q = 32. Factor -2/7*p**q + 4/7 + 2/7*p.
-2*(p - 2)*(p + 1)/7
Let c(y) be the second derivative of -y**5/90 - 11*y**4/54 + 80*y**3/27 + 100*y**2 + 21*y - 10. Factor c(p).
-2*(p - 9)*(p + 10)**2/9
Solve -2074*m**4 + 2078*m**4 - 3*m**3 - m**3 = 0.
0, 1
Suppose 4 = 2*v - 0, 0 = d + 3*v - 3. Let k = -1 - d. Solve k*r**4 + 7*r**3 - r**4 + 17*r**3 - 19*r**4 - 8*r**2 = 0.
0, 2/3
Let h(p) = p**4 - 2*p**2 - p + 1. Let r(x) = 7*x**4 + 5*x**3 - 18*x**2 - 6*x + 6. Let v(d) = -30*h(d) + 5*r(d). Find a such that v(a) = 0.
-6, 0, 1
Let k(p) be the first derivative of 9*p**5/5 + 3*p**4/2 - 9*p**3 - 18*p**2 - 12*p + 32. Let k(j) = 0. Calculate j.
-1, -2/3, 2
Let y be 12/5 + 4/(-10). Find q such that -65*q**y + 10*q + 2*q + 9 + 68*q**2 = 0.
-3, -1
Let o(n) = 2*n**2 - 2*n + 200. Let q(v) = 3*v**2 - 7*v + 400. Let z(m) = -11*o(m) + 6*q(m). Factor z(w).
-4*(w - 5)*(w + 10)
Let m = 25/2 + -49/4. Let r(n) be the first derivative of -2 + 2/15*n**3 + 3/10*n**2 - m*n**4 + 0*n. Factor r(s).
-s*(s - 1)*(5*s + 3)/5
Let x = -3 + 5. Suppose -12 = 9*r - 30. Factor -3*f - r*f**x - f**2 - 6 - 6*f.
-3*(f + 1)*(f + 2)
Suppose l**4 + 0 + 7/5*l**3 - l**2 - 1/5*l**5 - 6/5*l = 0. What is l?
-1, 0, 1, 6
Let z(v) be the third derivative of -v**7/315 - v**6/36 - 2*v**5/45 - 4*v**2 - 32*v. What is m in z(m) = 0?
-4, -1, 0
Let z be 135098/130 + 18/(-30). Let b = z + -1038. Factor 0 - 10/13*x**2 + b*x**3 + 2/13*x.
2*x*(x - 1)*(4*x - 1)/13
Suppose -12*q + 7*q = 30. Let l(o) = -o**2 + 2*o - 3. Let f(v) = 1. Let t(b) = q*f(b) - 3*l(b). Factor t(g).
3*(g - 1)**2
Let n(k) = k**3 - 4*k**2 + 5*k - 5. Suppose 54*w = -28*w + 492. Let z(p) be the third derivative of p**3/6 + p**2. Let t(x) = w*z(x) + 2*n(x). Factor t(c).
2*(c - 2)*(c - 1)**2
Let x(j) be the first derivative of -4/3*j**6 + 0*j**3 + j**4 + 0*j**2 + 4/5*j**5 + 0*j - 31. Suppose x(p) = 0. What is p?
-1/2, 0, 1
Solve 22/21 - 20/21*c - 2/21*c**2 = 0.
-11, 1
Let q = 2815/2 + -1407. Let o(t) be the first derivative of -5 - 1/6*t**6 - q*t**2 + 0*t**3 + 1/2*t**4 + 0*t + 0*t**5. Factor o(p).
-p*(p - 1)**2*(p + 1)**2
Suppose 9 = 31*b - 12*b - 48. Determine c, given that 8/3*c + 16/3 - 4/3*c**2 - 2/3*c**b = 0.
-2, 2
Let p(w) = 265*w**3 - 30*w**2 - 155*w + 30. Let b(g) = 19*g**3 - 2*g**2 - 11*g + 2. Let c(y) = -55*b(y) + 4*p(y). Factor c(r).
5*(r - 1)*(r + 1)*(3*r - 2)
Let r be 3/(-4) - (-590)/1000. Let u = 13/75 - r. Factor -1 - u*j**2 - 4/3*j.
-(j + 1)*(j + 3)/3
Let l be (-1218)/(-2940) + 9/(-42). Find x such that 0 - 1/2*x**2 - l*x = 0.
-2/5, 0
Let s be 17 + 1 - (-2442)/(-148). Solve s + 5/4*f + 1/4*f**2 = 0.
-3, -2
Suppose 2*a - l = -3*l + 2, -13 = -5*a - l. Suppose 3*o + o = 8. What is k in -7*k**2 + 4*k**2 - 4*k - 1 - o*k - k**a + 3*k = 0?
-1
Suppose -4*m + 11 = -3*m. Suppose -4*r + m = -h, -4*h - 23 + 7 = -2*r. Solve 5/6*z**5 - 1/3 - 3/2*z + r*z**4 - 5/3*z**2 + 2/3*z**3 = 0 for z.
-1, -2/5, 1
Determine m, given that -20/7*m - 37/7*m**3 - 3/7*m**5 + 39/7*m**2 + 4/7 + 17/7*m**4 = 0.
2/3, 1, 2
Let a(u) be the first derivative of -4*u**3/3 - 424*u**2 - 44944*u - 659. Factor a(j).
-4*(j + 106)**2
Suppose 4*j + 0 - 21 = -c, 0 = 2*j - 2*c + 2. Let 0*u**2 + 6*u**3 + 6*u**j + 0 + 3/2*u**5 + 0*u = 0. What is u?
-2, 0
Let y(q) = -8*q + 6. Let k be y(-8). Suppose k = -n + 8*n. Let n*u + 18 + u**2 + 10 - 3 = 0. Calculate u.
-5
Let m(s) = -4*s**2 + 1037*s - 66569. Let q(n) = -2*n**2 + 519*n - 33285. Let t(j) = 3*m(j) - 5*q(j). Let t(w) = 0. Calculate w.
129
Factor -2*n**2 + n - 6*n**2 - 2*n**3 - 5*n**2 + 16 + 3*n**2 - 5*n.
-2*(n - 1)*(n + 2)*(n + 4)
Let d(c) be the second derivative of 1/3*c**3 + 0 - 1/12*c**4 - 12*c + 0*c**2. Find j such that d(j) = 0.
0, 2
Let m(f) be the first derivative of 0*f**3 + 0*f**4 + 0*f + 0*f**2 - 2/25*f**5 + 1/3*f**6 - 14. What is z in m(z) = 0?
0, 1/5
Factor 4810*k - 228*k**3 + 4940*k - 4095*k**2 - 3*k**4 - 624*k.
-3*k*(k - 2)*(k + 39)**2
Suppose 5*p - 10 = -f, -4*f + 20 - 3 = -3*p. Factor -6*t**4 - 4*t - t**4 + 6*t**2 + f*t**4.
-2*t*(t - 1)**2*(t + 2)
Let a(m) be the first derivative of 3*m**4/5 + 3*m**3/5 - 3*m**2/10 - 202. Factor a(x).
3*x*(x + 1)*(4*x - 1)/5
Determine w, given that -22*w**2 - 2*w**3 - 14*w + 27*w - 33*w = 0.
-10, -1, 0
Let l(m) be the third derivative of 0 + 23/180*m**6 + 8*m**2 - 8/9*m**3 + 1/24*m**8 - 11/9*m**4 - 3/5*m**5 + 62/315*m**7 + 0*m. Solve l(z) = 0 for z.
-2, -1, -2/3, -2/7, 1
Solve -157*j**4 + 316*j**4 - 260*j**3 - 132*j**2 - 151*j**4 = 0 for j.
-1/2, 0, 33
Let u(r) be the third derivative of -r**8/672 + r**7/60 - r**6/24 + 280*r**2. Find j, given that u(j) = 0.
0, 2, 5
Let x(p) = -3*p**4 + 30*p**3 - 47*p**2 - 2. Suppose 0 = -42*r + 37*r + 5. Let s(g) = -g**4 + g**2 + 1. Let q(f) = r*x(f) + 2*s(f). Factor q(a).
-5*a**2*(a - 3)**2
Let v be (5 - 0)/(14/(-14)). Let s(g) = -g**3 - 4*g**2 - 3. Let o be s(v). Suppose 4*u**3 - 3*u**4 - 39*u**2 - 13 + 14*u + 1 + 14*u**3 + o*u = 0. What is u?
1, 2
Let u(c) be the first derivative of 9*c**4/32 - c**3/3 - 43*c**2/16 - 13*c/4 - 19. Factor u(o).
(o + 1)**2*(9*o - 26)/8
Let g(s) be the first derivative of -21*s**4/16 - 19*s**3/4 - 3*s**2 + 3*s + 82. What is d in g(d) = 0?
-2, -1, 2/7
Let u(j) = -3*j**3 + 18*j**2 - 15*j - 12. Suppose 0 = 5*n - 22 - 28. Let b(o) = -o + 0*o + 9 + o**2 - n. Let w(s) = -12*b(s) + u(s). Solve w(t) = 0 for t.
0, 1
Let i(t) be the second derivative of 0 - 1/8*t**2 - 32*t - 1/12*t**3 - 1/48*t**4. What is v in i(v) = 0?
-1
Suppose -9/5 - 6*f + 23/5*f**2 - 4/5*f**3 = 0. What is f?
-1/4, 3
Factor 0*c**3 + 0*c - 2/3*c**2 + 1/3 + 1/3*c**4.
(c - 1)**2*(c + 1)**2/3
Let s(b) be the second derivative of -b**6/150 - b**5/25 - b**4/15 + 10*b**2 + 42*b. Let u(w) be the first derivative of s(w). Solve u(o) = 0.
-2, -1, 0
Factor -224 + 32*x - 6*x + 2*x - x**2 + 28.
-(x - 14)**2
Let t = 223/256 + 1/256. Let f(m) be the first derivative of -1/2*m - t*m**2 - 5/16*m**4 - 1/20*m**5 - 7 - 3/4*m**3. Determine s so that f(s) = 0.
-2, -1
Let i(q) = -12*q**2 - 76*q - 312. Let s(m) = -26*m**2 - 152*m - 624. Let a(x) = -9*i(x) + 4*s(x). Factor a(l).
4*(l + 6)*(l + 13)
Let z(c) = 13*c**2 - 209*c + 21. Let t be z(16). Solve -5/4*l**2 + 15/4*l**3 - 15/4*l**4 + 5/4*l**t + 0*l + 0 = 0.
0, 1
Let p(f) be the first derivative of f**7/1260 - f**6/135 + f**5/36 - f**4/18 - 4*f**3 - 2. Let m(b) be the third derivative of p(b). Factor m(i).
2*(i - 2)*(i - 1)**2/3
Factor 2/7*w**3 + 2*w**2 - 16/7*w + 0.
2*w*(w - 1)*(w + 8)/7
Let a(x) = x**3 - 3*x**2 - 3*x + 6. Let w be a(4). Let z(h) = 2*h**2 - h + 9. Let t(f) = f**2 + 5. Let m(u) = w*t(u) - 6*z(u). Solve m(k) = 0.
1, 2
Let z = 8568 + -17133/2. Determine u, given that -63/2*u - 18*u**2 - z*u**3 - 15 = 0.
-10, -1
Let s(c) = 4*c + 32. Let o be s(-6). Let v(f) be the first derivative of 22*f**2 - o*f + 7*f**4 - 64/3*f**3 - 8. Factor v(n).
4*(n - 1)**2*(7*n - 2)
Let u(a) = -10*a + 3. Let c be u(0). Let z = 0 + 2. Factor 16 - 4*f**z + c*f + f - 16.
-4*f*(f - 1)
Let l(u) be the first derivative of 7*u**6/4 + 12*u**5 - 9*u**4/2 - 111. What is v in l(v) = 0?
-6, 0, 2/7
Let b(r) be the second derivative of -r**4/72 - 4*r**3/9 - 7*r**2/3 + 105*r. Factor b(d).
-(d + 2)*(d + 14)/6
Let z(q) be the first derivative of q**4/14 - 6*q**3/7 - q**2/7 + 18*q/7 - 257. Suppose z(x) = 0. Calculate x.
-1, 1, 9
Let f = 45 + -42. Factor -3/2*n - 3/2*n**2 + f.
-3*(n - 1)*(n + 2)/2
Suppose y - 40 = -16. Factor -49*l**4 + y*l**2 + 43*l**4 - 2*l**3 + 3*l**5 - 7*l**3 - 12*l.
3*l*(l - 2)*(l - 1)**2*(l + 2)
Let z(v) be the first derivative of v**3/5 - 6*v**2/5 - 3*v + 43. Factor z(t).
3*(t - 5)*(t + 1)/5
Let f(q) be the first derivative of -1/15*q**3 + 2/5*q**2 - 12 + 12/5*q. Let f(k) = 0. Calculate k.
-2, 6
Find r such that 0 + 205*r**2 - 5/2*r**3 + 0*r = 0.
0, 82
Let v = -157 - -257. Let c = 103 - v. Solve 0 + 0*t**2 - 2/11*t**c + 8/11*t = 0 fo