3*b**2 + 4/3 + 7/6*b**3 + 1/6*b**4 + 10/3*b = 0.
-2, -1
Let r(q) be the first derivative of q**6/120 + 3*q**5/20 + 9*q**4/8 - 2*q**3 + 5. Let o(u) be the third derivative of r(u). What is l in o(l) = 0?
-3
Let u(z) = 5 - 4 + z + 1. Let p be u(0). Factor -2/7*r + 4/7 - 2/7*r**p.
-2*(r - 1)*(r + 2)/7
What is a in -4*a**2 + 87 - 87 + 4*a = 0?
0, 1
Let q(v) be the second derivative of -v**6/80 - v**5/60 + v**4/16 + v**3/6 - 3*v**2/2 + 3*v. Let d(m) be the first derivative of q(m). Factor d(u).
-(u - 1)*(u + 1)*(3*u + 2)/2
Let k = -5/54 - -253/108. Factor k + 1/4*t**2 - 3/2*t.
(t - 3)**2/4
Factor 2/7*y + 10/7*y**2 + 8/7*y**3 + 0.
2*y*(y + 1)*(4*y + 1)/7
Let y = -4 - -6. Factor -5*u**4 + 28*u + 30*u**4 + 57*u**2 + 4 + 12*u**y + 70*u**3.
(u + 1)**2*(5*u + 2)**2
Let g(u) = -u + 3. Let r be g(3). Let a(t) be the first derivative of 0*t**2 - 1 - 2/3*t**3 + r*t - 1/2*t**4. Let a(k) = 0. What is k?
-1, 0
Let j be (21/126)/((-2)/(-3)). Factor -1/4*o + 1/4*o**3 + j*o**2 - 1/4.
(o - 1)*(o + 1)**2/4
Suppose -9 = -3*b + 4*c - 3*c, c + 3 = 0. Factor -2 - 1/2*h**b - 2*h.
-(h + 2)**2/2
Suppose 5*k = 3*s + 4 - 21, 17 = 5*s + 3*k. Factor 2*t - 2 - 3 - 2*t**3 - t**2 + 2 + s.
-(t - 1)*(t + 1)*(2*t + 1)
Let c(g) = -g**2 + 9*g - 14. Let q be c(7). Suppose -y + 17 = 5*p - 0*p, q = -p + 3. Factor 24/7*w**3 + 4/7*w - 10/7*w**4 - 18/7*w**y + 0.
-2*w*(w - 1)**2*(5*w - 2)/7
Let p = 36 - 34. Factor 4/7*b**p + 0*b + 0 + 4/7*b**3.
4*b**2*(b + 1)/7
Let -5*n**4 + 12 + 261*n**2 + 90*n**4 - 96*n - 4*n**4 - 270*n**3 = 0. What is n?
1/3, 2/3, 2
Let k be (30/(-5) + 2 + 4)/1. Let -2*y**4 + 0*y + 0*y**2 + 2/3*y**3 + 4/3*y**5 + k = 0. What is y?
0, 1/2, 1
Let l be (-36)/(-40) + (-2)/5. Let w be (-2)/1*(-5)/8. Factor -l*k**3 + 0*k**2 + 0*k + w*k**4 + 0.
k**3*(5*k - 2)/4
Suppose 5*m - 3*g - 24 = -g, 5*g + 14 = m. Factor m*t**4 - 3*t**5 - 4*t**2 + t**2 - 2*t**3 - t**4 + 5*t**3.
-3*t**2*(t - 1)**2*(t + 1)
Let z(j) = -8*j + 56. Let g be z(7). Let u(k) be the third derivative of 0*k + 1/60*k**6 + 0 + 0*k**3 + 2*k**2 + g*k**5 + 0*k**4. What is v in u(v) = 0?
0
Suppose 0 = 5*r - 6*r + 2. Factor -9*y**r - 2*y**3 - 14*y - y**2 - 6 + 0*y**3.
-2*(y + 1)**2*(y + 3)
Let y be 120/(-21) + (-1 - -9). Suppose -10/7*u**2 + 8/7 + y*u = 0. What is u?
-2/5, 2
Let o(i) be the first derivative of 2*i**3/3 - 2*i + 6. Let o(n) = 0. Calculate n.
-1, 1
Let d(q) be the first derivative of -q**8/7560 - q**7/3780 + q**3 + 1. Let t(j) be the third derivative of d(j). Factor t(r).
-2*r**3*(r + 1)/9
Let p(c) = -7*c + 39. Let d be p(5). Let f(k) be the first derivative of -3/20*k**5 + 1 - 3/2*k**3 - 3/4*k - 3/4*k**d - 3/2*k**2. Factor f(i).
-3*(i + 1)**4/4
Let o(b) be the second derivative of -2*b + 0 + 0*b**2 + 1/48*b**4 - 1/24*b**3. Factor o(i).
i*(i - 1)/4
Suppose -3*j - 3 + 9 = 0. Factor 8 + 17*q + 3*q**3 - 5*q - 2*q**3 + 6*q**j.
(q + 2)**3
Let c(l) be the second derivative of 7/5*l**5 - 2/15*l**6 - 5*l**4 + 6*l**3 - l + 0*l**2 + 0. Factor c(f).
-4*f*(f - 3)**2*(f - 1)
Let i be -9 - -10 - 129/(-8). Let u = i - 93/8. Suppose -9/2*y**2 + u*y - 1 = 0. Calculate y.
2/9, 1
Suppose 3*s + 5*d - 20 = s, 0 = -5*s + d - 4. Let o(y) be the second derivative of s*y**2 + 3*y + 0 + 1/48*y**4 - 1/24*y**3. Factor o(u).
u*(u - 1)/4
Let y be (-1)/(-2)*8 - 2. Factor 16*d**3 - 2*d + 88*d**2 + 5*d - 68*d**y + 4*d**4 + 5*d.
4*d*(d + 1)**2*(d + 2)
Let b(d) be the third derivative of -1/75*d**6 + 0 - 1/3*d**4 + 4/15*d**3 + 17/150*d**5 + 0*d - d**2. Suppose b(i) = 0. What is i?
1/4, 2
Let q be (0*(-2 - -1))/1. Let g(y) be the second derivative of q*y**2 + 7/12*y**4 - 2*y + 0 - 1/3*y**3 + 1/5*y**5. Factor g(a).
a*(a + 2)*(4*a - 1)
Suppose 0 = w + 3*i - 2, 2*w - 2 = i + 9. Factor -2*c**2 - c + 2*c**w - c**4 - c**5 + 5*c**4 - 2*c**4.
c*(c - 1)*(c + 1)**3
Suppose 2*k**2 + 4*k**4 + 16*k**5 - 15*k**5 + 0*k**3 + 5*k**3 = 0. Calculate k.
-2, -1, 0
Let v be (-5)/(45/(-6))*3. Factor -3 + o + 2 - o**v + 1.
-o*(o - 1)
Let g be (-19)/(-21) + 32/(-56). Let p(o) be the first derivative of 2/5*o**5 + 0*o + 1/2*o**4 - 2/3*o**3 + 1 + 0*o**2 - g*o**6. Solve p(k) = 0.
-1, 0, 1
Suppose -5*c = 3*c. Let d(s) be the first derivative of 1/6*s**4 + c*s - 2/15*s**5 + 2/9*s**3 - 1/3*s**2 + 3. What is m in d(m) = 0?
-1, 0, 1
Let v be 2 + (4/(-6))/(91/234). Solve 0*z + 0*z**2 - 2/7*z**5 + 0 + 0*z**3 + v*z**4 = 0.
0, 1
Let j = 3 + -10. Let c be 7/j*(1 + -1). Suppose 2*p**3 - 2*p**5 + 2*p**4 - 6*p**2 + 4*p**2 + c*p**5 = 0. What is p?
-1, 0, 1
Let k(r) be the second derivative of 3*r**5/20 + 5*r**4/4 + 27*r. Factor k(s).
3*s**2*(s + 5)
Factor 8 - 2*l**4 + 20*l - 4*l**3 - 8*l**2 - 2*l**4 + 15*l**2 + 5*l**2.
-4*(l - 2)*(l + 1)**3
Let f(r) = r**2. Let g(c) = 16*c + 16. Let d(l) = -4*f(l) - g(l). Determine m, given that d(m) = 0.
-2
Let w(u) = -3*u**2 + u. Let z be w(0). Determine n, given that 0*n - 2/3*n**2 + z - 2/3*n**3 = 0.
-1, 0
Let p(s) = 8*s**5 - 7*s**4 + 6*s**3 + 7. Let l(d) = -7*d**5 + 6*d**4 - 5*d**3 - 6. Let v = 1 + -8. Let t(u) = v*l(u) - 6*p(u). Factor t(f).
f**3*(f - 1)*(f + 1)
Let s(f) be the third derivative of 0 + 0*f + 3/8*f**4 + 4*f**2 - 1/40*f**5 - 9/4*f**3. Factor s(l).
-3*(l - 3)**2/2
Find y such that 0 + 1/3*y - 1/6*y**3 + 1/6*y**2 = 0.
-1, 0, 2
Solve 3/4*k**5 - 3/4*k**2 - 3/4*k**3 + 0*k + 3/4*k**4 + 0 = 0 for k.
-1, 0, 1
Let b(m) be the second derivative of 1/50*m**5 - m + 0*m**4 - 2/5*m**2 - 1/5*m**3 + 0. Let b(w) = 0. What is w?
-1, 2
Let w(o) be the second derivative of -o**6/10 + 3*o**5/20 + o**4/4 - o**3/2 + 2*o. Factor w(c).
-3*c*(c - 1)**2*(c + 1)
Let h = 373 + -373. Factor 0*p + h + 1/4*p**2.
p**2/4
Let a(o) be the first derivative of -o**4/4 + 4*o**3/3 - 2*o**2 - 5. Factor a(m).
-m*(m - 2)**2
Suppose -372 = -0*s - 2*s. Suppose 0*j - h + 74 = 2*j, -3*h + s = 5*j. Solve -162/5*m**3 + 16/5 - j*m**2 - 24/5*m = 0.
-2/3, 2/9
Let w(h) = -20*h**5 - 65*h**4 + 25*h**3 + 255*h**2 - 165*h. Let o(c) = 5*c**5 + 16*c**4 - 6*c**3 - 64*c**2 + 41*c. Let v(a) = 15*o(a) + 4*w(a). Factor v(m).
-5*m*(m - 1)**2*(m + 3)**2
Suppose 6*b + 938 = 968. Solve -4/3*i**2 + 4/3 + 2*i + 0*i**4 - 8/3*i**3 + 2/3*i**b = 0.
-1, 1, 2
Let g be (-8)/6 + 4/3. Let f be -2 - (-56)/20 - g. Let f + 32/5*p**2 + 22/5*p + 14/5*p**3 = 0. What is p?
-1, -2/7
Suppose -s + 4*s - 6 = 3*h, 2*h = 0. Suppose s*f = -f. Suppose 1/2*m**2 + f*m - 1/2 = 0. Calculate m.
-1, 1
Let y(b) be the second derivative of -b**4/48 + 2*b. Factor y(i).
-i**2/4
Let p = -20 - -27. Let g(u) = 83*u**3 - 114*u**2 + 24. Let k(i) = -55*i**3 + 76*i**2 - 16. Let z(d) = p*k(d) + 5*g(d). Factor z(r).
2*(r - 1)*(3*r - 2)*(5*r + 2)
Suppose -j = 2*j - 6. Factor -2 + b**4 - 5*b**3 - 11*b**j - 2*b**4 + 2*b**2 - 7*b.
-(b + 1)**3*(b + 2)
Let -1/4*q**5 + 1/2*q**2 + 0*q**3 - 1/2*q**4 + 1/4*q + 0 = 0. What is q?
-1, 0, 1
Let r(j) = -j**4 - j**3 + j**2 + 1. Let v = 2 + 0. Let k(u) = -3*u**4 - 6*u**3 - 4*u**2 - 4*u + 1. Let h(z) = v*r(z) - k(z). Factor h(a).
(a + 1)**4
Let x(k) = -3*k**2 - 10*k + 4. Let r(j) = 11*j**2 + 41*j - 16. Let w(h) = 4*r(h) + 18*x(h). Suppose w(d) = 0. Calculate d.
-2, 2/5
Let i = 11 + -10. Factor 8*p**2 - i + 3/2*p + 2*p**4 + 15/2*p**3.
(p + 1)**2*(p + 2)*(4*p - 1)/2
Let m be (-16)/(-12) + 2/3. Let u = 2 - m. Find z, given that -1/2*z**5 + u - 1/2*z**4 + 1/2*z**2 + 0*z + 1/2*z**3 = 0.
-1, 0, 1
Let i(f) be the first derivative of f**4/20 - f**3/15 - 5. Factor i(s).
s**2*(s - 1)/5
Let a(i) be the third derivative of i**7/1470 + i**6/420 + 12*i**2. Factor a(t).
t**3*(t + 2)/7
Let l(p) = p**3 + 9*p**2 + 7*p - 4. Let s be l(-8). Factor -u**s - 2*u**3 + 0*u + u**2 + 4*u - u - u.
-u*(u - 1)*(u + 1)*(u + 2)
Let x = -18 + 21. Solve -3/2*h**2 - 3*h - 2 - 1/4*h**x = 0 for h.
-2
Let z = 7 + -3. Factor -2*b**2 + b**3 - b**5 + 3*b**2 - 5*b**4 + 4*b**z.
-b**2*(b - 1)*(b + 1)**2
Suppose 4*s = -k + 35, -4*k - 4*s = s - 107. Let g = 70/3 - k. Factor -g*l**2 - 2/3*l + 0.
-l*(l + 2)/3
Determine p, given that -1/6*p**2 + 0 - 1/2*p = 0.
-3, 0
Let c be 132/(-72) - 2/(-6). Let x = c - -9/4. Suppose 1/4*u**4 + 0*u**2 - x*u**3 + 0 + u = 0. Calculate u.
-1, 0, 2
Let t be (-2)/(-1)*(-2)/3790. Let v = 6066/1895 + t. Suppose -2/5*d**4 + 2*d**3 - 8/5*d + v - 12/5*d**2 = 0. Calculate d.
-1, 2
Let k be 22/(-121) - 48/(-22). Let z be k/8 + (-2)/(-8). Find u such that z + u**3 - 1/2*u**2 - u = 0.
-1, 1/2, 1
Let d(a) = -a**2 - 43*a - 300. Let m b