2*u**2 - 2*u**2 + k = 0?
-2, 1
Suppose 19 = 2*c - 5*x, 10 = c + c - 2*x. Let g(l) be the first derivative of -1/2*l**3 - 3/2*l**2 + c + 3/8*l**4 + 0*l. Solve g(z) = 0 for z.
-1, 0, 2
Let k = -6 + 9. Suppose -2*p - 2*n = -4*n - 10, k*n + 9 = 0. Let -5*w**2 + 0*w**p + 2*w**2 + 18*w - 27 = 0. What is w?
3
Let j = -22679/42 - -540. Let z(x) be the second derivative of 0*x**2 + x + 0 + 2/21*x**3 - j*x**4. Let z(y) = 0. Calculate y.
0, 2
Let b be 16/72 + (-129)/(-27). Factor b - 2*o - 5 + 3*o - o**2.
-o*(o - 1)
Let x be (1 - -1)/(3 + -1). Let u be 3/1 + -1 + x. Find t, given that 3*t**3 - 2*t**2 + 2 - 2*t - t**u + 0 = 0.
-1, 1
Factor 4/3*t**2 + 0 + 0*t + 32/3*t**4 + 8*t**3.
4*t**2*(2*t + 1)*(4*t + 1)/3
Let g(z) = -z**3 - 10*z**2 - z - 7. Let t be g(-10). Suppose -n - 2*n = 0. Let 3/4*i**2 + 1/4*i + n + 1/4*i**4 + 3/4*i**t = 0. Calculate i.
-1, 0
Let i = -8 - -17/2. Let z(g) be the first derivative of 3 + 0*g + i*g**4 + 0*g**2 + 2/3*g**3. What is y in z(y) = 0?
-1, 0
Let m = 263 + -781/3. Determine b, given that 2/3*b**3 + m*b**2 + 10/3*b + 4/3 = 0.
-2, -1
Let s(z) = 5*z**4 + 14*z**3 + 19*z**2 + 4*z - 6. Let r(x) = 6*x**4 + 14*x**3 + 19*x**2 + 4*x - 7. Let q(o) = 2*r(o) - 3*s(o). Solve q(m) = 0.
-2, -1, 1/3
Factor 4/9*b**4 + 4/3*b**3 + 0 + 8/9*b - 20/9*b**2 - 4/9*b**5.
-4*b*(b - 1)**3*(b + 2)/9
Let p(t) be the third derivative of -5/8*t**4 - 7/20*t**5 + t**3 + 3*t**2 + 0 + 0*t. Factor p(y).
-3*(y + 1)*(7*y - 2)
Let f(d) be the third derivative of 0*d**4 + 0*d**3 + 4/105*d**7 + 0*d - 1/20*d**6 + 0 - 1/30*d**5 - 2*d**2. Solve f(c) = 0.
-1/4, 0, 1
Factor 9*q**2 + 1 - 2*q**3 + 6*q + 5*q**3 - 1.
3*q*(q + 1)*(q + 2)
Suppose 0 = -2*z + 2*w + 180, -4*z + 0*w = 2*w - 336. Let d be z/10 + -4 + -4. Factor -1/5*t**5 + d*t**4 - 1/5 - 2/5*t**3 + 3/5*t - 2/5*t**2.
-(t - 1)**4*(t + 1)/5
Let a(l) = 13*l**3 - 11*l**2 - 23*l - 4. Let b(x) = 2 - 7*x**3 + 6*x**2 + 3*x + x + 8*x. Suppose 6*f - 14 = 16. Let w(u) = f*b(u) + 3*a(u). Factor w(o).
(o - 2)*(o + 1)*(4*o + 1)
Let c(f) = 34*f - 204. Let k be c(6). Factor k + 6/7*w + 3/7*w**2.
3*w*(w + 2)/7
Let r(a) = a**3 - 5*a**2 + 5*a. Let m be r(4). Let q(p) be the second derivative of 0*p**2 - 1/18*p**m + 0 - p + 1/9*p**3. Factor q(v).
-2*v*(v - 1)/3
Let w(g) be the second derivative of g**6/540 + g**5/90 + 2*g**3/3 - 3*g. Let i(h) be the second derivative of w(h). Factor i(v).
2*v*(v + 2)/3
Determine b, given that -153*b - 3 - 9*b**2 + 12*b**2 - 2*b**3 + 150*b + 5*b**3 = 0.
-1, 1
Let z(k) = -k**3 - 5*k**2 + k + 3. Let a be z(-5). Let w be a/10 + 17/35. Factor -w + 2/7*q**2 + 0*q.
2*(q - 1)*(q + 1)/7
Let x(n) be the second derivative of n**6/165 - n**5/110 - n**4/66 + n**3/33 + 8*n. Suppose x(t) = 0. What is t?
-1, 0, 1
Let b = 659/12 - 209/4. Let 2*c**3 - b*c**4 + 10/9*c**5 - 4/9*c**2 + 0*c + 0 = 0. What is c?
0, 2/5, 1
Let g = 30 - 30. Factor 0 - 2/7*l**3 - 2/7*l**2 + g*l.
-2*l**2*(l + 1)/7
Let 3/4*a**4 + 5/4*a - 1/4*a**2 - 5/4*a**3 - 1/2 = 0. Calculate a.
-1, 2/3, 1
Let w(d) = d**2 + 2*d. Let i be w(-2). Let a(n) be the first derivative of -2*n**2 + 21/2*n**4 + i*n - 2/3*n**3 + 1. Factor a(q).
2*q*(3*q - 1)*(7*q + 2)
Suppose 3*u = -2*u + 20. Let w = u - 4. Factor 2/7*f - 2/7*f**3 + 0 + w*f**2.
-2*f*(f - 1)*(f + 1)/7
Let y(d) be the second derivative of d**5/60 - d**4/4 + 3*d**3/2 - 3*d**2 + 3*d. Let b(f) be the first derivative of y(f). Determine n so that b(n) = 0.
3
Let t(g) be the second derivative of 1/21*g**3 + 1/70*g**5 - 1/21*g**4 - g + 0 + 0*g**2. Factor t(n).
2*n*(n - 1)**2/7
Let w(a) be the first derivative of -a**4/4 + a**3/2 + 3*a**2 + 3*a + 3. Let y(m) be the first derivative of w(m). Suppose y(z) = 0. Calculate z.
-1, 2
Let q(f) be the third derivative of 1/108*f**4 + 0 - 1/540*f**6 - 1/270*f**5 - 10*f**2 + 0*f**3 + 0*f + 1/945*f**7. Factor q(c).
2*c*(c - 1)**2*(c + 1)/9
Let k(i) be the second derivative of i**4/66 + 8*i**3/33 + 16*i**2/11 + 7*i. Let k(t) = 0. Calculate t.
-4
Let o(a) be the second derivative of -a**4/12 - 7*a**3/6 - 5*a**2 + 3*a - 6. What is q in o(q) = 0?
-5, -2
Let z be (2/5)/(3/45). Let r be (12/(-32))/(z/(-4)). Factor 1/4 + 1/2*p + r*p**2.
(p + 1)**2/4
Let t = 17 + -7. Let -t*o - 6*o**2 - 3*o**3 + 15*o + 6 - 2*o = 0. Calculate o.
-2, -1, 1
Let u(l) = 3*l**2 - 2*l + 4. Let t(k) = -3*k - k**2 + 0*k + 0*k + 4*k - 2. Let o(p) = 5*t(p) + 2*u(p). Factor o(q).
(q - 1)*(q + 2)
Let q(l) = l**2 - 18*l + 19. Let n be q(17). Factor -1/4*v**4 + 0 + 1/4*v**n + 1/2*v**3 - 1/2*v.
-v*(v - 2)*(v - 1)*(v + 1)/4
Let c(b) be the second derivative of -b**6/120 - 5*b**3/6 + 8*b. Let x(q) be the second derivative of c(q). Let x(k) = 0. Calculate k.
0
Let 0*g + 0 + 5/2*g**2 + 3*g**3 = 0. What is g?
-5/6, 0
Let s(f) be the third derivative of f**7/1260 + f**6/360 - f**5/120 - f**4/36 + 4*f**3/3 + 2*f**2. Let l(t) be the first derivative of s(t). Factor l(c).
(c - 1)*(c + 2)*(2*c + 1)/3
Let t(m) = -m**2 + 5*m - 4. Let n be t(3). Factor -b**n + 78*b - 50*b**2 - 181*b**2 + 172*b**3 - 32 + 66*b + 8*b**5 - 60*b**4.
4*(b - 2)**3*(b - 1)*(2*b - 1)
Let b be 7/15 - 1/(-3). Let f = 62 + -60. Determine k so that -2/5*k**f + b + 2/5*k = 0.
-1, 2
Let q = -1/5 + 11/30. Let b(y) be the first derivative of -q*y**3 + 1 + 0*y**2 + 1/12*y**6 + 1/10*y**5 + 0*y - 1/8*y**4. Let b(t) = 0. Calculate t.
-1, 0, 1
Let u(g) be the second derivative of g**7/357 - 4*g**6/255 + g**5/34 - g**4/51 - 5*g. Factor u(k).
2*k**2*(k - 2)*(k - 1)**2/17
Factor -200/3 - 2/3*k**2 - 40/3*k.
-2*(k + 10)**2/3
Let y(n) = n**4 - n**3 - 1. Let d = 7 - 6. Let f(a) = 8*a**2 + 6*a - 10*a**4 + 6 + 2*a**5 + 9*a - 7*a. Let b(r) = d*f(r) + 6*y(r). Factor b(o).
2*o*(o - 2)**2*(o + 1)**2
Let r(i) be the first derivative of -i**4/20 + i**2/10 + 42. Factor r(k).
-k*(k - 1)*(k + 1)/5
Let c(j) be the second derivative of j**4/16 - 29*j**3/24 + 9*j**2/4 - 40*j. Factor c(t).
(t - 9)*(3*t - 2)/4
Determine u, given that -2*u + 8*u**2 + 2*u + 11*u**4 - 3*u**4 + 20*u**3 = 0.
-2, -1/2, 0
Suppose 0 = d - 5, -3*d = -3*c + 2*c - 15. Factor c*s**3 + 24*s**2 - s**4 + 12*s**3 + 12*s + 3*s**3 + 4*s**4.
3*s*(s + 1)*(s + 2)**2
Let d be (0 + -1)*(-1 - 4). Factor 2 + 2*c**4 + 2*c - 4*c**2 + 0*c**5 + c**d + c**5 - 4*c**3.
2*(c - 1)**2*(c + 1)**3
Let i = -35 - -3. Let k = -29 - i. Factor 0 - 4/5*q**2 - 2/5*q**k + 0*q.
-2*q**2*(q + 2)/5
Let u(k) = 12*k**2 + 9*k + 4. Let p(r) = -4*r**3 + r. Let t be p(1). Let q(o) = 35*o**2 + 28*o + 12. Let g(j) = t*q(j) + 8*u(j). Factor g(a).
-(3*a + 2)**2
Let a(g) be the first derivative of g**4/20 - 3*g**2/10 + 2*g/5 - 6. Factor a(l).
(l - 1)**2*(l + 2)/5
Let j(c) be the first derivative of 5*c**4/4 + 25*c**3/3 + 20*c**2 + 20*c + 26. Factor j(f).
5*(f + 1)*(f + 2)**2
Suppose 0 - 12*v**2 - 2*v - 45/2*v**3 - 25/2*v**4 = 0. What is v?
-1, -2/5, 0
Let z = -9 - -12. Let w = 5 - z. Factor -1/2*s**w + 1/4*s**5 + 1/2*s**4 + 0 + 0*s**3 - 1/4*s.
s*(s - 1)*(s + 1)**3/4
Let l(g) be the first derivative of -2 + 0*g + 4/3*g**3 - 3/2*g**4 + 0*g**2 + 2/5*g**5. Determine h, given that l(h) = 0.
0, 1, 2
Let s(i) be the third derivative of i**7/525 - i**6/75 + i**5/25 - i**4/15 + i**3/15 + 2*i**2. Factor s(a).
2*(a - 1)**4/5
Let q = -132 - -136. Let -9/4*t**q - 6*t**3 - 11/2*t**2 - 1/4 - 2*t = 0. Calculate t.
-1, -1/3
Suppose h + 9 = 2*h - 5*s, -5*s - 3 = -2*h. Let j = 6 + h. Factor -2*f**2 - 2*f**2 - f**5 + f**4 + 2*f**4 + j*f**4.
-f**2*(f - 2)**2*(f + 1)
Suppose -m = m + 214. Let n = 759/7 + m. Find o, given that 2*o**3 - n*o**4 - 16/7*o + 8/7 + 2/7*o**2 + 2/7*o**5 = 0.
-1, 1, 2
Let f = -32 + 27. Let q be 3 + -1*f/(-3). Factor -10/3*m - q - 2/3*m**3 - 8/3*m**2.
-2*(m + 1)**2*(m + 2)/3
Let u(x) be the first derivative of x**6/2 + 21*x**5/20 + 3*x**4/8 - x**3/4 + 7. Factor u(b).
3*b**2*(b + 1)**2*(4*b - 1)/4
Find j such that 3*j + 1/2 + 5/2*j**2 = 0.
-1, -1/5
Let o be ((-2)/6)/(8/(-6)). Suppose -33 + 9 = -8*p. What is i in 1/4*i**p + 0*i + 1/4*i**4 - 1/4*i**5 - o*i**2 + 0 = 0?
-1, 0, 1
Let q(c) be the third derivative of 1/20*c**4 - 2*c**2 + 1/175*c**7 - 1/75*c**5 + 0 - 1/150*c**6 - 1/15*c**3 + 0*c - 1/840*c**8. Factor q(w).
-2*(w - 1)**4*(w + 1)/5
Let s(l) be the first derivative of l**4/20 - l**3/5 + l**2/5 + 4. Let s(d) = 0. What is d?
0, 1, 2
Let d(x) be the third derivative of x**7/1155 + x**6/165 + x**5/66 + x**4/66 - 14*x**2. Factor d(m).
2*m*(m + 1)**2*(m + 2)/11
Le