*s. Determine o so that a(o) = 0.
0, 2
Let b(v) be the second derivative of 3*v**5/10 - v**4/4 - v**3/2 + 6*v. Suppose b(p) = 0. What is p?
-1/2, 0, 1
Let p(g) be the second derivative of -3*g**5/10 + 7*g**4/8 - g**3/2 - 3*g**2/4 - 53*g. Suppose p(u) = 0. Calculate u.
-1/4, 1
Let n be 1/(-2)*(2 + -2). Let w be ((-4)/18)/(1/((-9)/6)). Determine h so that n + w*h**4 - 1/3*h**2 - 1/3*h**3 + 1/3*h**5 + 0*h = 0.
-1, 0, 1
Factor -10*b**4 - 65/2*b**2 - 15*b - 30*b**3 - 5/2.
-5*(b + 1)**2*(2*b + 1)**2/2
Let j(p) = 8*p**3 + 25*p**2 - 133*p + 203. Let l(d) = -3*d**3 - 8*d**2 + 44*d - 68. Let f(s) = -4*j(s) - 11*l(s). Factor f(q).
(q - 4)**3
Let u(k) be the third derivative of 0 + 1/240*k**6 - k**2 + 0*k**3 + 0*k**4 + 0*k + 1/120*k**5. Determine d, given that u(d) = 0.
-1, 0
Let b(w) be the second derivative of w**7/2100 - w**6/900 + 2*w**3/3 - 3*w. Let h(u) be the second derivative of b(u). Find z such that h(z) = 0.
0, 1
Let v(c) be the third derivative of 0*c + 1/15*c**5 - 1/4*c**4 - 1/35*c**7 + 0 - c**2 + 1/3*c**3 + 1/30*c**6 + 1/168*c**8. Let v(m) = 0. Calculate m.
-1, 1
Factor -12/7*p**2 + 8/7*p + 2/7*p**4 + 10/7 - 8/7*p**3.
2*(p - 5)*(p - 1)*(p + 1)**2/7
Let z(r) = 8*r**4 + 14*r**3 + 14*r**2 + 8*r + 5. Let g(x) = 9*x**4 + 15*x**3 + 15*x**2 + 9*x + 6. Let y(u) = -5*g(u) + 6*z(u). Suppose y(o) = 0. What is o?
-1, 0
Let t = 13/244 + 12/61. Find l, given that 0 + 1/2*l**2 + 0*l - t*l**3 = 0.
0, 2
Let n be 0 - 0 - (-2)/6. Suppose 6*t + 4*i = 2*t + 16, 3*i = 3. Find g such that 1/3 + 1/3*g - 1/3*g**t - n*g**2 = 0.
-1, 1
Suppose n**2 + 36 + 22*n + 9*n - 43*n = 0. Calculate n.
6
Let z(h) = -4*h**2 + 16*h - 34. Let q(a) = -a**2 - 1. Let i(d) = -2*q(d) + z(d). Solve i(p) = 0 for p.
4
Let p be (12*4/138)/2. Let v = p - -34/69. Suppose 1/3 - 1/6*t**3 + v*t**2 - 5/6*t = 0. What is t?
1, 2
Let j be ((-12)/42 + 48/21)/1. Factor 2/11*y - 4/11*y**3 + 2/11*y**j + 0.
-2*y*(y - 1)*(2*y + 1)/11
Suppose 5 - 5 = 18*n. Let -1/7*c**2 + n + 0*c + 2/7*c**3 - 1/7*c**4 = 0. What is c?
0, 1
Let c(w) = w**4 - w**2 + w - 1. Let z(n) = 2*n**4 - 3*n**3 + 2*n**2 - 1. Let g(m) = c(m) - z(m). Factor g(i).
-i*(i - 1)**3
Let h be (-6 - 23/(-4))/(-12). Let d(i) be the second derivative of -1/8*i**2 + 0 - h*i**4 + 2*i - 1/12*i**3. Factor d(x).
-(x + 1)**2/4
Suppose 5*v + a - 22 = 0, v - 3*a + 16 = 6*v. Determine y, given that 0 + 1 - 16*y**2 + 0 - v - 20*y = 0.
-1, -1/4
Solve 9*x**3 + 20*x**3 - 12*x + 3*x**4 - 6*x**4 - 20*x**3 = 0.
-1, 0, 2
Solve 4/7*w**2 + 4/7*w**4 - 8/7 - 12/7*w + 12/7*w**3 = 0.
-2, -1, 1
Let y(v) be the third derivative of v**5/30 + v**4/2 + 3*v**3 - 11*v**2. Factor y(i).
2*(i + 3)**2
Let r be (-1)/(-4 - -2)*(-3)/(-2). Determine b, given that -3/2*b**2 + 3/4*b**5 + 9/4*b**4 - 9/4*b - r + 3/2*b**3 = 0.
-1, 1
Let g be 2/12 + (-1)/30. Let d(c) be the first derivative of 0*c - 1/3*c**2 - 2 + 1/6*c**4 - g*c**5 + 2/9*c**3. Factor d(m).
-2*m*(m - 1)**2*(m + 1)/3
Determine l so that -4/3 - 2/3*l**2 - 2*l = 0.
-2, -1
Let y = 6/17 + 5/34. Solve 3*z - 2*z**5 - y - 4*z**2 + 9/2*z**4 - z**3 = 0.
-1, 1/4, 1
Suppose -15 = -3*l, 2*g - 4*g + 70 = 4*l. Let f be (-18)/(-15)*g/10. Factor 1/4*m + 0*m**2 + 0 - 1/4*m**f.
-m*(m - 1)*(m + 1)/4
Let v be (4/6)/((-7)/(-21)). Let 5*j**2 - 12*j + 5 + j**v - 3 + 20*j**3 = 0. What is j?
-1, 1/5, 1/2
Let k(l) = -4*l**3 + 5*l**2 + 2*l + 3. Let q(a) = 3*a**3 - 4*a**2 - a - 2. Let o(n) = -2*k(n) - 3*q(n). Suppose o(z) = 0. Calculate z.
0, 1
Let m(f) = -f**4 + f**3 + f**2 + f. Let r(u) = -2*u**4 + 11*u**3 + 11*u**2 + 6*u. Let d(s) = -4*m(s) + r(s). Factor d(c).
c*(c + 1)*(c + 2)*(2*c + 1)
Determine z, given that 12/5*z**3 + 0 + 8/5*z**2 - 2/5*z**5 - 2/5*z**4 - 16/5*z = 0.
-2, 0, 1, 2
Let k(v) be the third derivative of v**6/30 - v**5/3 + 4*v**4/3 - 8*v**3/3 + 6*v**2. Factor k(w).
4*(w - 2)**2*(w - 1)
Let n(z) = -7*z - 3. Let p(s) = -2*s + 15. Let w be p(8). Let o be n(w). Suppose 0*l**3 - l**2 + 1/2*l**o + 1/2 + 0*l = 0. What is l?
-1, 1
Let s = -15 + 18. Let x(t) be the third derivative of 1/36*t**4 - 2/315*t**7 + 3*t**2 + 0 + 0*t - 1/504*t**8 + 0*t**s + 1/45*t**5 + 0*t**6. Factor x(j).
-2*j*(j - 1)*(j + 1)**3/3
Let m(g) = 17*g**3 + 17*g**2 + 2*g - 2*g. Let p(j) = -8*j**3 - 8*j**2. Let h(t) = 6*m(t) + 13*p(t). What is u in h(u) = 0?
-1, 0
Let w be (-3)/(3 + (-18)/4). Let v be (-26)/(-12) + (-4)/6. Factor 0 - 1/4*o - v*o**3 - 1/4*o**5 - o**w - o**4.
-o*(o + 1)**4/4
Suppose 6*b = b. Let h(j) be the third derivative of -j**2 + 2/15*j**5 + b*j**3 + 7/60*j**6 + 0*j + 2/105*j**7 - 1/3*j**4 + 0. Factor h(a).
2*a*(a + 2)**2*(2*a - 1)
Let r(v) be the second derivative of 3*v**5/20 - 3*v**4/4 + 6*v**2 - 17*v. Factor r(a).
3*(a - 2)**2*(a + 1)
Let z = 75/7 - 218/21. Factor -z*k - 1/3*k**3 + 2/3*k**2 + 0.
-k*(k - 1)**2/3
Let b(n) = -n**3 + 3*n**2 + 2*n + 1. Let x be b(3). Suppose 4*d - 12 = 0, -o + d + 2*d = x. Determine u so that -o*u**4 - 4*u**3 - u**3 + 3*u**3 = 0.
-1, 0
Suppose 0 = -6*d + 3*d. Solve -q**2 + 0*q**2 + d - 3*q + 4*q + 2 = 0.
-1, 2
Let p(q) = -q**2 - 6*q + 1. Let d be p(-6). Suppose -5*h - u + d = -4, -5*h - 2*u + 10 = 0. Factor 1/5*t**2 + h + 1/5*t.
t*(t + 1)/5
Suppose 2*i - 3 - 17 = 3*y, y - 20 = -i. Let u be 2/(-6)*i/(-8). Factor 2/3*q**2 - 4/3*q + u.
2*(q - 1)**2/3
Solve 0*y + 4/5*y**3 + 2/5*y**2 + 0 + 2/5*y**4 = 0.
-1, 0
Let v(m) = 9*m**5 - 5*m**4 - 8*m**3 + 6. Let a(d) = 17*d**5 - 10*d**4 - 15*d**3 + 11. Let g(c) = 6*a(c) - 11*v(c). Factor g(q).
q**3*(q - 2)*(3*q + 1)
Suppose d = 2 + 1. Suppose -d*h + 4*h - 4 = 0. Solve 5*j**2 + 3 - h*j**2 - 4 = 0 for j.
-1, 1
Let b(r) be the second derivative of 1/14*r**7 + 0*r**2 + 0 - 7/30*r**6 + 3*r + 0*r**3 + 1/4*r**5 - 1/12*r**4. Find l, given that b(l) = 0.
0, 1/3, 1
Suppose -105 = -52*q + 31*q. What is f in 1/8*f - 11/8*f**4 - 7/4*f**3 + 1/8 - 3/4*f**2 - 3/8*f**q = 0?
-1, 1/3
Let g be (-88)/(-484) + 5/33. Solve -1/3 + 1/3*l**2 + 1/3*l - g*l**3 = 0 for l.
-1, 1
Let m be -1 - 2 - (-10)/2. Factor 1 + 2 - 17*z**2 + 14*z**m.
-3*(z - 1)*(z + 1)
Let x be 16/7 - (-2)/(-7). Let -x + 2*u**2 - 8*u**2 - 7*u + u**2 = 0. Calculate u.
-1, -2/5
Suppose 0 - 1/5*q**4 - 1/5*q**3 + 1/5*q**5 + 1/5*q**2 + 0*q = 0. What is q?
-1, 0, 1
Let s(f) = 4*f**5 - 4*f**3 - 7*f + 7. Let j(h) = -4*h**5 + 4*h**3 + 6*h - 6. Let w(r) = -7*j(r) - 6*s(r). Factor w(b).
4*b**3*(b - 1)*(b + 1)
Let a(b) be the second derivative of b**7/945 - b**6/270 + b**4/54 - b**3/27 - 2*b**2 - 5*b. Let g(w) be the first derivative of a(w). Factor g(j).
2*(j - 1)**3*(j + 1)/9
Let m(q) = -7*q**5 + 2*q**4 + 7*q**3 + 3*q**2 + 5*q - 5. Let o(i) = -8*i**5 + 2*i**4 + 8*i**3 + 4*i**2 + 6*i - 6. Let x(p) = -6*m(p) + 5*o(p). Solve x(w) = 0.
-1, 0, 1
Let p(z) = -z + 5. Let v be p(13). Let t be 35/168 + (-1)/v. Factor 1/3*a - 1/3*a**3 + 0 + t*a**2 - 1/3*a**4.
-a*(a - 1)*(a + 1)**2/3
Suppose 4*o - 25 = -o. Suppose -o*l + 3 + 8 = -3*x, -5*x = 2*l - 23. Factor -9*y**4 + 12*y**2 - 3*y**x + 4*y - 3*y**3 - y**2 - 4.
-(y + 1)**2*(3*y - 2)**2
Let z be (-19)/(-30) - (-42)/(-70). Let o(i) be the third derivative of 0*i**3 - 1/12*i**4 - z*i**5 + 0*i + 0 + 1/30*i**6 + i**2. Factor o(h).
2*h*(h - 1)*(2*h + 1)
Let w(z) be the first derivative of -z**4/12 + z**3/6 + 2*z - 2. Let f(r) be the first derivative of w(r). Let f(g) = 0. Calculate g.
0, 1
Suppose -1/3*h + 7/6*h**2 - 7/6*h**4 + 1/3*h**3 + 0 = 0. Calculate h.
-1, 0, 2/7, 1
Let t = 3702/5 + -740. Factor -t*f**5 - 6/5*f**3 + 0*f + 18/5*f**2 - 2*f**4 + 0.
-2*f**2*(f - 1)*(f + 3)**2/5
Suppose 21*m - 42 = 7*m. Let l(j) be the second derivative of 0 - 2/9*j**2 + 1/54*j**4 - 1/27*j**3 - m*j. Factor l(x).
2*(x - 2)*(x + 1)/9
Suppose 0 + 2/3*m**2 + 2*m**3 + 2/3*m**5 + 0*m + 2*m**4 = 0. Calculate m.
-1, 0
Find b such that -12/11*b - 6/11*b**2 + 18/11 = 0.
-3, 1
Let q = 11 + -9. Factor 1 + 3 + l**q + 16*l + 6*l**2.
(l + 2)*(7*l + 2)
Factor -1/3*s**3 + s**2 - s + 1/3.
-(s - 1)**3/3
Let a(u) be the first derivative of 1/3*u**3 + 0*u + 1/2*u**2 + 2. Factor a(b).
b*(b + 1)
Let q(n) = n**3 - 2*n**2 - 4*n - 4. Let s(k) = 6*k**3 - 9*k**2 - 21*k - 21. Let w(r) = 21*q(r) - 4*s(r). Find o, given that w(o) = 0.
-2, 0
Suppose -4 = -r - r. Let u(n) be the third derivative of 1/3*n**3 + 2*n**r - 1/4*n**4 - 1/60*n**6 + 0 + 0*n + 1/10*n**5. Determine x so that u(x) = 0.
1
Let b(n) be the first derivative of -2*n**3/3 + 8*n + 18. Find t such that b(