0, 1
Suppose -3*o = -2 - 1. Let a be o/1*(1 + 2). Determine n, given that -2*n**4 - 2*n**2 + 3*n - 3*n**3 - 2*n**a - 2*n**2 - 4*n = 0.
-1, -1/2, 0
Let q be 52/6 + 2/(-3). Let s = -6 + q. Suppose 6*b**2 + b + s - 3*b + 2*b**3 + 8*b = 0. What is b?
-1
Suppose 2*t - 15 = -3*t. Suppose -t*z + 2*q = 4 - 14, 5 = -z - q. Determine r so that 0 + 3/4*r**3 - 3/4*r**4 + 1/4*r**5 - 1/4*r**2 + z*r = 0.
0, 1
Let r(x) be the third derivative of -x**6/40 - x**5/4 - 7*x**4/8 - 3*x**3/2 + 10*x**2. Factor r(g).
-3*(g + 1)**2*(g + 3)
Let a(p) be the third derivative of p**10/105840 + p**9/26460 - p**7/4410 - p**6/2520 - p**4/24 - p**2. Let b(d) be the second derivative of a(d). Factor b(t).
2*t*(t - 1)*(t + 1)**3/7
Suppose 3*g - 2*o - 20 + 4 = 0, -o = -g + 7. Let p be (2 + -3 + 1)/g. Factor p - 2*s**2 + 2*s + 1/2*s**3.
s*(s - 2)**2/2
Let c be -69*(-4)/(-148) - -2. Let h = c + 123/185. Let h*i + 2/5*i**2 + 0 = 0. What is i?
-2, 0
Suppose 0*x**2 - 3/8 - 3/4*x**3 + 3/4*x + 3/8*x**4 = 0. Calculate x.
-1, 1
Let t(z) be the third derivative of 0 + 6*z**2 + 1/90*z**5 + 0*z + 1/18*z**4 + 1/9*z**3. Solve t(k) = 0 for k.
-1
Factor 59 - 55 - 3*c**2 + c**4 - c - 3*c**3 + c**3 + 5*c.
(c - 2)**2*(c + 1)**2
Let x = 49/6 - 23/3. Factor -x*r**2 + 0 + r**3 - 1/2*r.
r*(r - 1)*(2*r + 1)/2
Let k = 0 + 2. Find a such that -2 + 7*a**k + 2*a + 1 - 2*a**3 - 1 - 5*a**2 = 0.
-1, 1
Let o(l) be the first derivative of l**6/168 - l**5/210 - 5*l**4/168 + l**3/21 + 3*l**2/2 - 2. Let b(x) be the second derivative of o(x). Factor b(d).
(d - 1)*(d + 1)*(5*d - 2)/7
Let y(b) be the second derivative of -b**6/60 + b**5/30 + b**2/2 - 4*b. Let l(x) be the first derivative of y(x). Factor l(c).
-2*c**2*(c - 1)
Factor 0 + 7/5*x - 1/5*x**2.
-x*(x - 7)/5
Let y(a) be the first derivative of a**4/6 - a**2 - 4*a/3 + 19. Factor y(i).
2*(i - 2)*(i + 1)**2/3
Let r(n) be the third derivative of -n**8/1176 - n**7/105 - n**6/30 - n**5/105 + 5*n**4/28 + 3*n**3/7 - 18*n**2. Determine j, given that r(j) = 0.
-3, -1, 1
Let w(y) be the second derivative of 0*y**5 + 0 + 0*y**3 + y - 1/21*y**7 + 0*y**6 + 0*y**2 + 0*y**4. What is k in w(k) = 0?
0
Let t(c) be the third derivative of -c**6/60 - c**5/15 - c**4/12 + 7*c**2. Let t(d) = 0. Calculate d.
-1, 0
Suppose -5*f - 4*k = -2*f - 4, 3*f - 3*k - 18 = 0. Factor 3 + 3 - 3*t**f + 3*t**2 - 6 + 3*t - 3*t**3.
-3*t*(t - 1)*(t + 1)**2
Let f(u) be the first derivative of -2 + 2/3*u**3 + 1/3*u**2 + 0*u. Determine n so that f(n) = 0.
-1/3, 0
Suppose 3/8*r**5 + 123/8*r + 15/4 + 21/4*r**4 + 24*r**2 + 69/4*r**3 = 0. What is r?
-10, -1
Let f(s) = 7*s**5 - 6*s**4 - 11*s**3 + 4*s**2 + 6*s + 2. Let l(o) = -20*o**5 + 18*o**4 + 33*o**3 - 12*o**2 - 19*o - 7. Let p(y) = -7*f(y) - 2*l(y). Factor p(q).
-q*(q - 1)**2*(3*q + 2)**2
Let h(v) = v**2 + v - 6. Let d(j) = j**2 + j - 6. Let c(n) = 6*d(n) - 7*h(n). Suppose c(s) = 0. Calculate s.
-3, 2
Let m(l) = l. Let r(s) = -s - 2. Let i be r(-2). Let b be m(i). Factor 1/3*z**3 + b + 0*z**2 - 1/3*z**5 + 0*z**4 + 0*z.
-z**3*(z - 1)*(z + 1)/3
Let g(a) be the first derivative of 9*a**4/5 - 52*a**3/5 - 58*a**2/5 - 4*a - 20. Solve g(i) = 0.
-1/3, 5
Let y(w) be the second derivative of -w**7/105 - w**6/30 - w**5/30 - 2*w**2 - 4*w. Let x(o) be the first derivative of y(o). Factor x(b).
-2*b**2*(b + 1)**2
Let h be (5 + -3)*(-10)/(-4). Suppose -4*k**2 + 2*k**4 + k - 13*k**5 + 2*k**2 + 12*k**h = 0. Calculate k.
-1, 0, 1
Let l(i) be the first derivative of -i**6/300 + i**4/60 - i**2 + 4. Let j(f) be the second derivative of l(f). Factor j(c).
-2*c*(c - 1)*(c + 1)/5
Let 0 - 4/3*g**3 + 4*g**2 - 8/3*g = 0. Calculate g.
0, 1, 2
Let p be 1/(-5)*(-6 - (-1 + -3)). Find y such that 0 + p*y**3 + 0*y - 2/5*y**2 = 0.
0, 1
Let r(k) = -2 + 1 + 7 + k. Let t be r(0). Factor n - n**4 + n + 6*n**3 + t*n**2 + 3*n**4.
2*n*(n + 1)**3
Let p(d) = -11*d**4 + 11*d**3 + 15*d**2 + 7*d - 7. Let t(g) = -6*g**4 + 6*g**3 + 8*g**2 + 4*g - 4. Let l(o) = 4*p(o) - 7*t(o). Factor l(h).
-2*h**2*(h - 2)*(h + 1)
Let u(c) = c**2 - 6*c + 5. Let z be u(6). Let 2*f**2 + f - z*f**2 + 0*f + 2*f**2 = 0. Calculate f.
0, 1
Let x(m) be the first derivative of -m**5/30 + m**4/6 + m**3 + 4*m**2 - 6. Let q(f) be the second derivative of x(f). Factor q(y).
-2*(y - 3)*(y + 1)
Let i = 487/195 + -37/15. Let t = 3/13 - i. Find n such that 0 + 3/5*n**3 + 1/5*n**4 + 3/5*n**2 + t*n = 0.
-1, 0
Factor 0 - 8/3*o**5 + 1/6*o**2 + 4*o**4 + 0*o - 3/2*o**3.
-o**2*(o - 1)*(4*o - 1)**2/6
Let u(j) = -6*j**2 + 4*j - 2. Let k(w) = -w**2 - 1 - 1 + w + 3 - 2. Let n(s) = 4*k(s) - u(s). Factor n(z).
2*(z - 1)*(z + 1)
Let k(d) be the third derivative of -5*d**5/18 - 5*d**4/9 - 4*d**3/9 + 32*d**2. Let k(w) = 0. Calculate w.
-2/5
Let v(s) be the second derivative of -s**6/15 + s**5/20 + s**4/6 - s**3/6 - 6*s. Determine c, given that v(c) = 0.
-1, 0, 1/2, 1
Let i(n) be the second derivative of 5*n**4/12 - n**3/2 - 4*n**2 - 74*n. Determine o so that i(o) = 0.
-1, 8/5
Let p(r) be the second derivative of 3*r**5/40 + r**4/4 - r**3/4 - 3*r**2/2 - 14*r. Factor p(k).
3*(k - 1)*(k + 1)*(k + 2)/2
Let x(c) be the second derivative of -c**8/3360 + c**6/360 - c**4/6 - c. Let b(r) be the third derivative of x(r). Factor b(w).
-2*w*(w - 1)*(w + 1)
Suppose 4*k - 9 - 10 = -3*b, k + 5*b = -8. Suppose f = -4*m + 3, -k - 5 = -m + 2*f. Find j such that 36/5*j**3 + 81/5*j**4 + 0 + 0*j + 4/5*j**m = 0.
-2/9, 0
Let t(v) be the second derivative of -3*v**5/20 - 5*v**4/4 - 4*v**3 - 6*v**2 - 5*v. Let t(m) = 0. Calculate m.
-2, -1
Let i = -7 - -10. Suppose -h + 16 = 3*r, 8 = h + i*r - 2*r. Factor h*g**2 + g - 5*g - 6*g**2.
-2*g*(g + 2)
Let r(c) = 3*c**3 - c**2 + 2*c - 1. Let l be r(1). Factor 1/2 + 1/2*n**4 - n**2 + 0*n**l + 0*n.
(n - 1)**2*(n + 1)**2/2
Let v(b) be the third derivative of b**8/5040 - b**6/1080 - 2*b**3/3 + 3*b**2. Let o(y) be the first derivative of v(y). Factor o(h).
h**2*(h - 1)*(h + 1)/3
Let a = 26/21 - -2/21. Factor a*d + 4/3*d**2 + 0 + 1/3*d**3.
d*(d + 2)**2/3
Let g(x) be the third derivative of -x**5/90 + 5*x**4/36 - 2*x**3/3 + 5*x**2. Solve g(d) = 0.
2, 3
Let w(m) = 7*m**2 - 43*m + 36. Let u(p) = 8*p**2 - 44*p + 36. Let t(v) = -3*u(v) + 4*w(v). Suppose t(h) = 0. What is h?
1, 9
Suppose -6*b = -2*b - 672. Let 16 + 3*q**3 - b*q**2 + 180*q**2 + 24*q - q**3 = 0. Calculate q.
-2
Let d(l) be the third derivative of 1/96*l**5 + 0*l - 1/24*l**3 - 6*l**2 - 1/192*l**4 - 1/560*l**7 + 0 + 1/960*l**6. Solve d(s) = 0 for s.
-1, -2/3, 1
Solve -2/5 + 7/5*y**2 + 1/5*y - y**4 + 1/5*y**3 - 2/5*y**5 = 0 for y.
-2, -1, 1/2, 1
Suppose -4*f = -3*f - 3. Suppose 13 = 5*o - f*i, -o - 5*i - 1 = -2*i. What is g in -2/11*g**o + 0 + 2/11*g = 0?
0, 1
Let r = 13/2 + -269/42. Let n(u) be the first derivative of r*u**3 + 8/7*u + 4/7*u**2 - 3. Factor n(i).
2*(i + 2)**2/7
Let l = 185/3 - 61. Factor -4/3*x + 2/3 + l*x**2.
2*(x - 1)**2/3
Let k(g) be the first derivative of 1/21*g**3 - 1 + 3/28*g**4 + 0*g + 0*g**2 + 1/42*g**6 + 3/35*g**5. Factor k(h).
h**2*(h + 1)**3/7
Let j be (-1 - -1)*1/2. Let x = 37 + -35. Factor -1/4*o - 1/4*o**3 - 1/2*o**x + j.
-o*(o + 1)**2/4
Let i(y) be the third derivative of y**9/302400 + y**8/33600 + y**7/12600 + y**5/30 + 4*y**2. Let z(t) be the third derivative of i(t). Let z(o) = 0. What is o?
-2, -1, 0
Let a be (-2 - (-8)/4)*-1. Factor 0*x**4 + a*x**3 - 8 - 4*x**3 - 2*x**4 + 0*x + 6*x**2 + 8*x.
-2*(x - 1)**2*(x + 2)**2
Let l(p) be the third derivative of 0*p**3 + 7*p**2 + 0 + 0*p - 1/330*p**5 - 1/132*p**4. Solve l(c) = 0 for c.
-1, 0
Suppose -2*c = 3*s - 4*s + 8, -2*c - 8 = 0. Let a(z) be the first derivative of 0*z**2 + s*z**3 - 2 + 0*z + 1/16*z**4. Suppose a(u) = 0. Calculate u.
0
Let w be 11 + -4*(-4)/16. Suppose 0 = -4*k - 0 + w. Determine x, given that 0 + 1/4*x**k + 0*x + 1/4*x**2 = 0.
-1, 0
Let z be (136/12)/(6/9). Find x, given that 3*x**2 - z*x**2 - x**2 - 27*x**4 - 66*x**3 + 18*x**3 + 6*x = 0.
-1, 0, 2/9
Let b(x) = 2*x**2 + 1. Let t(o) be the second derivative of o**4/12 + o**2/2 + o. Let h(g) = 2*b(g) - 3*t(g). Factor h(q).
(q - 1)*(q + 1)
Let z(p) be the third derivative of -p**8/20160 - p**7/3360 - p**5/15 + 3*p**2. Let w(g) be the third derivative of z(g). Factor w(f).
-f*(2*f + 3)/2
What is i in -4*i**4 - 5*i**2 - 5 + 24*i**4 + 15*i**3 - 7*i**4 - 3*i**4 - 15*i = 0?
-1, -1/2, 1
Let k(b) be the first derivative of -b**4/36 - b**3/18 + 2