 1
Suppose 2*i = 4*c - 5 - 3, 21 = 5*c + 3*i. Let f(p) be the first derivative of 0*p - 1/15*p**c - 1/25*p**5 + 1/10*p**4 - 1 + 0*p**2. Let f(n) = 0. What is n?
0, 1
Solve -5*h**2 + 0*h**3 - 2 - 11*h + 2*h**3 + 7*h**4 + 2*h + 7*h**3 = 0.
-1, -2/7, 1
Let f(z) be the first derivative of -7*z**6/39 + 24*z**5/65 + 2*z**4/13 - 28*z**3/39 + 3*z**2/13 + 4*z/13 - 10. Suppose f(h) = 0. What is h?
-1, -2/7, 1
Factor 5/4*t**2 + 0 - 5/4*t**4 + 5/4*t**3 - 5/4*t.
-5*t*(t - 1)**2*(t + 1)/4
Let x(k) be the second derivative of -3*k + 0 + 2/21*k**3 + 0*k**2 + 1/42*k**4. What is q in x(q) = 0?
-2, 0
Let w(h) be the first derivative of -h**6/3 + 11*h**4/2 + 12*h**3 + 8*h**2 - 4. Determine g, given that w(g) = 0.
-2, -1, 0, 4
Let z be -14 - -14 - (-2)/8. Let q(w) be the first derivative of -z*w**2 - 1/12*w**3 - 2 + 0*w. Factor q(i).
-i*(i + 2)/4
Let x(m) be the third derivative of m**5/210 + m**4/42 + m**3/21 - 13*m**2. Factor x(y).
2*(y + 1)**2/7
Let w(g) be the second derivative of g**7/189 + g**6/27 + g**5/15 - 2*g**4/27 - 8*g**3/27 + 20*g. Determine c, given that w(c) = 0.
-2, 0, 1
Let l(w) = 3*w**2 - 8*w. Let c(r) = -30*r**2 + 81*r. Let i(d) = 2*c(d) + 21*l(d). Determine h so that i(h) = 0.
0, 2
Let n(v) be the first derivative of 0*v - 1/2*v**2 - 3 - 1/3*v**3. Let l(a) = 5*a**2 + 3*a + 1. Let g(m) = 2*l(m) + 9*n(m). Factor g(j).
(j - 2)*(j - 1)
Let u(c) = -c**2 - 2*c - 1. Let f be u(-1). Let v be (6/21)/((-4)/(-28)). Factor -3/2*r**4 + 3/2*r**3 + 0*r + 3/2*r**v - 3/2*r**5 + f.
-3*r**2*(r - 1)*(r + 1)**2/2
Let l(g) be the second derivative of g + g**2 + 1/12*g**4 - 1/2*g**3 + 0. Suppose l(i) = 0. Calculate i.
1, 2
Suppose 2*z + 22 = 3*z. Factor 4*s - 18 + 32*s**3 + 18 - 14*s**4 - z*s**2.
-2*s*(s - 1)**2*(7*s - 2)
Let h(o) = o**3 - 10*o**2 + 5. Let k be h(10). Factor -4*m + m**3 + 14*m**k - 46*m**5 - 20*m**2 + 2*m - 80*m**4 - 67*m**3.
-2*m*(m + 1)**2*(4*m + 1)**2
Let s be (0 + -3)/(9/(-12)). Let i(d) be the first derivative of -2 + 0*d**2 + 2/15*d**3 - 4/15*d**6 + 3/10*d**s + 0*d**5 + 0*d. Factor i(v).
-2*v**2*(v - 1)*(2*v + 1)**2/5
Suppose 5*g = 297 + 163. Let v be 12/(-4) - g/(-28). What is m in -2/7*m**3 - 2/7*m**2 + 2/7*m + v = 0?
-1, 1
Let x be (1 + 2 - -2)*-10. Let g be x/18 + (7 - 4). Factor -g + 0*f + 2/9*f**2.
2*(f - 1)*(f + 1)/9
Let i(l) = l**3 + 11*l**2 + 17*l - 5. Let u be i(-9). Let f(w) be the second derivative of 0*w**3 - 1/12*w**u + 0*w**2 + 2*w + 0. Find a, given that f(a) = 0.
0
Let n = 77 - 73. Let i(t) be the second derivative of -t**2 + 5/12*t**n + 1/2*t**3 + 0 - 3*t. Factor i(h).
(h + 1)*(5*h - 2)
Let v = -474 - -474. Let -3/7 + v*f - 6/7*f**5 + 12/7*f**2 - 9/7*f**4 + 6/7*f**3 = 0. What is f?
-1, 1/2, 1
Let o(n) = -n**3 + 14*n**2 + 3*n + 2. Let u be o(13). Determine b, given that -115/4*b**2 - 196*b**5 + 55/4*b**3 + 1 + 0*b + u*b**4 = 0.
-1/4, 2/7, 1
Let y = -87 - -195. Let q be 51/y - 4/18. Factor 0 + 0*z - 1/4*z**2 + q*z**3.
z**2*(z - 1)/4
Let i(o) = 3*o + 72. Let h be i(-23). Factor 1/3*n**h - 1/3*n**2 + 0 + 0*n.
n**2*(n - 1)/3
Let d = 80 - 78. Let f(y) be the third derivative of -1/60*y**6 - 3*y**d + 0*y**3 + 0*y**4 - 1/15*y**5 + 1/35*y**7 + 0*y + 0. Factor f(w).
2*w**2*(w - 1)*(3*w + 2)
Let f = 9 - 4. Let t(n) be the first derivative of 2/9*n**3 + 0*n - 2/15*n**f + 1/6*n**4 - 1/3*n**2 - 2. What is h in t(h) = 0?
-1, 0, 1
Let x(i) be the second derivative of i**5/90 - i**3/9 + i**2 - 3*i. Let c(o) be the first derivative of x(o). Determine a so that c(a) = 0.
-1, 1
Let h(q) be the first derivative of 0*q + 4/45*q**5 + 0*q**4 - 4/27*q**3 + 1/27*q**6 - 1/9*q**2 + 4. Find p, given that h(p) = 0.
-1, 0, 1
Suppose 106*h = 9*h + 291. Suppose 0 + 2/17*k**4 - 2/17*k**2 + 2/17*k - 2/17*k**h = 0. Calculate k.
-1, 0, 1
Factor 1/2*l**2 - l + 1/2.
(l - 1)**2/2
Let v(m) = -m**2 + 9*m - 2. Let w be v(7). Let r = -9 + 12. Factor -2*h**5 - 2*h**2 - w*h**r - 2*h - 8*h**2 + 2*h**2 - 8*h**4.
-2*h*(h + 1)**4
Let x(z) be the second derivative of -z**4/30 - 2*z**3/15 + 4*z. Let x(w) = 0. What is w?
-2, 0
Let j(l) be the third derivative of -l**6/200 + l**5/20 - l**4/10 + 31*l**2. Factor j(i).
-3*i*(i - 4)*(i - 1)/5
Let x(f) be the third derivative of -f**6/240 + f**5/120 + 5*f**4/48 + f**3/4 + 43*f**2. Determine j, given that x(j) = 0.
-1, 3
Let d be 28/(-36) - (0 + -3) - 2. Find t such that 0*t**2 + 2/9*t - d*t**3 + 0 = 0.
-1, 0, 1
Let h(f) be the second derivative of 5*f**4/18 + 8*f**3/9 + f**2 - 8*f. Solve h(n) = 0.
-1, -3/5
Let 15*g + 5*g**3 - 21 + 47 - 21 + 15*g**2 = 0. What is g?
-1
Suppose -23 = -5*g - 4*h, -2*g + 0*g + 5*h = 4. Factor -6/5 + 3*d - 12/5*d**2 + 3/5*d**g.
3*(d - 2)*(d - 1)**2/5
Let x = -3 + 9. Factor -4*z**2 + x - 8 + 6.
-4*(z - 1)*(z + 1)
Let h(c) = -5*c**4 + 5*c**3 - c**2 + c + 3. Let s(t) = -10*t**4 + 9*t**3 - 2*t**2 + 3*t + 7. Let f = -7 - -10. Let n(m) = f*s(m) - 7*h(m). Solve n(z) = 0.
-2/5, 0, 1
Let j(c) = -4*c**3 - 5*c**2 + 2*c - 3. Let w = -7 - -8. Let o(l) = l**3 + l**2 - l + 1. Let t(f) = w*j(f) + 3*o(f). Find z such that t(z) = 0.
-1, 0
Suppose 0 = 4*y - 6*y + 4. What is j in 23 + j**y - 23 - j**4 = 0?
-1, 0, 1
Let q be (0 - -2 - 2)/(-4 - -2). Let m be (-1*(-4)/2)/1. Find y such that -4/9*y + 14/9*y**m - 10/9*y**3 + q = 0.
0, 2/5, 1
Factor -2/5*h**3 + 1/5*h + 1/5*h**2 + 0.
-h*(h - 1)*(2*h + 1)/5
Let b = 3631/9 - 214034/531. Let j = b - 2/59. Suppose 1/3*k**4 + 0 + j*k - 1/3*k**2 - 1/3*k**3 = 0. What is k?
-1, 0, 1
Let t(c) = 4*c**2 + 2*c - 2. Let h be t(-2). Let o be 11/h - (-15)/(-25). Determine x so that 1/4*x**5 - o*x**4 + 0*x + 1/4*x**3 + 0*x**2 + 0 = 0.
0, 1
Let c(n) be the first derivative of 1/4*n**2 + 1/12*n**6 + 2/5*n**5 + 0*n + 2/3*n**3 + 3/4*n**4 - 1. Factor c(b).
b*(b + 1)**4/2
Let g(l) = -9*l**2 + 6*l - 4. Suppose s = 9 - 6. Let k(n) = -4*n**2 + 3*n - 2. Let d(t) = s*g(t) - 7*k(t). Find j such that d(j) = 0.
1, 2
Let a(w) = w**3 - 6*w**2 - w + 6. Let g be a(6). Factor -6*h**2 + g*h**3 + 7*h + 6*h**4 - 3*h - 4*h**3.
2*h*(h - 1)*(h + 1)*(3*h - 2)
Let j(u) be the third derivative of -u**8/20160 + u**6/2160 + u**4/24 - 3*u**2. Let w(a) be the second derivative of j(a). Determine z so that w(z) = 0.
-1, 0, 1
Let o(p) be the second derivative of p**8/3840 + p**7/5040 - 7*p**6/2880 - p**5/240 - p**4/4 + p. Let q(z) be the third derivative of o(z). Factor q(w).
(w - 1)*(w + 1)*(7*w + 2)/4
Let d be 5/1*(-117)/(-325). Let -3/5*g**3 - d*g**2 - 9/5*g - 3/5 = 0. What is g?
-1
Let q(n) = -12*n**4 + 21*n**3 + 27*n**2 - 3*n - 24. Let d(w) = -3*w**4 + 5*w**3 + 7*w**2 - w - 6. Let g(s) = 9*d(s) - 2*q(s). Factor g(h).
-3*(h - 2)*(h - 1)*(h + 1)**2
Let m(x) be the third derivative of -x**5/180 - x**4/72 - 4*x**2. Factor m(k).
-k*(k + 1)/3
Let s(v) = -8*v**4 + 15*v**3 - 20*v**2 - v - 2. Let m(q) = q**4 + q**2 + q + 1. Let y(u) = 4*m(u) + s(u). Factor y(l).
-(l - 2)*(l - 1)**2*(4*l + 1)
Let x(i) be the first derivative of 16*i**6/5 - 528*i**5/25 + 459*i**4/10 - 218*i**3/5 + 93*i**2/5 - 18*i/5 + 16. Let x(c) = 0. Calculate c.
1/4, 1, 3
Suppose -5*x + 9*b + 4 = 11*b, 0 = -4*x + 2*b + 14. Solve 0 - 4/9*o + 2/9*o**x + 2/9*o**3 = 0.
-2, 0, 1
Let l be (-5 - -5)*(1 + 0). Suppose l + 4/5*w + 2/5*w**2 = 0. What is w?
-2, 0
Let j(k) = 12*k - 6. Let h(c) = -c**2 + 23*c - 12. Let d(u) = -3*h(u) + 5*j(u). Find a such that d(a) = 0.
1, 2
Let n(d) be the second derivative of -d**4/72 - d**3/36 - 5*d. Factor n(m).
-m*(m + 1)/6
Let o(r) = -22*r**3 + 8*r**2 + 8*r - 8. Let w(m) = 15*m**3 - 5*m**2 - 5*m + 5. Let x(h) = 5*o(h) + 7*w(h). Factor x(v).
-5*(v - 1)**2*(v + 1)
Factor 8/5*u**3 + 2/5*u - 3/5*u**4 - 7/5*u**2 + 0.
-u*(u - 1)**2*(3*u - 2)/5
Factor 0*o + 0*o**2 + 3/2*o**3 + 0.
3*o**3/2
Let k be (-1)/(-4) + (-18)/(-24). Suppose 3*g = -k + 10. What is l in -l**2 + l**4 + 0*l**g - l**3 + l**3 = 0?
-1, 0, 1
Let d(f) be the first derivative of 2/3*f**3 + 0*f + f**2 - 3. Factor d(l).
2*l*(l + 1)
Let b = 212 + -207. Determine c, given that 2/3*c**b + 0*c + 0 + 2/3*c**3 + 0*c**2 + 4/3*c**4 = 0.
-1, 0
Let m(x) be the second derivative of x**9/720 + x**8/840 - 11*x**7/2520 + x**6/360 + x**4/4 - x. Let o(j) be the third derivative of m(j). Factor o(s).
s*(s + 1)*(3*s - 1)*(7*s - 2)
Let t(n) = -n**3 + 4*n**2 - 3*n + 1. Let f be t(3). Let o(a) = a + 1. Let d(c) = -c**2 - 4*c - 7. Let m(j) = f*d(j) - 2*o(j). Solve m(q) = 0.
-3
Let h(p) = -p**3 - 10*p**2 + 