*2 + 216*c + 427. Let s(p) = -10*p**3 - 54*p**2 - 324*p - 641. Let q(o) = 5*s(o) + 7*y(o). Find z, given that q(z) = 0.
-6
Let g(d) be the second derivative of 7*d**4/36 + 11*d**3/6 - 5*d**2/3 - 15*d. Suppose g(m) = 0. Calculate m.
-5, 2/7
Factor -d**2 - 4*d + 6*d**2 - 2*d**2 + d**3.
d*(d - 1)*(d + 4)
Let -4/3*s**2 + 0*s - 1/3*s**3 + 0 = 0. Calculate s.
-4, 0
Let h = 3 + 0. Suppose -12*i**5 - 2*i**3 - 9*i + 4*i**3 - 3*i**2 + h + 19*i**3 = 0. Calculate i.
-1, 1/2, 1
Let a(i) = -i + 1. Let p(o) = 2*o**3 + 4*o**2 + 2. Let t = 7 - 5. Let c(v) = t*a(v) - p(v). Factor c(n).
-2*n*(n + 1)**2
Let a be 0 + (-2510)/(-11) - 3. Let y = a + -225. Factor 2/11*x**3 - y*x**2 + 0*x + 0.
2*x**2*(x - 1)/11
Let k(l) be the first derivative of -3 - 1/7*l**4 + 8/7*l + 0*l**3 + 6/7*l**2. Solve k(j) = 0 for j.
-1, 2
Let z(v) = v - 3. Let r be z(6). Find g such that -r*g**2 - 2 + 6*g**5 + 16*g**2 + 0*g - 2*g + 28*g**3 + 22*g**4 - g**2 = 0.
-1, 1/3
Let i(x) be the third derivative of x**7/525 + x**6/75 + 2*x**5/75 + 21*x**2. Find u, given that i(u) = 0.
-2, 0
Suppose -2*j + 22 = 4*u, -15 = -3*u - 6. Suppose 10 = -4*f + j*s, -3*f + s - 1 = 1. Determine h so that 0 - 2/5*h**3 + 0*h**2 + f*h = 0.
0
Let j = -7 + 2. Let i = -1 - j. Solve -4*f**2 + 10*f**i - 6*f**4 - 6*f**5 + 2*f**3 + 4*f**4 = 0 for f.
-2/3, 0, 1
Let x(u) be the third derivative of u**8/840 - u**7/105 + u**6/45 + u**3/2 + 2*u**2. Let z(m) be the first derivative of x(m). Factor z(i).
2*i**2*(i - 2)**2
Let w(p) be the third derivative of p**7/420 - p**5/120 - 7*p**2. Solve w(y) = 0.
-1, 0, 1
Suppose -2*s = -3*c + 5*c + 6, 3*s = 4*c - 23. Suppose -c*n - n = 0. Suppose 2/9*k**2 + 0*k + n = 0. What is k?
0
Factor 6*a + 48*a**2 - 8*a - 21*a**3 - 31*a + 6 + 0*a.
-3*(a - 1)**2*(7*a - 2)
Let z(l) = 9*l**4 - 12*l**3 + 4*l**2 + 2*l + 3. Let r(i) = -18*i**4 + 25*i**3 - 9*i**2 - 3*i - 5. Let f(x) = -6*r(x) - 10*z(x). Factor f(j).
2*j*(j - 1)*(3*j - 1)**2
Let g(c) be the third derivative of -1/3*c**3 + 0 - 1/12*c**4 + 7/120*c**5 + 0*c + 1/90*c**6 - c**2. Let l(i) be the first derivative of g(i). Factor l(a).
(a + 2)*(4*a - 1)
Let j(u) be the first derivative of u**2 - 6*u**3 + 4*u**3 + 6*u**3 - 4. Find k such that j(k) = 0.
-1/6, 0
Let a(s) = 3*s**3 + s**2 - 1. Let g be a(1). Let 4*i**g + 5*i**4 - 2 + 2*i**2 - 3*i**4 + 2 = 0. What is i?
-1, 0
Let g(b) be the third derivative of -6*b**2 + 0*b**3 - 1/12*b**6 - 1/12*b**4 + 2/15*b**5 + 0*b + 0 + 2/105*b**7. Suppose g(f) = 0. What is f?
0, 1/2, 1
Let m(b) be the first derivative of b**6/480 - b**5/160 - b**3/3 + 1. Let c(x) be the third derivative of m(x). Solve c(j) = 0 for j.
0, 1
Let s(t) be the third derivative of t**7/2520 + t**6/270 + t**5/90 + t**3/6 + 2*t**2. Let r(n) be the first derivative of s(n). Solve r(q) = 0.
-2, 0
Suppose c - 2*c + 20 = -4*v, 12 = -2*c - 5*v. Find q, given that -7*q**2 + q**2 + c - 3*q - 3*q**2 + 2 = 0.
-1, 2/3
Let o(r) be the second derivative of -r**7/126 - r**6/45 + r**4/18 + r**3/18 - 7*r. Find m, given that o(m) = 0.
-1, 0, 1
Factor 0 - 4/3*k**3 + 0*k**2 + 4/3*k.
-4*k*(k - 1)*(k + 1)/3
Let v be 5/(10/4) + 0. Suppose -v*m + 9 = -1. Factor -k**3 - k**3 - 5*k**5 + 7*k**m.
2*k**3*(k - 1)*(k + 1)
Solve 3*h**3 + 7*h**2 + 8*h**2 - 7*h**3 - h**2 + 4 - 14*h = 0.
1/2, 1, 2
Let s be -3*(-2 + 1 + 0). Let i = 51/7 + -7. Factor 0 + 2/7*b**4 + 2/7*b**s - i*b**2 - 2/7*b.
2*b*(b - 1)*(b + 1)**2/7
Let v(l) = l**2 - 7*l - 5. Let w = -9 + 17. Let f be v(w). Let -x**5 + 4*x**5 + 15*x**3 - 18*x**f = 0. What is x?
-1, 0, 1
Let d be 486/117 - (-4)/(-26). Find n such that 1/2*n**3 - 1/2*n + 1/4 + 0*n**2 - 1/4*n**d = 0.
-1, 1
Factor 56*i**2 + 5*i**3 + 10 - 15*i - 27*i**2 - 29*i**2.
5*(i - 1)**2*(i + 2)
Suppose -5*t - 3*d = -17, 5*t + 4*d - 16 = -0*t. Factor -3*q - 16 - 3*q**t + 0*q + 13 - 3*q**5 + 6*q**3 + 6*q**2.
-3*(q - 1)**2*(q + 1)**3
Let u(y) = 4*y**2 + 16*y - 4*y - 2 - 4*y**2 + 14*y**2. Let a(b) = 9*b**2 + 8*b - 1. Let c(x) = 8*a(x) - 5*u(x). Factor c(q).
2*(q + 1)**2
Let n(j) be the second derivative of j**6/300 - j**5/75 + j**4/60 + j**2 + 3*j. Let h(l) be the first derivative of n(l). Factor h(c).
2*c*(c - 1)**2/5
Let d(q) be the first derivative of -q**5/120 + q**4/48 + q**2/2 - 5. Let b(g) be the second derivative of d(g). Factor b(o).
-o*(o - 1)/2
Factor 8*s - 11*s**3 + s**3 - 4*s**2 + 6*s**3 + 0*s**3.
-4*s*(s - 1)*(s + 2)
Let j = 1025 + -16395/16. Let q(w) be the second derivative of -1/4*w**3 + j*w**4 + 1/40*w**6 + 0 + 0*w**2 - 3/20*w**5 - 3*w. Factor q(g).
3*g*(g - 2)*(g - 1)**2/4
Suppose -4*k - 8 + 20 = 0. What is g in 2/3*g**2 + 2/9 + 2/9*g**k + 2/3*g = 0?
-1
Let s(d) be the second derivative of 0 + 0*d**2 - 625/147*d**7 - 15/7*d**5 + 100/21*d**6 + d + 10/21*d**4 - 1/21*d**3. Factor s(j).
-2*j*(5*j - 1)**4/7
Suppose 4*z = 7*z. Let f(c) be the second derivative of z + 2*c + 1/60*c**4 - 1/10*c**2 + 0*c**3. Find l such that f(l) = 0.
-1, 1
Let o(q) = 9*q**2 + 60*q + 180. Let v(t) = -8*t**2 - 60*t - 180. Let x(u) = -3*o(u) - 4*v(u). Find k, given that x(k) = 0.
-6
Solve 4*h - 3*h**3 - 18*h**3 + 16*h - 2*h - 57*h**2 = 0 for h.
-3, 0, 2/7
Let w(n) = 3 - 3 - 2 - 8*n - n**2 + 12*n. Let p be w(2). Let -3/2*y**3 - 1 + p*y**2 + 1/2*y = 0. Calculate y.
-2/3, 1
Let i = -1 + 2. Suppose -4*m + i + 11 = 0. Factor 3*g**m - g**3 - 2*g**2 - 3*g**3 + 3*g**2.
-g**2*(g - 1)
Let x(h) be the second derivative of 5*h**7/42 - 5*h**6/6 + 5*h**5/2 - 25*h**4/6 + 25*h**3/6 - 5*h**2/2 - 9*h. Suppose x(d) = 0. What is d?
1
Factor -i**5 + 38*i - 38*i + 2*i**4.
-i**4*(i - 2)
Find d, given that 3/4*d**2 + 0*d - 3/4*d**4 + 0 + 0*d**3 = 0.
-1, 0, 1
Let q(a) be the third derivative of -a**6/240 - a**5/60 - a**4/48 + 5*a**2. Factor q(h).
-h*(h + 1)**2/2
Let u = -11 - -16. Let h**3 - u*h**3 + 0*h**3 + 3*h**3 = 0. What is h?
0
Let r(l) be the first derivative of 3*l**4/4 - 3*l**2/2 + 28. Find w, given that r(w) = 0.
-1, 0, 1
Let d(r) be the first derivative of -1/5*r**4 - 4 + 2/25*r**5 + 1/15*r**6 + 0*r**2 + 0*r**3 + 0*r. Factor d(u).
2*u**3*(u - 1)*(u + 2)/5
Let h be (-8)/6 + (-10)/15. Let i = h - -5. Factor 5*d**3 + 2*d - 3*d**i - 3*d**2 + 8*d**2 - d**2.
2*d*(d + 1)**2
What is m in 0 - 2/3*m**3 + 4/9*m - 2/9*m**2 + 2/9*m**4 + 2/9*m**5 = 0?
-2, -1, 0, 1
Let z(l) = -l**2 + 15*l - 4. Let r(u) = u**2 - 30*u + 9. Let d(t) = -4*r(t) - 9*z(t). Suppose d(a) = 0. Calculate a.
0, 3
Let o(p) be the second derivative of 0 - 3*p + 0*p**2 + 1/6*p**3 + 1/3*p**4. Let o(q) = 0. Calculate q.
-1/4, 0
Factor 0 - 2/7*k**2 - 2/7*k.
-2*k*(k + 1)/7
Let h(g) be the first derivative of g**3/3 - 6. Factor h(r).
r**2
Let k = 79/2 + -157/4. Find m such that 0 + 0*m**3 - k*m + 1/2*m**2 - 1/2*m**4 + 1/4*m**5 = 0.
-1, 0, 1
Let t be (12 - 1210/70) + 7*1. Factor 0*k**2 + 0 - 3/7*k**3 + t*k.
-3*k*(k - 2)*(k + 2)/7
Let a(j) be the first derivative of j**5/120 + j**4/48 - j**3/6 + 5*j**2/2 + 1. Let m(w) be the second derivative of a(w). Suppose m(c) = 0. Calculate c.
-2, 1
Let z(l) = l**4 + l**3 + l**2. Let h(a) = 5*a**5 - 5*a**3 + 15*a**2 + 5*a - 5. Let q(j) = h(j) - 5*z(j). Let q(w) = 0. What is w?
-1, 1
Let j(i) be the third derivative of i**6/120 - i**5/20 - i**2. Let w be j(3). Let 6*p**2 + w*p**4 + 3*p - 6*p**3 + 2*p**4 - 6*p + p = 0. What is p?
0, 1
Suppose 4*v - 1 - 1 = 3*i, 0 = -3*v - 3*i + 12. Let p(h) be the first derivative of -1/3*h**2 - v - h**3 + 0*h. Factor p(j).
-j*(9*j + 2)/3
Let v(j) be the second derivative of j**4/138 + 4*j**3/69 + 4*j**2/23 + j + 2. Factor v(w).
2*(w + 2)**2/23
Find g, given that 15*g**2 + 30*g**2 - 20 + 39*g + 41*g = 0.
-2, 2/9
Let k be 57/38*(-2)/(-1) + 0. Factor -10/3 + 5/3*y**k - 5/3*y + 10/3*y**2.
5*(y - 1)*(y + 1)*(y + 2)/3
Suppose 3*s + 25 = -2*v - 0*v, 2*s + 4*v + 22 = 0. Let h be (s - (-1 + -2))*-2. Factor -7*x**2 + 7 - 3 - 14*x - h*x**2 - 3*x**2.
-2*(x + 1)*(9*x - 2)
Let s(q) be the second derivative of q**4/4 - 2*q**3 - 15*q**2/2 + 21*q. Suppose s(f) = 0. Calculate f.
-1, 5
Let s(k) be the third derivative of -k**9/90720 - k**8/5040 - k**7/630 - k**6/135 - k**5/60 - 4*k**2. Let h(c) be the third derivative of s(c). Factor h(v).
-2*(v + 2)**3/3
Find s, given that -4/5*s**2 + 24/5*s - 36/5 = 0.
3
Let w(f) = 2*f - 15. Let y be w(10). Let z = 5 - y. Factor -2/3*o**2 - 2/3*o**3 + 0*o + z.
-2*o**2*(o + 1)/3
Factor 1/11*m**2 - 2/11 - 1/11*m.
(m - 2)*(m + 1)/11
Factor -8/9 - 1