be the third derivative of -g**7/1050 - g**6/200 - g**5/150 + 6*g**2. Find c, given that k(c) = 0.
-2, -1, 0
Let v be (-96)/(-42) - (26/(-7) + 4). Factor -2*a**v + 2/3*a**3 + 0*a + 8/3.
2*(a - 2)**2*(a + 1)/3
Let y = 51 - 48. Let i(m) be the first derivative of -3/2*m**2 - 2 + 1/3*m**y + 2*m. Factor i(a).
(a - 2)*(a - 1)
Let h = -14 - -18. Let u(d) be the third derivative of -1/20*d**6 + d**2 - 1/6*d**5 - 1/6*d**h + 0*d + 0 + 0*d**3. Factor u(s).
-2*s*(s + 1)*(3*s + 2)
Let l(a) be the second derivative of 1/16*a**4 - 8*a + 0 + 0*a**2 + 1/8*a**3. Factor l(x).
3*x*(x + 1)/4
Let u(j) be the first derivative of 2*j**3/9 + j**2 - 1. Factor u(s).
2*s*(s + 3)/3
Let d = -182 - -182. Let n(o) be the second derivative of 1/36*o**4 - 2*o - 1/90*o**6 + 0 - 1/60*o**5 + 1/126*o**7 + 0*o**2 + d*o**3. Factor n(b).
b**2*(b - 1)**2*(b + 1)/3
Suppose -40 = 3*y - 7*y. Let q(d) = d**2 - 11*d + 14. Let l be q(y). Factor 1/3*m**l + 0*m**3 + 2/3*m - m**2 + 0.
m*(m - 1)**2*(m + 2)/3
Let p(x) = 8*x**3 - 8*x**2. Suppose 4*s = -0*s. Suppose -o + 1 = -s*o. Let l(n) = -n**3 + n**2. Let h(w) = o*p(w) + 6*l(w). Suppose h(i) = 0. What is i?
0, 1
Factor 6/5*r**2 - 4/5*r + 14/5*r**4 + 0 + 24/5*r**3.
2*r*(r + 1)**2*(7*r - 2)/5
Let k(p) be the third derivative of -1/8*p**4 + 0 - 1/20*p**5 - 1/448*p**8 + 3/160*p**6 - 10*p**2 + 0*p + 0*p**3 + 1/140*p**7. Solve k(a) = 0.
-1, 0, 2
Let u(y) be the first derivative of -y**5/180 + y**4/72 + y**3/9 + y**2 + 4. Let n(p) be the second derivative of u(p). Factor n(w).
-(w - 2)*(w + 1)/3
Let i be (-3)/6*-4 - (-70)/(-40). Find s, given that 0*s**3 - 1/4*s**4 + 0 + i*s**2 + 0*s = 0.
-1, 0, 1
Let i(r) be the first derivative of -r**5/30 - r**4/6 + r**2 + 2. Let y(d) be the second derivative of i(d). Factor y(f).
-2*f*(f + 2)
Let u be ((-96)/(-22))/2 - (-2)/(-11). Let v(n) be the first derivative of -8/3*n**3 - 5*n**u + 1 - 2*n. Let v(h) = 0. Calculate h.
-1, -1/4
Suppose -2*n = -4*h, 0*n - 5*n + 30 = 5*h. Suppose y - 2 = -v - 2*v, -5*v - n = -2*y. Factor a**2 + y*a + 0*a**2 - 3*a**2.
-2*a*(a - 1)
Let d = -4/9 - -10/9. Let n(b) be the first derivative of -1 - b**2 - d*b - 2/3*b**3 - 1/6*b**4. Factor n(f).
-2*(f + 1)**3/3
Let q be 5/((-3225)/1538) + 2. Let z = 2/129 - q. Let 0*n + z*n**4 - 6/5*n**3 + 0 + 4/5*n**2 = 0. What is n?
0, 1, 2
Let d(r) be the second derivative of 1/70*r**5 + 0*r**2 + 0 - 7*r + 1/14*r**4 + 2/21*r**3. Find o such that d(o) = 0.
-2, -1, 0
Let q(u) be the third derivative of u**8/120960 - u**5/30 - 6*u**2. Let j(p) be the third derivative of q(p). Let j(h) = 0. Calculate h.
0
Let d = 5 - 2. Let o(x) be the first derivative of -1/12*x**d + 1/16*x**4 + 1 + 0*x + 1/20*x**5 - 1/8*x**2. Factor o(g).
g*(g - 1)*(g + 1)**2/4
Factor 1/7*n**3 + 0 + 1/7*n + 2/7*n**2.
n*(n + 1)**2/7
Let z(a) be the first derivative of 2*a**5/35 + a**4/7 - 6. Let z(h) = 0. What is h?
-2, 0
Let n(l) be the first derivative of 2*l**5/35 - l**4/14 - 2*l**3/7 + l**2/7 + 4*l/7 + 2. What is g in n(g) = 0?
-1, 1, 2
Solve 23*d**4 + 3*d**3 - 3*d**2 - 8*d**4 - 5*d**4 - 7*d**4 - 3*d = 0.
-1, 0, 1
Let d be (-8*1/(-24))/(1 - -1). Let r(c) be the second derivative of 1/120*c**6 - 1/20*c**5 + 2*c + 1/8*c**2 + 1/8*c**4 - d*c**3 + 0. Factor r(n).
(n - 1)**4/4
Let t be ((-10)/(-480))/((-2)/(-4)). Let p(h) be the third derivative of 0*h - h**2 + 0*h**4 + 0*h**3 - 1/30*h**5 - t*h**6 + 0. Solve p(o) = 0.
-2/5, 0
What is c in 4/3*c**3 - 2*c**2 + 0*c + 2/3*c**4 + 0 = 0?
-3, 0, 1
Let s(t) = -3*t**3 + 6*t**2 - 3. Let b(f) be the first derivative of -f**2/2 + f - 1. Let p(v) = 3*b(v) + s(v). Factor p(j).
-3*j*(j - 1)**2
Let d(n) = -6*n**4 + 14*n**3 - 9*n**2 - 5. Let a(o) = 18*o**4 - 42*o**3 + 26*o**2 + 14. Let i(r) = 5*a(r) + 14*d(r). Suppose i(y) = 0. Calculate y.
0, 1/3, 2
Let o be 2/(-7) - 0 - 6/(-21). Let k(m) be the second derivative of 0 + o*m**2 - 3/20*m**5 + 1/4*m**4 - 1/6*m**3 + 2*m + 1/30*m**6. Find r, given that k(r) = 0.
0, 1
Let s = 59/3 + -58/3. Factor s*d**2 - 1/3 - 2/3*d**3 + 2/3*d.
-(d - 1)*(d + 1)*(2*d - 1)/3
Let o(l) be the second derivative of -l**7/39 + 16*l**6/195 - 11*l**5/130 + l**4/39 - l. Solve o(v) = 0 for v.
0, 2/7, 1
Let z(w) be the third derivative of -w**5/210 - w**4/28 + 4*w**3/21 - 34*w**2. Factor z(d).
-2*(d - 1)*(d + 4)/7
Let u(q) be the third derivative of -q**8/168 + q**7/210 + q**6/120 - 24*q**2. Solve u(r) = 0.
-1/2, 0, 1
Let a(f) be the second derivative of 0*f**3 + 2/5*f**6 - 4/21*f**7 - 3/10*f**5 + 1/12*f**4 + 2*f + 0 + 0*f**2. Let a(w) = 0. Calculate w.
0, 1/2
Suppose -3/7*o**2 + 0 - 3*o = 0. Calculate o.
-7, 0
Let l be 2/(-4) - 9*(-6)/12. Solve -4/5*v**5 + 0 - 2/5*v**l + 12/5*v**3 + 4/5*v + 14/5*v**2 = 0 for v.
-1, -1/2, 0, 2
Let x(n) be the third derivative of n**8/16800 - n**7/6300 - 5*n**4/24 - 7*n**2. Let w(c) be the second derivative of x(c). What is l in w(l) = 0?
0, 1
Let s(r) be the second derivative of r**4/2 - 4*r**3/3 + r**2 - 7*r. Factor s(n).
2*(n - 1)*(3*n - 1)
Factor -3*f**5 - 1 + 6*f**5 - 9*f**3 - 12*f + 6*f**4 + 1 - 24*f**2.
3*f*(f - 2)*(f + 1)**2*(f + 2)
Let i(r) = -5*r**2 - 62*r - 21. Let x be i(-12). Let 0*p**2 + 0*p**4 - 4/3*p**x + 2/3*p**5 + 0 + 2/3*p = 0. What is p?
-1, 0, 1
Let n = -4/13 - -54/91. Factor 0*j**2 - n + 2/7*j**4 + 4/7*j - 4/7*j**3.
2*(j - 1)**3*(j + 1)/7
Let u(p) = 6*p**4 - 10*p**3 + 4*p**2 + 4*p. Let v(m) = -5*m**4 + 9*m**3 - 4*m**2 - 3*m. Let s(q) = -3*u(q) - 4*v(q). What is o in s(o) = 0?
0, 1, 2
Let j(m) = -m - 1. Let w(l) = 2*l**3 + 6*l**2 + 5*l + 1. Let x(v) = -j(v) - w(v). Solve x(i) = 0.
-2, -1, 0
Let q(y) be the second derivative of y**6/30 - y**5/20 - y**4/12 + y**3/6 - 5*y. Find x such that q(x) = 0.
-1, 0, 1
Let j(c) = 9*c**2 + 17*c + 18. Let q(x) = -x**2 - x - 2. Let t(d) = 2*j(d) + 22*q(d). Factor t(h).
-4*(h - 2)*(h - 1)
Let h be (0 - 0)*(90/(-12) + 7). Factor 0*p - 4/3*p**2 - 2/3*p**3 + h.
-2*p**2*(p + 2)/3
Let t(m) be the third derivative of 2/33*m**3 - 2/165*m**5 + 0 + 0*m - m**2 - 1/132*m**4 + 1/220*m**6. Find u such that t(u) = 0.
-2/3, 1
Suppose -5*k = -3*j - 35, 5*j = 6*k - k - 25. Suppose -k + 0 = -r. Let 0*v**2 - r*v**5 + v**3 - 3/2*v**4 + 0 + 0*v = 0. What is v?
-2/5, 0, 1/4
Let a(j) = -j**2 + 4*j - 3. Let i be a(2). Suppose 0 = -u - i + 5. What is w in -2*w + 6 - 2*w + 2*w**2 - u = 0?
1
Let r(z) be the third derivative of z**6/300 - z**4/60 - 6*z**2. Factor r(h).
2*h*(h - 1)*(h + 1)/5
Suppose f + 4*b - 11 = -4, -1 = -b. Let d(p) be the first derivative of 0*p - 1/6*p**2 - 2 + 1/12*p**4 + 0*p**f. Factor d(r).
r*(r - 1)*(r + 1)/3
Let c(i) be the first derivative of 2*i**5/75 + i**4/10 + 2*i**3/45 - i**2/5 - 4*i/15 - 9. Suppose c(a) = 0. What is a?
-2, -1, 1
Let y(k) be the second derivative of k**5/110 + k**4/66 - k**3/33 - k**2/11 + k. Factor y(w).
2*(w - 1)*(w + 1)**2/11
Let n(u) be the second derivative of -u**4/42 - 4*u**3/21 - 3*u**2/7 + 14*u. What is r in n(r) = 0?
-3, -1
Let d(o) be the first derivative of -o**2 + 0*o - 3/5*o**5 + o**3 + 1/2*o**4 + 1. Factor d(a).
-a*(a - 1)*(a + 1)*(3*a - 2)
Let b(z) be the second derivative of z**7/168 + z**6/40 + 3*z**5/80 + z**4/48 + 5*z. What is t in b(t) = 0?
-1, 0
Let q(h) = 7*h**5 + 6*h**4 + 2*h**3 - h**2 + h - 5. Let n(z) = 6*z**5 + 6*z**4 + 2*z**3 - 2*z**2 - 4. Let r(m) = 5*n(m) - 4*q(m). Factor r(l).
2*l*(l - 1)*(l + 1)**2*(l + 2)
Let t(h) be the second derivative of h**7/140 + h**6/45 + h**5/60 - h**3/3 + 2*h. Let d(o) be the second derivative of t(o). Suppose d(g) = 0. Calculate g.
-1, -1/3, 0
Let d(b) = -b**2 + 4*b. Suppose 6 = 3*z - 3. Let f be d(z). Find r such that -8/7 - 8*r - 18/7*r**4 - 122/7*r**2 - 12*r**f = 0.
-2, -1/3
Suppose 2*m = -3 + 1. Let x be ((-15)/(-6) - 1) + m. Suppose 1/2*h**3 - 1/4 - 1/4*h**5 - 1/4*h**4 - 1/4*h + x*h**2 = 0. What is h?
-1, 1
Let m(l) be the first derivative of l**6/105 - l**5/35 + 2*l**3/21 - l**2/7 - 4*l + 1. Let f(z) be the first derivative of m(z). Factor f(x).
2*(x - 1)**3*(x + 1)/7
Let w(q) = -q**2 + 8*q + 11. Let k be w(9). Suppose -2*t = -k*s - 4, 0*t + 2*t = 4. Let s*a**2 + 0 + 0*a - 2/9*a**3 = 0. Calculate a.
0
Suppose -2*b = -2*k - 7*b + 3, -5*b - 5 = 0. Suppose 0 = 6*z - 7 - 5. Determine u, given that 1/2*u**5 + 0 + 0*u + 0*u**z + 1/2*u**k + 0*u**3 = 0.
-1, 0
Let p(v) = -v - 6. Let a be p(-6). Let g(q) be the third derivative of 1/120*q**6 + 1/72*q**4 - 1/60*q**5 - 1/6