 be the third derivative of -q**6/120 - 7*q**5/60 - q**4/24 - 2*q**3/3 - 2*q**2. Let r be b(-7). Let -2/7*i**r - 2/7*i**2 + 2/7*i + 2/7 = 0. What is i?
-1, 1
Let m be (-1 - -3)/1 - -1. Factor -j**5 - 1 - 2*j**2 - 2*j**3 + 4*j - 2*j + m*j**4 + j.
-(j - 1)**4*(j + 1)
Let v(u) be the second derivative of 0*u**2 + 0 - 3*u + 0*u**5 + 1/60*u**6 + 0*u**4 + 0*u**3. Factor v(a).
a**4/2
Let a(k) be the third derivative of k**8/3696 + k**7/462 + k**6/132 + k**5/66 + 5*k**4/264 + k**3/66 + 6*k**2. Factor a(d).
(d + 1)**5/11
Let v(n) be the first derivative of 3 + 1/9*n**3 + 0*n - 1/6*n**2. Factor v(k).
k*(k - 1)/3
Let o(r) be the second derivative of 0*r**2 + 0 - 1/70*r**5 - 1/7*r**3 + 8*r - 2/21*r**4. Factor o(t).
-2*t*(t + 1)*(t + 3)/7
Let m = -6 - -8. Let h be (1 - 0) + m + -1. Factor -i**2 + 4*i + 0*i**h + 3*i**2.
2*i*(i + 2)
Let x(p) be the second derivative of p**4/36 + p**3/9 + 22*p. Solve x(z) = 0.
-2, 0
Let k(a) = -9*a**3 - 5*a**2 + 4*a + 5. Let y(o) = -4*o**3 - 2*o**2 + 2*o + 2. Let x(c) = -2*k(c) + 5*y(c). Solve x(d) = 0 for d.
-1, 0, 1
Let x(v) be the third derivative of 0*v + 2*v**2 + 1/330*v**5 + 0 + 0*v**3 - 1/660*v**6 + 0*v**4. Determine o so that x(o) = 0.
0, 1
Factor -3/5*z**4 + 0 - 3/5*z**3 + 3/5*z**2 + 3/5*z.
-3*z*(z - 1)*(z + 1)**2/5
Let n(i) be the third derivative of -i**11/1663200 - i**10/756000 - i**5/30 + i**2. Let a(m) be the third derivative of n(m). What is t in a(t) = 0?
-1, 0
Let w(a) be the first derivative of 5*a**6/18 + a**5/5 - a**4/6 + 11. Factor w(n).
n**3*(n + 1)*(5*n - 2)/3
Let n(z) be the third derivative of z**5/240 - 12*z**2. What is f in n(f) = 0?
0
Let u(a) = -3*a**3 - 6*a**2 + 6*a - 3. Let l = -23 + 16. Let r(f) = -f**4 - 6*f**3 - 13*f**2 + 13*f - 7. Let h(m) = l*u(m) + 3*r(m). Factor h(k).
-3*k*(k - 1)**2*(k + 1)
Suppose -5*m = -2*g - 6 - 12, m - g - 6 = 0. Factor 4*n - 11*n**2 - 2*n**4 - 4*n**3 + 10*n**m + 3*n**2.
-2*n*(n - 1)*(n + 1)*(n + 2)
Solve 6/7*b**2 - 1/7*b - 1/7*b**5 - 3/7 + 2/7*b**3 - 3/7*b**4 = 0 for b.
-3, -1, 1
Let p be (5/210)/((-6)/(-7)). Let d(l) be the third derivative of 1/90*l**5 + 0 + 1/180*l**6 + 0*l - 1/9*l**3 - p*l**4 - l**2. What is x in d(x) = 0?
-1, 1
Suppose 0 = 3*w - 7*w + 8. Let l = w + 1. Factor 4*j**5 + 3*j**5 - 4*j**l - 5*j**5 + 2*j.
2*j*(j - 1)**2*(j + 1)**2
Let y = 60 - 57. Let b(n) be the second derivative of 0 + 1/4*n**4 + 4*n - 2*n**y + 6*n**2. Find j such that b(j) = 0.
2
Let h(g) be the third derivative of -g**9/15120 + g**8/6720 + g**7/1260 - g**4/24 + 4*g**2. Let l(m) be the second derivative of h(m). Let l(t) = 0. What is t?
-1, 0, 2
Let r be 1*(2 - 0)/8. Find o such that r*o**3 + 1/4*o + 0 - 1/2*o**2 = 0.
0, 1
Let g(c) be the first derivative of -c**6/6 + c**5/5 + 3*c**4/4 - 5*c**3/3 + c**2 + 13. Factor g(l).
-l*(l - 1)**3*(l + 2)
Suppose 72 = -2*c + 6*c. Let p be (-3)/c*(-6)/2. Factor 1/2*a**2 - 1/2 - p*a**3 + 1/2*a.
-(a - 1)**2*(a + 1)/2
Let u be ((-3)/(-6))/(90/144). Let a be 0/(1/(3/3)). Solve -2/5*b**2 - 2/5*b**4 - u*b**3 + 0 + a*b = 0 for b.
-1, 0
Let t be (5 - 5)/(2/2). Suppose t = -3*m - 3 + 6, 2*w = -m + 5. Solve -2/3*h**w - 2/3*h**3 + 2/3*h + 0 + 2/3*h**4 = 0 for h.
-1, 0, 1
Factor -18*p**2 - 10*p - 3*p**3 - 24 + 0*p - 26*p.
-3*(p + 2)**3
Let z be -23 + 29 + -6*1. Factor -1/5*f**3 + 0 + z*f - 1/5*f**5 + 0*f**2 - 2/5*f**4.
-f**3*(f + 1)**2/5
Let z(b) = b**4 + b**2 - b - 1. Let p(f) = 2*f**4 + 5*f**3 - 13*f**2 + 3*f + 3. Let a(k) = -p(k) - 3*z(k). Factor a(c).
-5*c**2*(c - 1)*(c + 2)
Let z be 4 - 8 - 16/(-4). Let h(m) be the first derivative of z*m - 2 - 1/12*m**3 - 1/8*m**2. Factor h(b).
-b*(b + 1)/4
Let s = 586/5 - 114. Suppose -104/5*g**2 - s*g + 266/5*g**4 + 0 + 294/5*g**5 - 116/5*g**3 = 0. Calculate g.
-1, -2/7, 0, 2/3
Let j(n) be the third derivative of 0*n + 4*n**2 + 1/8*n**4 - 1/80*n**5 - 1/2*n**3 + 0. Suppose j(r) = 0. What is r?
2
Let v be (4/14)/(-1*(-1 + 0)). Solve 0*m + 0*m**2 + 0*m**3 - v*m**4 + 0 = 0 for m.
0
Let g(k) be the third derivative of -k**7/105 - k**6/20 + k**5/15 + k**4 + 8*k**3/3 - 6*k**2. Solve g(q) = 0 for q.
-2, -1, 2
Let b(o) be the second derivative of 0*o**2 + 0 + o + 1/6*o**4 + 1/3*o**3. Factor b(l).
2*l*(l + 1)
Let n(c) = 4*c**4 - 14*c**3 + 4*c**2 + 10*c - 10. Let f(y) = -y**3 - y - 1. Let s(x) = -2*f(x) + n(x). Determine q so that s(q) = 0.
-1, 1, 2
Let s = 2 + 0. Factor 2*t**2 + 4*t**4 + 0*t**5 - 6*t**3 - s*t**5 + 2*t**4.
-2*t**2*(t - 1)**3
Let r = -29532 + 118715/4. Let b = r - 146. Suppose 3/2*v**2 + 0 - b*v - 3/4*v**3 = 0. Calculate v.
0, 1
Let n(u) = -9*u**3 - u**2 - 3. Let w(h) = -10*h**3 - 4. Let i(l) = 4*n(l) - 3*w(l). Find a, given that i(a) = 0.
-2/3, 0
Factor 6*w**4 + 16*w**2 + 2*w**2 - 9*w**4 + 24*w + 9.
-3*(w - 3)*(w + 1)**3
Let g be (8 + 4/(-2))/1. Suppose 4*u - 7*u = -g. Factor -4/5*r + 0 - 2/5*r**4 + 4/5*r**3 + 2/5*r**u.
-2*r*(r - 2)*(r - 1)*(r + 1)/5
Factor 0 + 4/9*w**3 - 4/3*w + 8/9*w**2.
4*w*(w - 1)*(w + 3)/9
Suppose 6 - 3 = 3*o - 3*a, 4*o + 4*a = -4. Solve o*i + 3/4 - 3/4*i**2 = 0.
-1, 1
Let t(x) be the first derivative of -5*x**4/4 + 5*x**3/3 + 5*x**2/2 - 5*x + 64. Factor t(w).
-5*(w - 1)**2*(w + 1)
What is f in -1/3*f**3 + 2/3*f + 0 - 1/3*f**2 = 0?
-2, 0, 1
Suppose 0 = i - 5 - 1. Factor -x - 3*x + 2*x + i*x**2.
2*x*(3*x - 1)
Suppose -3*a + 1 = -11. Let w(s) be the second derivative of -1/2*s**2 - 1/80*s**5 + 0 + 1/16*s**a + 3*s + 0*s**3. Suppose w(v) = 0. What is v?
-1, 2
Let k(q) be the third derivative of 9*q**2 + 1/3*q**4 + 4/15*q**3 - 7/25*q**7 + 0 + 21/40*q**8 + 0*q - 37/150*q**5 - 281/300*q**6. What is f in k(f) = 0?
-1/3, -2/7, 2/7, 1
Let h(p) = 11*p - 52. Let b be h(5). Factor -1/5*a**2 + 0 - 3/5*a**4 + 3/5*a**b + 0*a + 1/5*a**5.
a**2*(a - 1)**3/5
Let c(f) be the second derivative of 0 - 13/14*f**3 - 9/14*f**2 + 9*f - 1/7*f**4. Factor c(y).
-3*(y + 3)*(4*y + 1)/7
Suppose -3*c - 7 = -1. Let h be 0 + 5/c + 3. Solve -1/2*o**4 + o**3 - h*o**2 + 0*o + 0 = 0.
0, 1
Let r(f) be the second derivative of 1/8*f**2 + 1/80*f**5 + 9*f - 1/48*f**4 + 0 - 1/24*f**3. Factor r(o).
(o - 1)**2*(o + 1)/4
Factor -3/5*f + 0 - 3/5*f**2.
-3*f*(f + 1)/5
Let j(z) be the first derivative of z**7/945 - z**5/270 - 3*z**2/2 - 2. Let l(s) be the second derivative of j(s). Factor l(d).
2*d**2*(d - 1)*(d + 1)/9
Suppose 1/9*r**2 + 5/9*r + 4/9 = 0. Calculate r.
-4, -1
Let x(u) be the third derivative of u**6/240 - u**5/60 - 13*u**2. Solve x(b) = 0.
0, 2
Let h(y) be the third derivative of -5*y**8/336 + y**6/6 - y**5/6 - 5*y**4/8 + 5*y**3/3 + 13*y**2. Find b, given that h(b) = 0.
-2, -1, 1
Let h(m) be the third derivative of 2*m**7/105 - 2*m**5/15 + 2*m**3/3 + 16*m**2. Factor h(v).
4*(v - 1)**2*(v + 1)**2
Let m be (-24)/(-2) + 3 + 0. Let d**3 - 15 + m - d = 0. What is d?
-1, 0, 1
Factor -2/5*f**5 + 0 + 0*f**2 + 4/5*f**3 + 2/5*f**4 + 0*f.
-2*f**3*(f - 2)*(f + 1)/5
Let x(j) be the second derivative of -j**7/84 - j**6/20 - j**5/20 - 5*j. Determine n, given that x(n) = 0.
-2, -1, 0
Suppose -5*x + 15 = -2*x. Suppose 0 = -0*a - x*a + 15. Factor -m - 2*m + 4 + a*m**2 - 3*m - 1.
3*(m - 1)**2
Suppose -2*c - 4 = -5*r, 0*r = 3*r - c - 3. Find j, given that 6/7*j**r + 2/7 + 2/7*j**3 + 6/7*j = 0.
-1
Factor 625/2 + 135/2*d**3 + 1125/2*d + 675/2*d**2.
5*(3*d + 5)**3/2
Solve 6*r**3 + 2*r**5 + 7*r**3 - 15*r**3 = 0 for r.
-1, 0, 1
Suppose 36 = 33*t - 36*t. Let v be 5/6 + 2/t. Factor -6 - v*q**2 + 4*q.
-2*(q - 3)**2/3
Let b(o) be the second derivative of -o**4/12 - 4*o**3/3 + 3*o**2/2 + 2*o. Let j be b(-8). Factor -9*s**j - s**2 + 10*s**3 + 3*s**2 - s**4.
-s**2*(s - 2)*(s + 1)
Let n be 21/(-12) + 4/16. Let l = 2 + n. Factor l*m**2 + 1/2*m + 0.
m*(m + 1)/2
Factor -15*l**3 + 16*l + 83*l**3 - 20*l**4 + 436*l**2 - 500*l**2.
-4*l*(l - 2)*(l - 1)*(5*l - 2)
Factor 0*w**2 + 0*w**3 + 0*w + 0 + 8/5*w**4 + 4/5*w**5.
4*w**4*(w + 2)/5
Suppose 0*t - 4*a - 8 = -t, 0 = 3*t + 2*a + 18. Let q(b) = b**3 + 3*b**2 - 4*b + 3. Let y be q(t). What is f in y*f**5 - 4*f**5 + 3*f**3 - 2*f**4 - 4*f**3 = 0?
-1, 0
Let m(h) be the third derivative of h**8/70560 + h**7/4410 + h**6/630 - h**5/60 - 3*h**2. Let n(k) be the third derivative of m(k). Suppose n(z) = 0. What is z?
-2
Let g = -11 - -13. Suppose -g*z = 2*z - 8. Factor -3/4*p - 1/4*p**3 + 3/4*p**z + 1/4.
-(p - 1)**3/4
Let x(g) be the third derivative of -2*g**2 - 1/105*g**7 + 0*g**6 + 0 - 1/3*g**3 + 0*g**4 + 1/15*g**5 +