f -x**8/30240 - x**7/3780 - x**6/1080 + x**5/30 - x**2. Let k(h) be the third derivative of g(h). Let k(p) = 0. Calculate p.
-1
Let a be (-4)/3 + (-44)/297*-9. Factor -k + 1/2*k**3 - 1/2*k**2 + a.
k*(k - 2)*(k + 1)/2
Let 0*w - 8/5*w**4 + 2/5*w**2 + 6/5*w**3 + 0 = 0. What is w?
-1/4, 0, 1
Suppose -115 - 41 = -39*x. Let c = 12/5 + -88/45. Suppose 2/9*r**3 + 2/9*r**2 + 0 + 0*r - c*r**x = 0. Calculate r.
-1/2, 0, 1
Let f be 2 + -1 - (-1 + 0). Let t be (1/f)/((-2)/(-32)). What is p in t*p**2 + 41*p**4 + 9*p**4 + 60*p**3 - 20*p**3 = 0?
-2/5, 0
Let n be (6 - 1) + -1 - (-22 + 21). Let f(g) be the second derivative of 1/24*g**4 + g + 0*g**2 - 1/40*g**n + 0*g**3 + 0. Determine k so that f(k) = 0.
0, 1
Suppose -2*w = -5*w + 2*t + 17, 0 = -4*w - 5*t - 8. Let f be 35*(51/(-18) + w). Determine r so that 0*r**2 - 13/2*r**3 + 2/3*r + f*r**4 + 0 = 0.
-2/7, 0, 2/5, 1
Let w(x) be the third derivative of -2*x**7/315 + x**6/30 - 2*x**5/45 + 37*x**2. Factor w(r).
-4*r**2*(r - 2)*(r - 1)/3
Let h(i) = -i - 12. Let a be h(-14). Suppose -3*x + a = 5*k - 41, 0 = 3*x + 4*k - 44. Solve -18/5 + 32/5*n**3 - x*n**2 + 66/5*n = 0 for n.
3/4, 1
Let o(k) be the first derivative of k**6/60 + k**5/10 + k**4/4 + k**3/3 + 2*k**2 - 9. Let i(m) be the second derivative of o(m). Find n, given that i(n) = 0.
-1
Suppose -x = -5*c + x + 626, -3*c = -5*x - 368. Let l be 2/3 - 28/c. Suppose -2/9 - l*a**2 - 4/9*a**3 - 2/9*a**5 + 2/3*a**4 + 2/3*a = 0. Calculate a.
-1, 1
Let d(q) = q**2 + 6*q. Let z be d(-6). Let x(c) be the first derivative of z*c - 1 - 10/3*c**3 + 3/2*c**4 + 2*c**2. Factor x(g).
2*g*(g - 1)*(3*g - 2)
Let s(z) be the first derivative of -34*z**6/21 - 8*z**5/35 + 17*z**4/7 + 8*z**3/21 + 8. Suppose s(k) = 0. Calculate k.
-1, -2/17, 0, 1
Let q = 43/1485 + -2/297. Let t(f) be the second derivative of -1/30*f**5 + 3*f + 1/18*f**4 + 1/9*f**3 + 0 - q*f**6 + 0*f**2. Determine c, given that t(c) = 0.
-1, 0, 1
Suppose x + 3*x = 168. Let h be (-4)/x*1*-3. Suppose 0 + 2/7*b**2 - h*b = 0. What is b?
0, 1
Factor 0*v - 2/11*v**3 + 8/11 - 6/11*v**2.
-2*(v - 1)*(v + 2)**2/11
Let n(x) = x**2 + x + 1. Let u(r) = 3*r**2 + 6*r + 9. Let y be ((-6)/(-10))/1*10. Let l(t) = y*n(t) - u(t). Factor l(g).
3*(g - 1)*(g + 1)
Factor 8*b**2 + 0 - 14*b - 6*b**2 - 8*b**2 - 4.
-2*(b + 2)*(3*b + 1)
Let g(q) be the second derivative of q**5/8 - 5*q**4/24 - 5*q**3/3 + 5*q**2 + 7*q. Let g(i) = 0. What is i?
-2, 1, 2
Let s be -1*((0 - 4) + 1). Let l(o) be the first derivative of -1/5*o**5 + 1/4*o**4 + 3 + 1/3*o**s - 1/2*o**2 + 0*o. Suppose l(i) = 0. What is i?
-1, 0, 1
Let c(k) = -k**3 + 8*k**2 - 7*k + 2. Let x be c(7). Let b be -2*x*6/(-12). Factor -5/2*p**b + 3/2*p**3 - 2*p + 2.
(p - 2)*(p + 1)*(3*p - 2)/2
Let d = 9 + -9. Determine j, given that -4*j + 4*j**3 + 4*j**4 - 2*j**2 + d*j**3 - 2*j**2 = 0.
-1, 0, 1
Let g(z) be the first derivative of z**3/3 - 3*z**2/7 - z/7 + 3. Factor g(c).
(c - 1)*(7*c + 1)/7
Let f(s) be the first derivative of 1 + 2*s**2 + 2*s + 5/6*s**3 + 1/8*s**4. Factor f(p).
(p + 1)*(p + 2)**2/2
Let r(u) be the third derivative of u**3 + 0 + 1/30*u**5 - 10*u**2 - 1/3*u**4 + 0*u. Factor r(g).
2*(g - 3)*(g - 1)
Let q(i) = -i**2 - 4*i - 5. Let f be q(-5). Let h be ((-24)/20)/(27/f). Factor 2/9*g - 2/9*g**2 + h.
-2*(g - 2)*(g + 1)/9
Let o = 126 + -123. Solve 3/7*x**o + 0*x - 3/7*x**2 + 6/7*x**4 + 0 = 0 for x.
-1, 0, 1/2
Let g(v) be the second derivative of 0*v**2 + 3/50*v**5 - 4*v - 1/15*v**3 + 0*v**4 + 0 + 2/75*v**6. Factor g(n).
2*n*(n + 1)**2*(2*n - 1)/5
Let f = -60 + 27. Let q be f/(-5) - 3 - 0. Determine h so that q*h**2 + 2/5*h**4 + 14/5*h + 4/5 + 2*h**3 = 0.
-2, -1
Let c(j) be the first derivative of 0*j - 1/14*j**4 - 6/35*j**5 + 0*j**2 + 0*j**3 - 1. Solve c(t) = 0.
-1/3, 0
Let m(u) = u**2 + 4*u + 7. Let k be m(-3). Factor -8 - 4*h**3 - k*h**4 + 8.
-4*h**3*(h + 1)
Suppose 24 = 65*s - 53*s. What is x in 1/2 - 35/4*x**s + 3/4*x - 9*x**3 = 0?
-1, -2/9, 1/4
Let l = 24/11 + -277/132. Let v(i) be the first derivative of -l*i**4 + 1/6*i**2 - 2 + 1/3*i - 1/9*i**3. Factor v(f).
-(f - 1)*(f + 1)**2/3
Let i(g) be the second derivative of g**6/10 - 3*g**5/20 - 17*g. Factor i(s).
3*s**3*(s - 1)
Let k(h) be the second derivative of 3*h**5/160 - 3*h**4/32 + 3*h**2/4 - 12*h - 2. Suppose k(d) = 0. What is d?
-1, 2
Let b(u) = 2*u**2 + 4*u - 1. Let s be b(-3). Suppose 4 = -4*j + g, -s*j + 4*g - 12 - 4 = 0. What is k in -2*k**4 - 2 + 4*k**4 + j*k**3 + 4*k - 4*k**3 = 0?
-1, 1
Let r(q) be the first derivative of q**3 + 3*q**2/2 + 4. Suppose r(h) = 0. Calculate h.
-1, 0
Let p(o) = o**3 - 9*o**2 - 10*o + 5. Let t be p(10). Factor -t - 9 + 32*m + 12 - 128*m**2.
-2*(8*m - 1)**2
Determine s so that 375 - 4*s**3 + 6*s**2 - 225*s + 0*s**3 + s**3 + 39*s**2 = 0.
5
Let b be 1*12/(-9)*(-1 + -2). Let s(j) be the second derivative of 1/4*j**b + 1/20*j**5 + 0 - j - 1/6*j**3 - 1/30*j**6 - j**2. Suppose s(o) = 0. What is o?
-1, 1, 2
Let r(n) be the second derivative of 3*n**5/10 - 7*n**4/18 - 2*n**3/9 + 34*n. Factor r(t).
2*t*(t - 1)*(9*t + 2)/3
Factor -7/2*d**3 - 3/2*d - 1 + 6*d**2.
-(d - 1)**2*(7*d + 2)/2
Let i(y) = -43*y + 43. Let r be i(1). Determine h, given that 8/3*h + 2/3*h**2 + r = 0.
-4, 0
Let q be (11 - -1) + -4 + 2. Let r = q - 7. Determine n so that -1/2*n**2 - 1/2*n + 1/2*n**r + 1/2 = 0.
-1, 1
Suppose -1/3*d**2 - 16/3*d - 64/3 = 0. What is d?
-8
Factor 14/9*d + 2*d**2 + 2/9*d**4 + 10/9*d**3 + 4/9.
2*(d + 1)**3*(d + 2)/9
Suppose -65 = 5*y - 5*l, -y + 2*l = 4*y + 71. Let b be (-2)/(3 - (-51)/y). Factor -1/3*t - 7/3*t**2 - 3*t**4 + 0 - b*t**3.
-t*(t + 1)*(3*t + 1)**2/3
Let p(k) be the first derivative of 7/4*k**4 + 0*k + 0*k**2 + 49/20*k**5 + 1/3*k**3 - 1. Suppose p(g) = 0. Calculate g.
-2/7, 0
Let u(s) be the first derivative of -s**6/600 + s**5/60 - s**4/15 + 2*s**3/15 + 3*s**2/2 - 5. Let k(i) be the second derivative of u(i). Factor k(a).
-(a - 2)**2*(a - 1)/5
Suppose -1/2*l**2 - 1/4*l + 0 - 1/4*l**3 = 0. Calculate l.
-1, 0
Suppose 0 = -3*w - 3*o + 12, 2*o + 12 = -2*w + 4*w. Suppose -5*g + 8 = -v, -5*g + w*v - 8 = -4*g. Let -4 + 3 - 1 + 3*c**g - c = 0. What is c?
-2/3, 1
Let c(t) be the second derivative of -3*t**2 + 2/3*t**3 - 1/18*t**4 - 3*t + 0. Factor c(x).
-2*(x - 3)**2/3
Let o(l) = 3*l**2 + 8*l. Let w(h) = h**2 + h. Let s(x) = -5*o(x) + 20*w(x). Solve s(v) = 0.
0, 4
Suppose -5 = -2*w - 3*w - 5*z, 4*z = 4*w + 4. Solve 1/3*o**2 - 1/3*o - 1/3*o**4 + 1/3*o**3 + w = 0.
-1, 0, 1
Let h(p) be the second derivative of 0*p**3 + 0 - p + p**2 + 1/12*p**4 - 1/30*p**5. Let s(t) be the first derivative of h(t). Let s(z) = 0. What is z?
0, 1
Suppose -5*i + 30 = 5*u, -i + 12 = -u + 2. Determine g, given that -7*g + 6*g**3 - 6*g**4 - 1 - 9*g**2 - i*g**2 - 23*g**3 = 0.
-1, -1/2, -1/3
Suppose 0 = 5*g - 1 + 6. Let o be 2/2 + 0 - g. Factor 0 + 1/4*q**4 + 1/4*q**o - 1/2*q**3 + 0*q.
q**2*(q - 1)**2/4
Let y(o) be the first derivative of 4*o**5/5 - o**4/2 - 8. Suppose y(z) = 0. What is z?
0, 1/2
Let c(u) = -5*u. Let z be c(-1). Suppose d - 5*d**2 - z*d - d**4 - 4*d**3 + 2*d = 0. Calculate d.
-2, -1, 0
Let t(b) = b**5 + b**4 + 3*b**3 - b**2 - 6*b + 2. Let j(y) = 3*y**5 + 3*y**4 + 5*y**3 - 3*y**2 - 11*y + 3. Let z(w) = 2*j(w) - 5*t(w). Factor z(u).
(u - 1)**3*(u + 2)**2
Factor 0 + 0*w + 3/7*w**2 + 0*w**3 - 3/7*w**4.
-3*w**2*(w - 1)*(w + 1)/7
Let y(j) be the third derivative of j**5/20 + 3*j**4/8 + j**3 - 7*j**2. Determine u so that y(u) = 0.
-2, -1
Let j(m) be the first derivative of 14*m**3/33 + m**2 + 8*m/11 - 5. Factor j(g).
2*(g + 1)*(7*g + 4)/11
Let t = 15 - 1. Let y be ((-1)/2)/(t/(-14)). Factor -1 + 3/2*u - y*u**2.
-(u - 2)*(u - 1)/2
Solve -4*t**5 - 4*t**2 + 10*t**3 + 4*t**4 - 6*t**3 + 0*t**4 = 0.
-1, 0, 1
Let u be (-3)/(-2)*(6 - 30/9). Let -15*x + 9/2 + 10*x**3 + 13/2*x**2 + 2*x**u = 0. What is x?
-3, 1/2
Let y(w) be the third derivative of 0*w + 4*w**2 - 1/12*w**4 + 1/21*w**8 - 13/40*w**6 + 0 + 4/105*w**7 + 17/60*w**5 + 0*w**3. Suppose y(p) = 0. What is p?
-2, 0, 1/4, 1
What is a in 8/5*a**4 + 2/5*a**5 + 0 + 2/5*a + 8/5*a**2 + 12/5*a**3 = 0?
-1, 0
Let s(l) be the second derivative of 1/4*l**4 + 0*l**3 + 0 - 3/40*l**5 + 0*l**2 - 5*l. Let s(b) = 0. Calculate b.
0, 2
Let m(n) be the third derivative of -n**8/420 + 2*n**7/175 - n**6/50 + n**5/75 - 4*n**2. Factor m(y).
-4*y**2*(y - 1)**3/5
Suppose -m + 4*m + 2*p - 10 = 0, -2*m + 2