1*(-5)/((-20)/(-12)). Let k be -6*((-40)/12 - p). Determine z, given that -1/4*z**k + 0*z + 1/4 = 0.
-1, 1
Let w(d) = -3*d**2 - 2*d + 5. Let z(o) = 3*o**2 + o - 4. Let g be (-108)/26 - 8/(-52). Let j(v) = g*w(v) - 5*z(v). Suppose j(q) = 0. What is q?
0, 1
Let h(w) = w + 10. Let t be h(-8). What is o in 2*o + 0*o**2 - t*o**2 + 4*o**2 = 0?
-1, 0
Factor -k**4 + 2*k**2 - 2*k + 3*k + 3*k**3 - 4*k**2 - k**2.
-k*(k - 1)**3
Let z = -143 - -207. Solve -6*m**3 + 88*m**2 - 42*m**3 + 16 + 7*m**4 - z*m + 2*m**4 = 0 for m.
2/3, 2
Suppose -4/3*q + 0 - 2/3*q**2 = 0. What is q?
-2, 0
Factor -2/17*p**2 - 6/17 - 8/17*p.
-2*(p + 1)*(p + 3)/17
Let i be 0/((-2)/(-4)*-2). Suppose y - 4*y = -6. Factor 0 + i*a + 0*a**y + 2/7*a**3.
2*a**3/7
Suppose 0 = 3*h - n - 2*n + 12, 3*n + 2 = -4*h. Let m be ((-4)/45)/h*10. Factor 2/9 + 2/9*u**2 + m*u.
2*(u + 1)**2/9
Let v(c) be the second derivative of 7*c**6/225 + 37*c**5/150 + 59*c**4/90 + 7*c**3/9 + 2*c**2/5 - 2*c + 4. Suppose v(s) = 0. Calculate s.
-3, -1, -2/7
Let v(l) be the second derivative of -l**7/21 + 2*l**6/15 + l**5/10 - l**4/3 + 23*l. Solve v(u) = 0 for u.
-1, 0, 1, 2
Let u(p) be the first derivative of -3 - 1/12*p**6 - 1/4*p**2 + 0*p + 2/3*p**3 - 3/4*p**4 + 2/5*p**5. Let u(d) = 0. What is d?
0, 1
Suppose -4*f = 4*t - 76, -3*f + 55 = -5*t + 14. Suppose 23 + f = 4*g. Suppose -g*m**2 + 0 - 2*m - 25/2*m**3 = 0. What is m?
-2/5, 0
Let c(d) be the first derivative of -d**6/24 + 3*d**4/16 + d**3/6 - 9. Determine s, given that c(s) = 0.
-1, 0, 2
Let q(l) be the first derivative of -l**5 + 5*l**4 + 5*l**3/3 - 10*l**2 + 11. Factor q(n).
-5*n*(n - 4)*(n - 1)*(n + 1)
Factor 20*o - 8 + 12 - 32*o**4 - 6 + 80*o**3 - 66*o**2.
-2*(o - 1)**2*(4*o - 1)**2
Suppose 3*f + 0*f - 6 = 0. Suppose -g - 3 = -f*g. Solve u**2 + 0*u**5 + u**3 + 0*u**5 - u**4 + 0*u**g - u**5 = 0.
-1, 0, 1
Let p(h) be the second derivative of h**7/420 + h**6/300 - 3*h**5/200 - h**4/120 + h**3/30 - 9*h. Find v, given that p(v) = 0.
-2, -1, 0, 1
Let v(n) be the third derivative of -n**6/2160 + n**5/360 - n**3/6 + 3*n**2. Let y(k) be the first derivative of v(k). Factor y(r).
-r*(r - 2)/6
Let u(c) be the third derivative of c**6/420 - c**5/105 - c**4/84 + 2*c**3/21 + 5*c**2. Find g such that u(g) = 0.
-1, 1, 2
Suppose 5 - 30 = 5*u. Let g be (-28)/u + (-6)/10. Factor -8/11*v**g - 14/11*v - 50/11*v**3 - 38/11*v**2 - 2/11 - 32/11*v**4.
-2*(v + 1)**3*(2*v + 1)**2/11
What is w in 4*w + 3*w**2 + 2 + 1/8*w**4 + w**3 = 0?
-2
Let v(s) be the third derivative of -1/735*s**7 + 1/210*s**5 + 0*s + 0 - 1/420*s**6 + 0*s**3 + 1/84*s**4 + s**2. Determine h, given that v(h) = 0.
-1, 0, 1
Let 1/4*y**2 + 3/4*y + 1/2 = 0. Calculate y.
-2, -1
What is c in 0*c - 32/3*c**4 + 2*c**5 + 12*c**2 + 0 + 10*c**3 = 0?
-2/3, 0, 3
Let q(a) be the third derivative of a**6/200 - a**5/25 + a**4/10 - 27*a**2. Suppose q(p) = 0. Calculate p.
0, 2
Suppose -w + 1 = -1. Let -2 + 7 + 4*h + 3 - 4*h**w = 0. Calculate h.
-1, 2
Let c(s) = -s**3 + 6*s**2 - 6*s. Let z be c(5). Let x = 9 + z. Solve -2*d**5 - 3*d**x + d**5 + d**4 - d**3 = 0 for d.
-1, 0
Let x(s) be the first derivative of -2/3*s**3 - 5 + 0*s + s**4 - 2/5*s**5 + 0*s**2. Find i such that x(i) = 0.
0, 1
Let j = 251 + -251. Let i(x) = -x. Let a be i(-3). Solve 3/4*d**4 - 1/2*d + j + 1/2*d**a - 3/4*d**2 = 0 for d.
-1, -2/3, 0, 1
Let x(j) be the first derivative of 7*j**5/20 + 4*j**4/3 + 11*j**3/6 + j**2 - 3*j + 5. Let b(v) be the first derivative of x(v). Factor b(t).
(t + 1)**2*(7*t + 2)
Let w(v) be the second derivative of -v**6/108 + v**5/60 + v**4/18 + v**3/2 + 2*v. Let p(i) be the second derivative of w(i). What is s in p(s) = 0?
-2/5, 1
Let n(m) be the first derivative of -3*m**5/10 - 13*m**4/6 - 16*m**3/3 - 4*m**2 - 2*m - 3. Let d(j) be the first derivative of n(j). Factor d(u).
-2*(u + 2)**2*(3*u + 1)
Let d(w) = -2*w**3 - 14*w**2 - 5*w - 31. Let i be d(-7). Solve 2*t**i - 2*t**2 + 2/3*t**3 - 2/3*t + 0 = 0.
-1, -1/3, 0, 1
Let r(n) be the third derivative of n**6/900 - n**5/450 - n**4/180 + n**3/45 + 15*n**2. Factor r(i).
2*(i - 1)**2*(i + 1)/15
Let a(r) be the first derivative of r**6/2 + 3*r**5/5 - 3*r**4/2 - 2*r**3 + 3*r**2/2 + 3*r - 20. Factor a(t).
3*(t - 1)**2*(t + 1)**3
Let z be 80 + (-8)/(2 - -2). Let x = -232/3 + z. Suppose 0 + 2/3*h**3 + 0*h + x*h**2 = 0. Calculate h.
-1, 0
Suppose -4*w + 6 = -6. Suppose -w*q + 0*q = 0. Factor 1/2*l**3 - 1/2*l**2 + 0*l + q.
l**2*(l - 1)/2
Let -24*c - 3*c**3 - 8 - 42*c + 21*c - 19 - 21*c**2 = 0. Calculate c.
-3, -1
Let o(j) = -3*j**3 - 4*j**2 - 7*j + 7. Let z(i) = -5 + 2*i + i**3 + i**2 - 4 + 7. Let f(r) = -2*o(r) - 7*z(r). Factor f(k).
-k**2*(k - 1)
Let f = 1098 + -7684/7. What is k in f + 4/7*k + 2/7*k**2 = 0?
-1
Let p(l) be the second derivative of 0 - 15/56*l**7 - 1/10*l**6 + 7/24*l**4 + l - 7/24*l**3 - 1/4*l**2 + 13/20*l**5. Solve p(v) = 0.
-1, -1/3, 2/5, 1
Let i = 1/77 - -3/11. Let q be (-6)/28*-6 - 1. Factor 0 + 0*o**2 - q*o + i*o**3.
2*o*(o - 1)*(o + 1)/7
Let o be ((-260)/(-75) + -4)*-10. Let y(p) be the first derivative of 2*p - 7*p**2 + o*p**3 + 8*p**4 - 2. Determine g so that y(g) = 0.
-1, 1/4
Let a = -18 + 19. Let k(f) be the first derivative of 0*f - 1/9*f**3 + 1/6*f**2 + a. Factor k(b).
-b*(b - 1)/3
Let h(x) be the second derivative of x + 0 + 1/6*x**4 - 3/50*x**5 + 0*x**2 - 1/15*x**3 - 3/25*x**6. Factor h(k).
-2*k*(k + 1)*(3*k - 1)**2/5
Let s(u) be the first derivative of 2 - 1/9*u**3 - 1/12*u**4 + 0*u**2 + 0*u. Factor s(r).
-r**2*(r + 1)/3
Let s = -43 - -47. Let l(f) be the third derivative of -1/60*f**6 - 1/42*f**5 + 0 - 3*f**2 + 1/42*f**s + 0*f + 0*f**3. Solve l(z) = 0.
-1, 0, 2/7
Let g(u) be the second derivative of -u**6/90 - u**5/12 - u**4/4 - 7*u**3/18 - u**2/3 - 4*u. Let g(z) = 0. What is z?
-2, -1
Let x = -6 + 7. Let r(b) be the first derivative of 0*b - 1/2*b**4 + b**2 - 2/3*b**3 - x + 2/5*b**5. Factor r(g).
2*g*(g - 1)**2*(g + 1)
Let -3*g - 4*g**2 + 3*g**2 + 0*g = 0. What is g?
-3, 0
Let y(n) be the second derivative of -80*n**7/63 - 8*n**6/45 + 91*n**5/30 + 5*n**4/9 - 11*n**3/9 - 2*n**2/3 + 3*n. Suppose y(z) = 0. Calculate z.
-1, -1/4, 2/5, 1
Determine i, given that 6/17*i**3 - 2/17*i**4 + 0 - 2/17*i**5 + 4/17*i + 10/17*i**2 = 0.
-1, 0, 2
Let a(v) be the third derivative of -v**8/112 + v**7/70 + v**6/8 - v**5/20 - v**4 - 2*v**3 - 13*v**2. Factor a(l).
-3*(l - 2)**2*(l + 1)**3
Suppose -5*q = -k, -4*k = q - 2*q. Let x(f) be the third derivative of 3*f**2 + 1/30*f**5 + 1/6*f**4 + 0*f + 0 + q*f**3. Determine t, given that x(t) = 0.
-2, 0
Let v(c) be the second derivative of -5*c**4/12 - 5*c**3/6 + 5*c**2 + 14*c. Suppose v(a) = 0. What is a?
-2, 1
Let v(n) be the first derivative of n**4/16 + 5*n**3/12 + 3*n**2/4 - 9. Suppose v(m) = 0. What is m?
-3, -2, 0
Determine p, given that 0*p**2 + 3 + 9/2*p - 3/2*p**3 = 0.
-1, 2
Let o(s) be the third derivative of -s**7/315 - s**6/180 + 14*s**2. Factor o(b).
-2*b**3*(b + 1)/3
Let p(c) be the first derivative of 0*c + 2*c**2 - c**4 - 6/5*c**5 + 2*c**3 - 1. Let p(g) = 0. Calculate g.
-1, -2/3, 0, 1
Let b(p) be the third derivative of -p**7/1540 - p**6/180 - 2*p**5/165 + p**4/33 - p**3 + p**2. Let r(t) be the first derivative of b(t). What is z in r(z) = 0?
-2, 1/3
Let c(u) be the second derivative of 0 + 2*u**4 + 16*u**2 - 8*u**3 + 4*u - 1/5*u**5. Solve c(v) = 0.
2
Let k(a) be the third derivative of 0*a + 0*a**3 + 0*a**4 - 2*a**2 - 1/420*a**7 + 0 - 1/120*a**5 + 1/120*a**6. Solve k(m) = 0 for m.
0, 1
Let k(c) be the second derivative of -1/8*c**2 - 3*c - 1/48*c**4 + 0 - 1/12*c**3. Factor k(b).
-(b + 1)**2/4
Determine h so that 11*h - 3*h - 5*h**2 + 3*h - 20 + 14*h = 0.
1, 4
Let k = 32555/42 - 4169/6. Let y = k + -80. Factor -2/7*j**5 + 0 + 4/7*j**4 - 4/7*j**2 + 0*j**3 + y*j.
-2*j*(j - 1)**3*(j + 1)/7
Suppose 2*x - 11 = -7. Let m(w) = 2*w - 6. Let f be m(4). Find s such that -f*s**3 - 3*s + 4*s**2 - s + 0*s**x + 2*s = 0.
0, 1
Let l(u) be the third derivative of u**6/24 + u**5/12 - 5*u**4/24 - 5*u**3/6 + 9*u**2. Factor l(p).
5*(p - 1)*(p + 1)**2
Suppose -2*j + 5*d + 7 = -0*j, -j + 5*d - 9 = 0. Suppose j = -3*h + 94. Suppose -2 + 6*y - 3*y - 6*y**4 - h*y**2 + 2*y**2 + 9*y + 20*y**3 = 0. What is y?
1/3, 1
Factor -3/2*i**3 + 3/2*i - 3*i**2 + 3/4*i**4 + 9/4.
3*(i - 3)*(i - 1)*(i + 1)**2/4
Let r(g) be the first derivative of 1 - 1/24*g**4 + 1/6*g**3