Suppose m + 3*k = 5*m - 18, -5*m = -4*k - 23. Solve 1 + j*c**2 + 6*c + 4 - 3 + 2*c**m = 0 for c.
-1
Let u be 4 - 5/((-10)/(-4)). What is d in -6*d**3 - 3*d**2 + d**u + 2*d**2 - 2*d**4 - 4*d**2 = 0?
-2, -1, 0
Let g(n) = -8*n - 13*n**3 - 5 + 10*n**2 - 4*n**2 + 14*n**3. Let l be g(-7). Factor 3/2*s**3 + 0 + 1/2*s**4 + 1/2*s + 3/2*s**l.
s*(s + 1)**3/2
Let h(b) be the first derivative of 5*b**4/4 - 30*b**2 + 80*b + 23. Factor h(v).
5*(v - 2)**2*(v + 4)
Let z(m) = -3*m**3 + 4*m**2 - 10*m + 4. Let l(s) = -s**3 - s**2 + s + 1. Let b(j) = 2*l(j) - z(j). Let n(c) be the first derivative of b(c). Factor n(o).
3*(o - 2)**2
Let z(l) = l**2 - l + 1. Let x be 1*(-1 + -1 + 7). Let p(v) = 4*v**2 - 6*v + 5. Let a(d) = x*z(d) - p(d). Factor a(q).
q*(q + 1)
Let x(k) = -5*k - 1. Let y be x(-1). Let m = -598 + 607. Factor -4*v**2 - 6*v**3 - 5/2*v**5 + m*v**y + 0*v + 0.
-v**2*(v - 2)**2*(5*v + 2)/2
Let z(f) be the first derivative of 1/3*f**3 - 3*f - 3 + f**2. Find u, given that z(u) = 0.
-3, 1
Let r = -2 - -6. Suppose o + 4*s - 7 = 0, o + 6*s = r*s + 5. Factor -3*l**o - 3*l**4 + 4*l**4 + 4*l**3.
l**3*(l + 1)
Determine n so that -130*n + 10*n**3 - 2*n**4 + 7 + 7*n**4 - 20*n**2 + 8 + 120*n = 0.
-3, -1, 1
Determine h so that 12/5*h**2 - 14/5*h + 2/5 = 0.
1/6, 1
Let p(d) = d**2 + 3*d - 5. Let o be p(-5). Let r = o - 1. Let 1/4*q**r + 0 - 1/4*q**2 - 3/4*q**3 + 1/2*q**5 + 1/4*q = 0. What is q?
-1, 0, 1/2, 1
Let t(l) be the first derivative of 7*l**4/16 - l**3/4 - 4*l + 11. Let w(a) be the first derivative of t(a). Determine i so that w(i) = 0.
0, 2/7
Factor -8*j**4 - j**2 + 6*j**4 + 2*j**3 + j**4.
-j**2*(j - 1)**2
Let u be -7 - (-7)/(-84)*-93. Factor 3/4*c**3 + 3/2*c**2 + u*c + 0.
3*c*(c + 1)**2/4
Let g = -15 + 16. Let w be 14/7 + g + 0. Factor -1/3*p**w + 0 + 0*p - 1/3*p**2.
-p**2*(p + 1)/3
Let n = 13 + -5. Suppose 3*z - 5*z = -n. What is h in -h**5 + 1/2*h**2 + 5/2*h**z + 0*h + 0 - 2*h**3 = 0?
0, 1/2, 1
Let r = 6 + -4. Let f be 141/(-132) - -2 - 4/22. Suppose -1/4*u**3 - f*u + 1/4 + 3/4*u**r = 0. What is u?
1
Let o be ((-8)/140)/(30/(-112)). Let x(l) be the second derivative of -o*l**6 + l - 1/15*l**4 + 0*l**2 + 0 - 11/50*l**5 - 1/15*l**7 + 0*l**3. Factor x(p).
-2*p**2*(p + 1)**2*(7*p + 2)/5
Let r be ((-4)/(-80)*2)/((-1)/(-4)). Let 2/5*k + r*k**2 + 0 = 0. Calculate k.
-1, 0
Let f(z) be the first derivative of 7*z**4/24 - 8*z**3/9 + z**2/3 - 8. Factor f(c).
c*(c - 2)*(7*c - 2)/6
Let u(b) be the second derivative of 1/6*b**4 - 1/60*b**5 - 1/180*b**6 + 0 - 3*b + 0*b**2 - 1/2*b**3. Let k(f) be the second derivative of u(f). Factor k(m).
-2*(m - 1)*(m + 2)
Let a(h) be the first derivative of -h**6/18 - 14*h**5/15 - 73*h**4/12 - 172*h**3/9 - 88*h**2/3 - 64*h/3 - 17. Factor a(y).
-(y + 1)**2*(y + 4)**3/3
Let c be 13 + (-6)/(-3)*-1. Suppose -1 = 2*u - c. Factor 2*l**2 - 4*l**2 + 2*l - l**2 + u*l**2.
2*l*(l + 1)
Factor -1/2*i**3 - 3/2*i + 1/2 + 3/2*i**2.
-(i - 1)**3/2
Let r be -1 + (2 - -1) - 0. Determine a, given that 3*a**3 - a**4 - 5*a**3 + 2*a - a**4 - 7*a**r + 9*a**2 = 0.
-1, 0, 1
Let -1/2*a**4 + 3/4 + 3/4*a**3 + 3/4*a**2 - 7/4*a = 0. Calculate a.
-3/2, 1
Suppose 3/5*g**3 + 3 - 3*g**2 - 3/5*g = 0. What is g?
-1, 1, 5
Let b be 1/(-8) - (-117)/360. Solve -b + 1/5*i**2 + 0*i = 0 for i.
-1, 1
Let d(w) be the first derivative of 3*w**6/5 + 78*w**5/25 + 29*w**4/5 + 24*w**3/5 + 8*w**2/5 + 24. Find g such that d(g) = 0.
-2, -1, -2/3, 0
Suppose -38 = 5*j - 38. Let s(i) be the first derivative of -i**2 + 2/3*i**3 + 3 + j*i. What is n in s(n) = 0?
0, 1
Factor 1/8*k**2 + 1/4 - 3/8*k.
(k - 2)*(k - 1)/8
Let g(m) = 11*m**2 + 31*m + 49. Let p(w) = -w**3 + 4*w**2 - w - 1. Let n be p(3). Let j(a) = -39*a**2 - 108*a - 171. Let r(i) = n*j(i) + 18*g(i). Factor r(f).
3*(f + 3)**2
Suppose 0 = g + 3*c - 26 + 10, -3*c + 37 = 4*g. Factor 6 - g*n**4 + 2*n**4 - 11*n**3 + 9*n - 3*n**2 + 2*n**4 + 2*n**3.
-3*(n - 1)*(n + 1)**2*(n + 2)
Let y(b) be the first derivative of b**6/10 - b**5/4 + b**4/12 + b**3/6 - 4*b - 6. Let s(j) be the first derivative of y(j). Find n, given that s(n) = 0.
-1/3, 0, 1
Let x(g) be the third derivative of g**7/945 + g**6/45 + 8*g**5/45 + 20*g**4/27 + 16*g**3/9 - 54*g**2. Factor x(q).
2*(q + 2)**3*(q + 6)/9
Suppose -2*u + 1 = -2*h - 7, -3*u = 2*h + 8. Let c(n) be the third derivative of 0*n**3 + 0*n**5 + 0*n + 0*n**6 - 1/840*n**7 + 3*n**2 + 0 + u*n**4. Factor c(i).
-i**4/4
Suppose 3*d + 3*i - 72 = 0, 3*i = -3*d + 2*i + 64. Let j be d/45 - 2/(-9). Factor 0*q**4 + j*q + 0*q**2 - 4/3*q**3 + 2/3*q**5 + 0.
2*q*(q - 1)**2*(q + 1)**2/3
Factor -1/3*n**2 - 1 + 4/3*n.
-(n - 3)*(n - 1)/3
Let k = -53/2 - -375/14. Find u such that k - 1/7*u - 1/7*u**2 = 0.
-2, 1
Factor 21/2*k**5 + 18*k**4 + 0*k + 0 - 3*k**2 + 9/2*k**3.
3*k**2*(k + 1)**2*(7*k - 2)/2
Let c(b) = -b**2 + 8*b + 2. Let l be c(6). Let y = l - 10. Solve 4/5*h**3 + 0 - 2/5*h**5 + 0*h**2 + 0*h**y - 2/5*h = 0 for h.
-1, 0, 1
Let c(z) be the second derivative of -z**4/36 - 5*z**3/18 - 5*z. Factor c(m).
-m*(m + 5)/3
Factor -16/7*n**2 + 4/7*n**4 - 4/7 + 2/7*n**5 - 2*n - 4/7*n**3.
2*(n - 2)*(n + 1)**4/7
Determine r so that -44 + 15*r - 53 + 3*r**2 + 79 = 0.
-6, 1
Suppose 2*t - 20 = -3*g - 0*t, -g + t = -5. Let a be g/(-4)*(-1)/3. Factor d**3 + 0*d + 0*d**2 + 0 - a*d**4.
-d**3*(d - 2)/2
Let j be (-2 + 1)/(2/(-4)). Let g(h) = -1 - 3 + 3. Let m(n) = -n**2 - 2. Let u(x) = j*m(x) - 4*g(x). Find w such that u(w) = 0.
0
Suppose -2*r = 2*r - 8. Suppose -5*u = -2*u. Factor 0*v + u + 0*v**r + 1/2*v**3.
v**3/2
Let c(n) be the first derivative of 2*n**5/5 + 2*n**4 + 4*n**3 + 4*n**2 + 2*n + 4. Factor c(t).
2*(t + 1)**4
Factor -4/7 - 12/7*r**2 - 12/7*r - 4/7*r**3.
-4*(r + 1)**3/7
Suppose -b**5 - 324*b**2 - 126*b**3 + 554*b - 2 + 2 - 770*b - 19*b**4 = 0. Calculate b.
-6, -1, 0
Suppose -5 = -v + 7. Let b be v/(-4) - (-1 + -4). Determine m, given that -8/3 - 2/3*m**b - 8/3*m = 0.
-2
Suppose q + 6 = 4*q. Find u, given that 4*u**2 - 5*u - 2 + 0*u**2 - 2*u**q - 4*u**2 = 0.
-2, -1/2
Let x(d) be the third derivative of -d**8/2016 + d**7/315 - d**6/120 + d**5/90 - d**4/144 + 32*d**2. Factor x(s).
-s*(s - 1)**4/6
Suppose 5*m - z + 15 = 0, -6*m = -m + 4*z - 10. Let l = m - -4. Suppose -4*k + 0*k**l + 2*k**2 + k + 1 = 0. What is k?
1/2, 1
Suppose 5*w - 15 = 10. Let f(x) = -x**2 + 3*x. Let a(h) = 2*h**2 - 7*h. Let v(c) = w*f(c) + 2*a(c). Suppose v(y) = 0. Calculate y.
0, 1
Let d(r) be the first derivative of 9/2*r + 1/6*r**3 - 4 + 3/2*r**2. Suppose d(t) = 0. Calculate t.
-3
Let n(m) = m**2 - m. Let k(r) be the first derivative of -4*r**3/3 + 2*r**2 + 4*r - 5. Let s(l) = k(l) + 2*n(l). Find w, given that s(w) = 0.
-1, 2
Let x(h) = 12*h + 38. Let w be x(-3). Factor -1/5 + 2/5*y + 7/5*y**w + 4/5*y**3.
(y + 1)**2*(4*y - 1)/5
Let p(g) = -3*g**2 + 3*g + 40. Let w be p(-3). Find m, given that 2/5*m**2 + 0*m + 0 + 0*m**3 - 2/5*m**w = 0.
-1, 0, 1
Let r be (8/(-10))/(2/15). Let m(h) = -h**2 + 1. Let d(p) = 2*p**2 - p - 1. Let i(o) = r*d(o) - 15*m(o). Solve i(w) = 0 for w.
-3, 1
Let j(h) be the third derivative of -h**6/80 + h**5/10 + h**4/16 - h**3 + 2*h**2 - 26. Solve j(a) = 0.
-1, 1, 4
Suppose -2*g - h = -8, 5*g - 3*h = -2*h + 6. Let q(r) = -10*r + 7 + 0*r + 1 + 25*r**g - 4. Let c(l) = 1. Let t(n) = 3*c(n) - q(n). What is d in t(d) = 0?
1/5
Suppose -21*x + 13 = -29. Determine h so that 36/5*h**3 - 14/5*h**x + 0 + 16/5*h**5 - 8*h**4 + 2/5*h = 0.
0, 1/2, 1
Let o(m) be the first derivative of 8*m + 10/3*m**3 + 16*m**2 - 25/2*m**4 + 3. Suppose o(v) = 0. What is v?
-2/5, 1
Suppose 2*z + 3 - 7 = 0. Let n be (0 + 2)*(0 + 2). Factor -5*p**4 + n*p**z + 1 + p + 0 + 3*p - 2*p**5 - 2*p**3.
-(p - 1)*(p + 1)**3*(2*p + 1)
Let s(t) be the second derivative of -t**7/12600 + t**6/900 - t**5/150 + t**4/6 + 2*t. Let x(h) be the third derivative of s(h). Solve x(r) = 0.
2
Let w be (-176)/(-440) + (-2)/(-70). Factor 0 + 3/7*i**4 - 3/7*i**5 + 0*i + w*i**3 - 3/7*i**2.
-3*i**2*(i - 1)**2*(i + 1)/7
Factor -4*z + 3*z**2 + 4*z - 6*z**2 - 3*z.
-3*z*(z + 1)
Let q = -30/7 + 157/35. What is d in -1/5*d**3 + 2/5 - 2/5*d**2 + q*d = 0?
-2, -1, 1
Let c(z) = 5*z**2 + 4. Let r(b) = 9*b**2 - b + 8. Let p(s) = 7*c(s) - 4*r(s). Let p(l) = 0. What is l?
2
Let 5/2*r**4 + 5/2*r**3 - 5/2*r**2 + 0 - 5/2*r = 0. Calculate r.
-1, 0, 1
Suppose 0 = -3*x + 2 + 1. Factor 0 + 2 + x + 0*t**2 - 3*t**2.
-3*(t - 1)*(t + 1)
L