k + b*k + 4*k**2 = 0.
-1, 1, 2
Solve -37*r**2 - 39*r**2 - 10*r + 25*r**3 + 61*r**2 = 0 for r.
-2/5, 0, 1
Suppose -13*k + 55 = 16. Solve -6/13*r**k - 14/13*r**2 + 6/13*r + 4/13 + 10/13*r**4 = 0 for r.
-1, -2/5, 1
Let c be 4/(-8) - 16/(-30). Let i(h) be the third derivative of 2*h**2 - 1/3*h**4 + 0*h + c*h**5 + 0 + 1/15*h**6 - 1/3*h**3. Find l, given that i(l) = 0.
-1, -1/4, 1
Let k(u) = -5*u + u**3 + 5*u**2 + 2*u**2 + 2 - u**2 - 2*u**3. Let q be k(5). Factor 8/7*v - 8/7 - 2/7*v**q.
-2*(v - 2)**2/7
Let f = 0 - -10. Let a be 1/(-4) - (-5)/f. Suppose 0*w**2 + 0 - a*w**3 + 0*w = 0. What is w?
0
Let m(w) be the first derivative of -1/9*w**3 + 1/18*w**6 + 0*w - 3 - 1/5*w**5 + 0*w**2 + 1/4*w**4. Suppose m(y) = 0. What is y?
0, 1
Let k be 0 - 3/((-18)/7). Let i(y) be the first derivative of 9/5*y**5 - k*y**6 + 0*y**3 + 0*y - 1 - 1/2*y**4 + 0*y**2. Factor i(b).
-b**3*(b - 1)*(7*b - 2)
Suppose 0 = -4*b + 3*b + 1. Let x be -1*b*(-6)/18. What is g in -g - 1/3 - x*g**3 - g**2 = 0?
-1
Solve -4*b**2 - 4*b**4 - 6*b**3 - 6*b**3 + 20*b**3 = 0.
0, 1
Let g(d) = 9*d + 3. Let b be g(-1). Let z(w) = w**3 + 7*w**2 + 6*w + 2. Let a be z(b). Factor 3/5*n**a - 6/5*n + 0.
3*n*(n - 2)/5
Let i be 16/14*(-21)/(-30). Factor -2/5*z**2 - 6/5*z - i.
-2*(z + 1)*(z + 2)/5
Let n(r) be the second derivative of -1/9*r**3 + 1/54*r**4 + 0 + 2/9*r**2 + r. Factor n(z).
2*(z - 2)*(z - 1)/9
Let i be 2/(-5) - (-54)/10. Factor 81 + 22*m**2 + i*m**2 - 81*m + 0*m**3 - 3*m**3.
-3*(m - 3)**3
Suppose 3*k - 5*q = -100, 2*q - 24 = k + 5*q. Let l = k - -61/2. Factor 1/2*s**2 - s + l.
(s - 1)**2/2
Suppose -f + 5*o + 27 = 0, 5*o + 8 = -17. Determine i so that -50/9*i**4 - 8/9*i**f - 40/9*i**3 + 0*i + 0 = 0.
-2/5, 0
Suppose -29*g = -31*g + 12. Suppose 3*w + u = -2*u, 2*w - u - g = 0. Find v such that 3/4 - 3/4*v**w + 0*v = 0.
-1, 1
Suppose -5 = -3*y - 2*b, -2*b = 3*y - 6*b - 17. Suppose -2 = -s + 4*g, y*s + g + 2 = 4*s. Factor 0 - 4/3*d**s + 2/3*d**3 + 0*d.
2*d**2*(d - 2)/3
Let f(u) = -u**5 - u**4 + u**2 - u + 1. Let i(o) = o**5 - 6*o**4 - 5*o**3 + 4*o**2 - 2*o + 2. Let x(b) = 2*f(b) - i(b). Let x(m) = 0. Calculate m.
-1, 0, 1/3, 2
Let g be 14/(-5)*10/(-4). Suppose -4*n = -g*n + 9. Solve u - u**n + 6*u**2 + 8 + 0*u**2 - 13*u = 0.
2
Let u(w) be the first derivative of -w**3 - 2*w**2 + 6. Let o(d) = -d**2 - 2*d. Let g(l) = 5*o(l) - 2*u(l). Factor g(z).
z*(z - 2)
Determine s so that -2/13*s**5 - 24/13*s**2 - 18/13*s + 4/13*s**3 + 8/13*s**4 + 0 = 0.
-1, 0, 3
Let u(k) be the second derivative of k**4/24 - k**3/12 + 20*k. Solve u(w) = 0.
0, 1
Let -6/11*c**4 + 10/11*c + 10/11*c**2 - 4/11 - 10/11*c**3 = 0. Calculate c.
-2, -1, 1/3, 1
Suppose 45*c - 43*c = 0. Determine d so that c + 0*d + 2/5*d**2 + 2/5*d**3 = 0.
-1, 0
Let i(p) be the first derivative of 2*p**3/3 - p**2/2 + 3. Factor i(a).
a*(2*a - 1)
Suppose -3 = -2*a - a. Let z(v) be the first derivative of -2*v - 1/6*v**3 - v**2 + a. Factor z(o).
-(o + 2)**2/2
Let s = 37/84 + -4/21. Let 3/4*o + s*o**3 - 1/4 - 3/4*o**2 = 0. Calculate o.
1
Factor 12/7*k**3 - 3/7*k**4 + 0*k - 12/7*k**2 + 0.
-3*k**2*(k - 2)**2/7
Let o(q) be the first derivative of q**5/60 + q**4/24 - q**2 + 3. Let h(z) be the second derivative of o(z). Factor h(j).
j*(j + 1)
Let g = -25 - -127/5. Factor 0*z**2 + g*z + 0 - 2/5*z**3.
-2*z*(z - 1)*(z + 1)/5
Let i(o) be the third derivative of -o**6/1440 - o**5/180 - 5*o**4/288 - o**3/36 + 30*o**2. Suppose i(j) = 0. Calculate j.
-2, -1
Let z(s) be the first derivative of s**6/9 + 4*s**5/15 + s**4/6 + 14. What is m in z(m) = 0?
-1, 0
Let v(t) be the first derivative of 33/20*t**4 - 1 + 9/5*t**3 - 3/5*t + 12/25*t**5 + 3/10*t**2. Factor v(x).
3*(x + 1)**3*(4*x - 1)/5
Let 2*o - 1/2*o**4 + 5/2*o**3 + 0 - 4*o**2 = 0. What is o?
0, 1, 2
Let y(g) be the first derivative of -g**3/3 - 2*g**2 - 3*g + 14. Solve y(j) = 0.
-3, -1
Factor 1/4*n**2 + 1/4*n - 1/2.
(n - 1)*(n + 2)/4
Let -2/9*f**2 - 4/9 + 2/3*f = 0. Calculate f.
1, 2
Suppose 0 = 4*b + b + h - 10, b = -4*h + 2. Factor -3*v**2 + 1 + 0*v + b*v + 0*v.
-(v - 1)*(3*v + 1)
Let x(c) be the second derivative of c**7/42 + c**6/15 - c**4/6 - c**3/6 + 2*c. Factor x(s).
s*(s - 1)*(s + 1)**3
Let n(x) be the third derivative of -x**8/13440 - x**7/5040 + x**6/720 + 5*x**4/24 - 3*x**2. Let o(a) be the second derivative of n(a). Factor o(q).
-q*(q - 1)*(q + 2)/2
Factor -16*t**4 - 17*t - 36*t**3 - 2*t**5 + 3*t + 68*t.
-2*t*(t - 1)*(t + 3)**3
Let z(b) be the first derivative of -3*b**4/4 - b**3/3 + b**2 + 6. Factor z(q).
-q*(q + 1)*(3*q - 2)
Let j be (11 + -76)*6/(-10). Let i be (-6)/39 - (-32)/j. Find w such that 0 + i*w**2 - 1/3*w - 1/3*w**3 = 0.
0, 1
Let a(x) be the first derivative of x**8/336 - x**7/210 - x**2 + 6. Let m(d) be the second derivative of a(d). Suppose m(h) = 0. Calculate h.
0, 1
Let r(n) be the first derivative of n**4/16 + n**3/12 - n**2/4 + 13. Factor r(f).
f*(f - 1)*(f + 2)/4
Let a(k) be the first derivative of -16*k**6/27 + 112*k**5/45 - 73*k**4/18 + 86*k**3/27 - 11*k**2/9 + 2*k/9 - 43. Factor a(y).
-2*(y - 1)**3*(4*y - 1)**2/9
Solve -6*k**2 + 3 + 6*k**2 - 7*k + k + 3*k**2 = 0.
1
Let j(r) = -4*r + 3. Let x be j(3). Let q be (-29)/x - 6/27. Determine o, given that 0 + 8*o**q - 4*o**2 - 16/3*o**4 + 2/3*o = 0.
0, 1/2
Let w(s) be the first derivative of -s**5 + 5*s**4/4 + 5*s**3/3 - 5*s**2/2 - 12. Factor w(r).
-5*r*(r - 1)**2*(r + 1)
Let y = -5835 + 16762/3. Let t = -245 - y. Factor -2/3*f + 0 + t*f**2 - 6*f**5 + 4/3*f**3 - 8*f**4.
-2*f*(f + 1)**2*(3*f - 1)**2/3
Let h(n) = -n**3 + 7*n**2. Let y be h(7). Let z = -12 + 17. Solve -1/2*u**z + 3/2*u**4 - 3/2*u**3 + 1/2*u**2 + 0 + y*u = 0 for u.
0, 1
Factor 0 - 2/3*k**2 - 2/3*k.
-2*k*(k + 1)/3
Factor 31*y - 3*y**5 - 10*y - 38*y**4 + 44*y**4 + 6*y**3 - 6 - 24*y**2.
-3*(y - 1)**4*(y + 2)
Let r = 117 - 117. Factor 2/9*y**3 + 2/9*y - 4/9*y**2 + r.
2*y*(y - 1)**2/9
Let g(b) be the third derivative of -b**6/180 + b**5/60 - b**4/72 - 23*b**2. Factor g(f).
-f*(f - 1)*(2*f - 1)/3
Suppose 0 = -3*n + 4*a - 4, -5*a + 25 + 3 = 2*n. Let q = 1 + 1. Factor 2 - q + 2*g**n.
2*g**4
Determine i so that 24/7*i + 16/7 + 12/7*i**2 + 2/7*i**3 = 0.
-2
Let l(s) be the third derivative of s**8/20160 - s**7/5040 + s**5/20 - 3*s**2. Let h(i) be the third derivative of l(i). Factor h(p).
p*(p - 1)
Let l(w) be the second derivative of -1/24*w**3 + 0*w**2 - 1/48*w**4 + 6*w + 0. Factor l(x).
-x*(x + 1)/4
Let b be (1 + -3)*(-5)/2. Determine k, given that 2*k**3 - 8*k**2 - 2*k + 2*k**4 + b*k**2 + k**2 = 0.
-1, 0, 1
Let r(t) = -2*t - 7. Let w be r(-5). Let i be 2/(w - 12/(-8)). Suppose -2/9*n**2 + i + 2/9*n = 0. What is n?
-1, 2
Let k(y) = 3*y**3 - 15*y**2 + 15*y - 3. Let z(p) = -3*p**3 + 15*p**2 - 14*p + 2. Let f(u) = -7*k(u) - 6*z(u). Determine t so that f(t) = 0.
1, 3
Let k be 4/(-2) - (-16)/2. Let b be (8/k)/(2/3). Factor 4*x**3 + 0 + 1 - b*x**4 + 1 - 4*x.
-2*(x - 1)**3*(x + 1)
Let m(h) be the second derivative of -h**5/50 - h**4/15 + 4*h**3/3 - 24*h**2/5 + h - 11. Factor m(k).
-2*(k - 2)**2*(k + 6)/5
Factor 0 - 2/17*p**4 - 2/17*p - 6/17*p**3 - 6/17*p**2.
-2*p*(p + 1)**3/17
Let i(w) = w**2 + 4*w - 3. Let t be i(-6). Let v be (-6)/12 - t/(-10). Factor 0*h**3 - v*h**5 + 0 + 2/5*h + 4/5*h**2 - 4/5*h**4.
-2*h*(h - 1)*(h + 1)**3/5
Let x(o) be the first derivative of 0*o**3 + 10*o - 13*o - 1 - o**3 + 3*o**2. Solve x(m) = 0.
1
Let c(x) be the third derivative of -1/27*x**3 + 0*x - 2*x**2 + 0 + 1/270*x**5 + 0*x**4. Factor c(s).
2*(s - 1)*(s + 1)/9
Let a(f) = -14*f + 42. Let r be a(3). Let u = 8 - 5. Factor 0 + r*i - 2/5*i**2 - 1/5*i**u.
-i**2*(i + 2)/5
Let k(r) be the second derivative of -4*r + 0 + 0*r**2 + 0*r**3 - 1/4*r**4 - 3/20*r**5. Factor k(a).
-3*a**2*(a + 1)
Let b(u) be the first derivative of u**4/2 - 2*u**3/9 - 2*u**2/3 + 2. Determine l so that b(l) = 0.
-2/3, 0, 1
Let q(y) = -y**2 + 7*y - 7. Let h be q(5). Let g = -1 + h. Factor 1/3 + 4/3*t + 4/3*t**g.
(2*t + 1)**2/3
Let s(h) be the third derivative of h**5/660 + 7*h**4/132 + 49*h**3/66 + 35*h**2. Factor s(a).
(a + 7)**2/11
Let w be 3 - (-4)/(-16)*4. Let u(d) be the first derivative of -4/5*d**2 + 2/15*d**3 + 8/5*d - w. Let u(n) = 0. What is n?
2
Let g(y) be the first derivative of 14*y**6/3 - 48*y**5/5 - 4*y**4 + 56*y**3/3 - 6*y**2 - 8*y + 10. Factor g(v).
4*(v - 1)**3*(v + 1)*(7*v + 2)
Let g(o) be the second derivative of 3/2*o**