0, 2
Let c(a) be the second derivative of a**5/60 + a**4/8 + a**3/3 + 5*a**2/2 + 7*a. Let s(k) be the first derivative of c(k). Factor s(n).
(n + 1)*(n + 2)
Let j = -139/4 - -35. Let -1/4*t**2 + j - 1/4*t + 1/4*t**3 = 0. Calculate t.
-1, 1
Let f(b) be the second derivative of 9*b**4/5 - 6*b**3 + 15*b**2/2 + 17*b. Factor f(j).
3*(6*j - 5)**2/5
Let r be (-60)/(-25) - (3 + -1). Suppose 4*p = 56 - 48. Let r*l**p + 8/5 + 8/5*l = 0. Calculate l.
-2
Let h(f) be the second derivative of -1/20*f**6 + 0*f**3 + 1/28*f**7 + 0 - 3/40*f**5 + 0*f**2 + 2*f + 1/8*f**4. Factor h(r).
3*r**2*(r - 1)**2*(r + 1)/2
Let g(w) = 2*w - 1. Let j be g(2). Suppose -3*z - 17 = -3*h - 4*z, z + 7 = j*h. Factor -3*v**h + 67*v**4 - v + 0*v + 12*v**2 - 48*v**3.
v*(4*v - 1)**3
Factor 0 - 36/5*o**3 - 6*o + 3/5*o**4 + 63/5*o**2.
3*o*(o - 10)*(o - 1)**2/5
Let w(v) be the second derivative of -v**6/75 + v**4/30 - 5*v. Suppose w(m) = 0. Calculate m.
-1, 0, 1
Let r(b) = 3*b**2 - b. Let w be r(1). Determine m, given that -m + m**2 + m**3 - 2 - 5*m**4 + 4*m**4 + w*m**2 = 0.
-1, 1, 2
Let t(b) = -24*b**4 + 57*b**3 - 60*b**2 + 21*b - 3. Let m(r) = r**5 + r**4 - r**3 + r + 1. Let j(d) = 3*m(d) + t(d). Suppose j(w) = 0. Calculate w.
0, 1, 2
Let l be 43706/273 + 3/(-7). Let s = 161 - l. Find p, given that 0 - 4/3*p - s*p**2 - 1/3*p**3 = 0.
-2, 0
Let r(o) be the first derivative of -1/18*o**4 + 2/9*o**2 + 2/27*o**3 + 0*o - 2. Let r(v) = 0. Calculate v.
-1, 0, 2
Let t(f) = f**4 + 2*f**3 + 4*f - 2*f**3 - 4*f**2 - 6*f**3 - f**3. Let q(p) = -9*p**4 + 57*p**3 + 33*p**2 - 33*p. Let z(u) = -4*q(u) - 33*t(u). Factor z(j).
3*j**3*(j + 1)
Let j(w) be the second derivative of w**5/25 - 2*w**4/15 - 2*w**3/15 + 4*w**2/5 - 21*w. Determine q, given that j(q) = 0.
-1, 1, 2
Let v(n) = n**2 + 1. Let j(m) = -8*m**2 - 9*m - 6. Let c(u) = 5*j(u) + 20*v(u). Find a, given that c(a) = 0.
-2, -1/4
Let h(v) be the second derivative of v**6/200 - 3*v**5/100 + v**4/20 - 3*v**2 - 4*v. Let c(y) be the first derivative of h(y). Factor c(n).
3*n*(n - 2)*(n - 1)/5
Suppose -11 = -2*h - 3*o + 6, 3*h - 5*o = -22. Find x such that h + 3/2*x - 1/2*x**2 - 3/2*x**3 - 1/2*x**4 = 0.
-2, -1, 1
Let h be (1/(-4))/((-9)/108). Suppose -h*c + 4 + 11 = 0. Factor 1/2*l**c - 1/2*l**2 - 1/2*l**3 + 1/2*l**4 + 0*l + 0.
l**2*(l - 1)*(l + 1)**2/2
Solve 1 - 13*s**2 + 9*s**2 + 10*s - 5 - 2*s = 0.
1
Factor 12/5*n**3 - 2/5*n + 0 - 3/5*n**2 - 7/5*n**4.
-n*(n - 1)**2*(7*n + 2)/5
Let v(q) be the second derivative of -1/6*q**4 + 0 + q + 1/20*q**5 + 0*q**2 + 1/6*q**3. Factor v(x).
x*(x - 1)**2
Let x(d) = 6*d**3 - 64*d**2 + 96*d + 8. Let f(v) = -4*v**3 + 42*v**2 - 64*v - 5. Let c(j) = -8*f(j) - 5*x(j). Factor c(a).
2*a*(a - 4)**2
Factor 2/9 + 2/9*x**2 - 4/9*x**3 - 1/9*x**5 + 5/9*x - 4/9*x**4.
-(x - 1)*(x + 1)**3*(x + 2)/9
Suppose 7 = 3*r - 2. Suppose -w + 4*k = -2 - 0, -k - 6 = -r*w. Let i**2 - 2*i**4 + 2*i**w - i**2 = 0. Calculate i.
-1, 0, 1
Let o(d) = -d - 13. Let n be o(-14). Factor -n + m**5 - 8 + 15*m - 46*m**2 + 33*m**3 - 9*m**4 - 3*m**3 + 18*m.
(m - 3)**2*(m - 1)**3
Let w(q) be the third derivative of -q**8/28 + q**7/35 + 47*q**6/160 - 7*q**5/10 + 19*q**4/32 - q**3/4 + 14*q**2. Solve w(z) = 0.
-2, 1/4, 1
Let c(l) be the third derivative of -1/90*l**5 + 3*l**2 + 0*l - 1/15*l**3 + 1/900*l**6 + 0 + 7/180*l**4. Let c(d) = 0. What is d?
1, 3
Let z(y) be the third derivative of -1/30*y**5 + 0*y - 1/6*y**4 + y**2 + 0*y**3 + 0. Determine k, given that z(k) = 0.
-2, 0
Let a(d) be the second derivative of -9*d**7/14 + 39*d**6/10 - 201*d**5/20 + 57*d**4/4 - 12*d**3 + 6*d**2 - 10*d. Let a(g) = 0. What is g?
2/3, 1
Let l(i) be the second derivative of 5*i**4/42 - 4*i**3/21 - i**2/7 - i + 30. Solve l(q) = 0 for q.
-1/5, 1
Let k be ((-13)/39)/((-2)/(-24)*-1). Let n(g) be the first derivative of -3/5*g**5 - g**k + 2/3*g**3 + 2*g**2 + g + 4. What is w in n(w) = 0?
-1, -1/3, 1
Let c = -14 - -16. Let f be 1/2*(-8)/(-2). Factor -f - 2*d**c + 1 + 3*d**2.
(d - 1)*(d + 1)
Factor -8/5 - 2*o + 6/5*o**2 + 2/5*o**4 + 2*o**3.
2*(o - 1)*(o + 1)**2*(o + 4)/5
Let o(c) = c. Let y(u) = -3*u**2 - u + 12. Let a(w) = o(w) + y(w). Solve a(g) = 0 for g.
-2, 2
Let d(j) = -j + 1. Let z be d(-2). Determine f, given that 0*f - 4*f**5 - 11*f**4 - 9*f**3 - 2*f + z*f - f**2 = 0.
-1, 0, 1/4
Suppose -31 = 3*y - 43. Let k(m) be the first derivative of -2/3*m**3 + 4 - y*m + 3*m**2. Factor k(v).
-2*(v - 2)*(v - 1)
Determine z, given that -5*z**4 - z**3 + 4*z**4 - 2*z**4 - 6*z**2 + 8*z**2 = 0.
-1, 0, 2/3
Let v(u) be the first derivative of 2 + 0*u + 1/20*u**5 + 0*u**2 + 1/24*u**6 + 0*u**4 + 0*u**3. Factor v(q).
q**4*(q + 1)/4
Let d(o) be the third derivative of -o**8/392 - 2*o**7/245 - o**6/140 - 11*o**2. Solve d(y) = 0 for y.
-1, 0
Determine r, given that -10*r**3 - 35*r**4 - 5*r**5 + 7*r**2 - r**2 - 15*r**5 - r**2 = 0.
-1, 0, 1/4
Let d(l) = -l**2 - 7*l. Let h be d(-6). Suppose 9 + h = 3*f. Solve -r**3 - 3*r**3 + f*r**3 - r = 0 for r.
-1, 0, 1
Let q(d) be the second derivative of d**7/168 + d**6/20 + 3*d**5/20 + 5*d**4/24 + d**3/8 - 4*d - 5. Solve q(h) = 0 for h.
-3, -1, 0
Let a be -10*((-8)/(-5) - 2). Suppose -19 + 7 - 6*l - a*l**2 - 10*l = 0. Calculate l.
-3, -1
Let g(y) be the third derivative of 0*y**5 + 1/60*y**7 + 0*y**4 + 0*y + 0 - 1/120*y**6 - 5/672*y**8 + 2*y**2 + 0*y**3. Factor g(p).
-p**3*(p - 1)*(5*p - 2)/2
Let p(k) = -3*k**4 - 12*k**3 + 14*k**2 + 32*k - 23. Let x(i) = -3*i**4 - 12*i**3 + 16*i**2 + 31*i - 22. Let f(a) = 5*p(a) - 4*x(a). Factor f(u).
-3*(u - 1)**2*(u + 3)**2
Let v(z) be the first derivative of 1/8*z**2 + 1/12*z**3 + 0*z - 4. Solve v(w) = 0.
-1, 0
Let o = 23/35 - -1/105. Factor -o*s - 2/9*s**2 - 4/9.
-2*(s + 1)*(s + 2)/9
Let p(s) be the first derivative of -625*s**6/6 + 100*s**5 + 575*s**4/4 - 190*s**3/3 - 110*s**2 - 40*s + 13. Factor p(n).
-5*(n - 1)**2*(5*n + 2)**3
Let k = 7 + -4. Factor 12*g**2 - 3*g**2 - 5*g - 9*g**3 + k*g**4 + 2*g.
3*g*(g - 1)**3
Let k = -7 + 7. Let c(v) be the third derivative of 0*v**4 - 1/360*v**6 + 0 + v**2 + k*v**3 + 0*v + 0*v**5. Determine s, given that c(s) = 0.
0
Let b = 12 - 10. Let j be b/(-7) - (-354)/63. Suppose -j*v**2 - 2*v + 10/3*v**5 - 12*v**4 + 4/3 + 44/3*v**3 = 0. What is v?
-2/5, 1
Suppose 54 = 4*r + 3*t - 12, 0 = -4*r + 3*t + 54. Let f be 20/(-18)*r/(-25). Factor f*v**3 + 0 + 0*v**2 - 2/3*v**4 + 0*v.
-2*v**3*(v - 1)/3
Let r(a) be the second derivative of -a**8/1680 + a**7/420 - a**6/360 + a**3/6 - 5*a. Let t(w) be the second derivative of r(w). Solve t(s) = 0 for s.
0, 1
Let l(t) = -5*t**2 - 5*t + 10. Let f(a) = 29*a**2 + 31*a - 60. Let q(y) = 6*f(y) + 34*l(y). Find c such that q(c) = 0.
-5, 1
Let q(l) be the third derivative of -l**5/12 - 5*l**4/12 + 5*l**3/2 + 4*l**2. What is n in q(n) = 0?
-3, 1
Let y(n) be the second derivative of n**5/25 + n**4/5 - 2*n**3/15 - 6*n**2/5 - 4*n - 3. Factor y(b).
4*(b - 1)*(b + 1)*(b + 3)/5
Let c = -10 + 14. Suppose -2*b - 7*b**5 + b**c + 8*b**3 - b**2 + 4*b**5 - 3*b**5 = 0. What is b?
-1, -1/2, 0, 2/3, 1
Factor 4*t**3 - 4*t**2 - 4/3*t**4 + 4/3*t + 0.
-4*t*(t - 1)**3/3
Factor -6 + 3*h + 13*h**2 - 5*h**2 - 4*h**2 + 11*h**2 + 6*h**3.
3*(h + 1)*(h + 2)*(2*h - 1)
Let x be (((-3)/2)/1)/(99/(-88)). Suppose 1/3*j**2 - 4/3*j + x = 0. Calculate j.
2
Let a(s) be the first derivative of s**7/840 + s**6/240 - s**5/80 - s**4/24 + s**3/6 - s**2 + 3. Let j(w) be the second derivative of a(w). Factor j(r).
(r - 1)**2*(r + 2)**2/4
Let q(d) be the first derivative of d**6/48 + d**5/40 - 3*d**4/32 - d**3/24 + d**2/8 + 2. Factor q(t).
t*(t - 1)**2*(t + 1)*(t + 2)/8
Let f(l) = 2*l**2 - 4*l + 3. Let h be f(2). Suppose 13*p - 28 = 6*p. Determine n so that -5*n**p + 4*n**2 + n**4 + 0*n**4 + h*n - n - 2*n**5 = 0.
-1, 0, 1
Let i(d) be the first derivative of d**3/3 + d**2 - 3*d - 24. Factor i(z).
(z - 1)*(z + 3)
Let m(r) be the second derivative of 0 + 1/4*r**4 - 1/3*r**3 - 1/20*r**5 - 6*r + 0*r**2. Factor m(c).
-c*(c - 2)*(c - 1)
Find i such that 12/7*i + 3/7*i**2 + 12/7 = 0.
-2
Suppose -2*c + 0 = -4. Suppose -8*k**2 - 10*k + 4 - 7 + 0*k**c - 2*k**3 - 1 = 0. What is k?
-2, -1
Let y(h) = h**2 - 1. Let a(b) = 35*b**3 + 28*b**2 - 10*b - 3. Let w(d) = a(d) - 3*y(d). Determine v, given that w(v) = 0.
-1, 0, 2/7
Suppose 2*u - u = -5*j + 8, -8 = -3*u + j. Suppose 2*m**3 - 9*m**4 - 32*m**u - 15*m - 2 + m**3 - 33*m**2 = 0. Wha