*6/30 + p**4/12 - p**3/12 + 15*p. Factor f(d).
d*(d - 1)**3*(d + 1)/2
Let h(k) be the third derivative of 1/300*k**6 + 0*k + 1/15*k**4 + 0 + 0*k**3 + 2*k**2 + 2/75*k**5. Factor h(f).
2*f*(f + 2)**2/5
Let y(o) = -5*o**2 + 4*o + 9. Let u(h) = -3*h**2 + 2*h + 4. Let k(j) = -j**2 - 4*j + 4. Let p be k(-4). Let c(n) = p*y(n) - 9*u(n). Find z, given that c(z) = 0.
0, 2/7
Let -1/8*p**3 + 1/4*p + 0 + 1/8*p**2 = 0. What is p?
-1, 0, 2
Let q(r) be the third derivative of -r**6/30 - r**5/6 - r**4/4 + 2*r**3/3 + 6*r**2. Let p(g) = -g**2 - g + 1. Let a(l) = 4*p(l) - q(l). Factor a(i).
2*i*(i + 1)*(2*i + 1)
Let j(k) = 6*k**3 + 13*k**2 + 3*k - 4. Let u(q) = -3*q**3 - 2*q + 0*q**3 + 4 - 2 - 7*q**2. Suppose 3*p = 17 - 2. Let i(d) = p*u(d) + 3*j(d). Solve i(o) = 0.
-1, 2/3
Let m(h) be the third derivative of h**7/840 + h**6/80 + h**5/20 + h**4/8 - 2*h**2. Let s(w) be the second derivative of m(w). Factor s(d).
3*(d + 1)*(d + 2)
Let o be 9/(-12) - 142/(-168). Let f(v) be the second derivative of 1/35*v**5 + 0 - 1/105*v**6 + 0*v**4 - 4*v - o*v**3 + 1/7*v**2. Let f(t) = 0. Calculate t.
-1, 1
Let t(y) be the first derivative of -y**8/840 - y**7/420 + y**3/3 + 4. Let c(n) be the third derivative of t(n). Factor c(b).
-2*b**3*(b + 1)
Let u = -6 + 10. Determine d so that 35 - 35 + d**u = 0.
0
Suppose 3*t = 21 - 6. Suppose t - 1 = 2*f. Factor f*b**2 + 5*b - 2*b - b.
2*b*(b + 1)
Let n = -290 - -1745/6. Let j(f) be the second derivative of 3*f - 1/3*f**4 - n*f**3 + 0 - 1/2*f**2. Let j(p) = 0. Calculate p.
-1, -1/4
Let a(d) = -4*d**4 - d**3 - 6*d**2 + d + 5. Let u(b) = -3*b**4 - b**3 - 5*b**2 + b + 4. Let p(x) = 4*a(x) - 5*u(x). Solve p(o) = 0.
-1, 0, 1
Suppose 5*d - 81 = 219. Let s be 3/15 - (-8)/d. Suppose s*o**3 + 0 + 0*o - 2/3*o**2 = 0. Calculate o.
0, 2
Factor 17*n**2 + 4*n**3 + 12*n**2 + 3*n**4 - 2*n**2 + 21*n + 11*n**3 + 6.
3*(n + 1)**3*(n + 2)
Let h(j) be the second derivative of -2*j**6/105 - 3*j**5/35 - j**4/7 - 2*j**3/21 + 4*j. Factor h(l).
-4*l*(l + 1)**3/7
Let n(p) = -6*p**5 + p**4 - 9*p**3 - 5. Let k(z) = -5*z**5 - 8*z**3 - 4. Let q(b) = -5*k(b) + 4*n(b). Factor q(o).
o**3*(o + 2)**2
Suppose -5*u**3 - 24*u**4 + 8*u**4 + 4*u**3 - 4*u + 16*u**2 + 5*u**3 = 0. What is u?
-1, 0, 1/4, 1
Let l = 7/6 - 5/12. Solve 3/4*x**2 + 3/4*x**3 - 3/4*x - l = 0 for x.
-1, 1
Let p(i) = -i - 7. Suppose 2*t + 7 + 7 = 0. Let s be p(t). Solve 2/3*m**5 - 2/3*m**3 + 0*m**2 + 0 + s*m**4 + 0*m = 0 for m.
-1, 0, 1
Let j(d) be the third derivative of d**5/50 + 3*d**4/40 - d**3/5 + 7*d**2. Factor j(r).
3*(r + 2)*(2*r - 1)/5
Suppose 0 = 4*j - 2*j - j. Let i(u) be the third derivative of -1/24*u**4 + 2*u**2 + 0*u**3 + 0*u - 1/60*u**5 + j. Factor i(g).
-g*(g + 1)
Let -6*j**2 - 25 + 4*j + 25 = 0. Calculate j.
0, 2/3
Suppose -3*k = g + 8, 5*g + 1 = k + 9. Let c = k - -5. Factor -2*r**3 + 6*r**2 - 2*r**2 - c*r**2.
-2*r**2*(r - 1)
Let j(g) be the first derivative of 0*g + g**2 + 8 + 1/3*g**3. Determine r so that j(r) = 0.
-2, 0
Suppose 4*k - 5*r = -k + 35, 2*k + r - 8 = 0. Suppose 4*c**k - 6*c**4 + 0*c**5 - 2*c**2 + 6*c**3 - 2*c**5 = 0. Calculate c.
0, 1
Let h = 24 - 18. Suppose -2*v + 5*q = h, 3*q = 5*v + 7*q - 18. Let -5/2*t**v - 3/2*t**4 + 1/2*t + 7/2*t**3 + 0 = 0. What is t?
0, 1/3, 1
Let y(a) be the second derivative of 10*a**3 - 6*a**2 + 3*a**6 - 7*a + 0 - 23/4*a**4 - 51/20*a**5. Determine c, given that y(c) = 0.
-1, 2/5, 1/2, 2/3
Let y(h) be the second derivative of h**4/18 - 8*h**3/9 + 16*h**2/3 + 9*h. Determine l, given that y(l) = 0.
4
Let q(n) be the first derivative of n**5/5 - n**4/2 - 4*n**3/3 + n**2 + 3*n + 5. Determine f so that q(f) = 0.
-1, 1, 3
Suppose 22*c**2 - 33*c**3 + 0 - 7/2*c**5 - 4*c + 37/2*c**4 = 0. What is c?
0, 2/7, 1, 2
Let t(z) be the third derivative of -z**8/6720 - z**7/1260 - z**6/720 + z**4/24 + 5*z**2. Let f(u) be the second derivative of t(u). Let f(p) = 0. What is p?
-1, 0
Let w = -4 + 7. Suppose -3*h = -w - 3. Solve 3 - m**h + 2*m - 3*m - 1 + 2*m = 0.
-1, 2
Let h(j) be the first derivative of -4*j**6/3 - 4*j**5 - 3*j**4 + 4*j**3/3 + 2*j**2 - 39. Suppose h(c) = 0. Calculate c.
-1, 0, 1/2
Suppose 2*d - 5*d - 4*v - 2 = 0, -4*d - 2*v - 16 = 0. Let w(a) = -a - 3. Let h be w(d). Factor 0 - 2/3*l**h - 2/3*l**2 + 0*l.
-2*l**2*(l + 1)/3
Let v be 8/(-28) - 26/7. Let i be (v/(-10))/((-24)/(-20)). Factor -1/3*w**4 - i + 0*w + 0*w**3 + 2/3*w**2.
-(w - 1)**2*(w + 1)**2/3
Let x(l) be the third derivative of -1/40*l**6 - l**2 - 1/70*l**7 + 0*l + 0 + 0*l**5 + 0*l**4 + 0*l**3. Solve x(i) = 0 for i.
-1, 0
Let k(w) be the first derivative of -18*w**5/5 - 57*w**4/8 + 13*w**3/2 + 9*w**2/2 - 13. Determine v, given that k(v) = 0.
-2, -1/3, 0, 3/4
Let q(m) be the first derivative of m**4/16 - m**3/3 + m**2/2 + 10. Factor q(v).
v*(v - 2)**2/4
Let s be 2/3*(-117)/6. Let b be 2 + -2 + (-2)/s. Factor 0 + 0*a + b*a**2.
2*a**2/13
Let d(j) be the first derivative of -2*j**3/15 - j**2/10 + j/5 - 7. What is w in d(w) = 0?
-1, 1/2
Determine l so that -4/9*l**4 + 0 - 2/9*l**5 + 4/9*l**2 + 2/9*l**3 + 0*l = 0.
-2, -1, 0, 1
Suppose 1 = 4*x + 41. Let r be (x/15)/(4/(-18)). Factor -2/7*l**2 + 6/7*l**r - 4/7*l**4 + 0*l + 0.
-2*l**2*(l - 1)*(2*l - 1)/7
Suppose -i = -0*i - 4. Suppose 1 + 1 - 2*u + 6*u - 2*u**2 - i = 0. What is u?
1
Solve 16/5*o + 8/5*o**3 - 18/5*o**2 - 1 - 1/5*o**4 = 0 for o.
1, 5
Let i(p) be the first derivative of 2*p**4 + 10*p**3 + 12*p**2 - 8*p - 10. Determine o so that i(o) = 0.
-2, 1/4
Let v(k) = 4*k + 5*k - 2*k**3 + 3*k**3 - 3*k**3 - 4 - 3*k**2. Let n(y) = y**3 + y**2 - 3*y + 1. Let l(h) = -14*n(h) - 4*v(h). Let l(a) = 0. What is a?
-1, -1/3, 1
Factor -2*r**2 - 5*r**2 + 4*r**2 - r**4 + 5*r**3 - 9*r.
-r*(r - 3)**2*(r + 1)
Let w(l) be the third derivative of l**8/48 + 3*l**7/70 - l**6/24 - 3*l**5/20 - l**4/12 + 4*l**2. Factor w(d).
d*(d - 1)*(d + 1)**2*(7*d + 2)
Let x(r) = -r**3 + 7*r**2 + 9*r - 11. Let j be x(8). Let p be (7 - (-2 - -3)) + j. Suppose 2/9*n**p + 0 + 2/9*n + 4/9*n**2 = 0. Calculate n.
-1, 0
Let g(p) be the first derivative of 6 + 1/14*p**4 - 2/21*p**3 + 2/35*p**5 - 1/21*p**6 + 0*p**2 + 0*p. Factor g(w).
-2*w**2*(w - 1)**2*(w + 1)/7
Factor 2*k**2 + 2 + 9 + 12 - 31.
2*(k - 2)*(k + 2)
Solve -5*c**2 - 44*c**3 + 48*c**3 + c**2 = 0 for c.
0, 1
Determine c, given that -1/2*c**2 + 4 + c = 0.
-2, 4
What is n in n - 5/2*n**3 - 3/2*n**2 + 0 = 0?
-1, 0, 2/5
Let w(n) = 5*n**4 - 11*n**3 + 9*n**2 - n + 2. Let v(d) = -18*d**2 - 9*d**4 + 9*d**4 - 11*d**4 - 5 + 23*d**3 + d. Let o(q) = -2*v(q) - 5*w(q). Factor o(r).
-3*r*(r - 1)**3
Let g(m) be the first derivative of 1/75*m**6 + 1 - 4/15*m**3 + 1/5*m**2 + 2*m + 1/5*m**4 - 2/25*m**5. Let p(i) be the first derivative of g(i). Factor p(d).
2*(d - 1)**4/5
Find l such that -6*l + 6*l**2 - 3/2*l**3 + 0 = 0.
0, 2
Suppose 6 + 2/3*z**2 + 4*z = 0. What is z?
-3
Let h be 36/(-4)*(-1)/3. Let p be 2/h*(-9)/(-12). Factor 1/2*a**2 + a + p.
(a + 1)**2/2
Suppose -2*o + 3 - 5 = 0. Let x be 0/(2 + 0 + o). Factor -2/3*b**2 + 2/3*b + x.
-2*b*(b - 1)/3
Let p(g) = 8*g. Let j be p(-1). Let v be ((-4)/(-2))/(j/(-12)). Factor -8/7*b - 12/7*b**2 - 8/7*b**v - 2/7 - 2/7*b**4.
-2*(b + 1)**4/7
Let n(d) = -d**2 - 1. Let h(q) = -35*q**2 - 24*q - 3. Let o be (-2)/(-3)*9/(-6). Let u(m) = o*h(m) - n(m). Factor u(k).
4*(3*k + 1)**2
Let b(a) = -a**3 - a**2 - a. Let n(c) = -8*c**2 - 8*c + 4. Let d(f) = -4*b(f) + n(f). Factor d(h).
4*(h - 1)**2*(h + 1)
Let f(c) = c**2 - 19*c + 48. Let a be f(16). Determine n so that 2/5*n**4 + 0 + 4/5*n**2 + a*n + 6/5*n**3 = 0.
-2, -1, 0
Suppose -y = -50 + 48. Let v(w) be the first derivative of -2/15*w**3 - 2/5*w - 3 - 2/5*w**y. Factor v(z).
-2*(z + 1)**2/5
Let c(j) = 0*j + 0*j - j. Let l(y) = y**2 + 6*y. Let i(g) = 4*c(g) + l(g). Factor i(a).
a*(a + 2)
Let i = -219 - -84. Let x be 12/i*35/(-7). Factor -2/3*n**3 - 2/9*n**2 + 2/9*n + 10/9*n**4 - x*n**5 + 0.
-2*n*(n - 1)**3*(2*n + 1)/9
Let h = 197 - 194. Factor -10/7*y - 2/7*y**h + 8/7*y**2 + 4/7.
-2*(y - 2)*(y - 1)**2/7
Let w(x) = -2*x + 37. Let z be w(17). Factor 2/5*o**2 - 2/5 + 2/5*o**z - 2/5*o.
2*(o - 1)*(o + 1)**2/5
Let m be (3/12)/((-1)/(-2)). Let c = 8/9 + 11/18. Factor -m*a**3 + 3/2*a**2 + 1/2 - c*a.
-(a - 1)**3/2
Let o be (2/36)/(3 - 33/12). Factor 0*q - o*q**2 + 0.
-2*q**2/9
Factor -27*z**2 - z**3 - 5 - 2*z**3 + 30*z**2 + 3*z + 2.
-3*(z - 1)**2*(z + 1)
Let x = 0 - -3. Facto