. Let q be ((-2)/c)/(-10 - -11). Find r such that -1/3*r**4 + 1/3*r**2 + 0 + q*r - 1/3*r**3 = 0.
-1, 0, 1
Let f(p) be the first derivative of -p**7/1680 + p**6/180 - p**5/60 - 2*p**3/3 - 2. Let l(w) be the third derivative of f(w). What is o in l(o) = 0?
0, 2
Suppose 3*s + 3 = 0, 2*i - 21 = -s + 4. Let n be 12/(-36) - i/(-21). Factor n*q**3 + 0*q - 2/7*q**5 + 0*q**2 + 0*q**4 + 0.
-2*q**3*(q - 1)*(q + 1)/7
Let i = 7 + -5. Suppose -3*s - t = -11, i*s + 5*t - 25 = -3*s. Find q, given that 0 + 0*q - 2/7*q**2 - 2/7*q**s = 0.
-1, 0
Let d(f) = -7*f**2 - 18*f. Let g(x) = -120*x**2 - 305*x. Let m(q) = -35*d(q) + 2*g(q). Factor m(t).
5*t*(t + 4)
Suppose -4/13 - 18/13*d**5 - 12/13*d**4 - 18/13*d + 0*d**2 + 4*d**3 = 0. Calculate d.
-2, -1/3, 1
Let z(w) be the third derivative of -6*w**7/35 + w**6/10 + 8*w**5/15 - 2*w**4/3 + 14*w**2. Factor z(o).
-4*o*(o + 1)*(3*o - 2)**2
Let i(c) be the third derivative of -1/120*c**5 + 0 + c**2 - 1/16*c**4 + 0*c - 1/6*c**3. Let i(k) = 0. What is k?
-2, -1
Suppose l + 1 - 3 = 0. Solve 0*o**2 + o**3 + 3*o**l + 1 + 3*o + 0*o**3 + 0*o**2 = 0 for o.
-1
Determine m, given that 0*m - 1/2*m**5 - m**2 + 1/4 + 3/4*m**4 + 1/2*m**3 = 0.
-1, -1/2, 1
Factor -2/3*k**2 - 4/3*k - 2/3.
-2*(k + 1)**2/3
Let b = 17 + 1. Let x be (-4)/b - (-141)/27. Let 0*g**3 + 2*g**4 + 5*g**5 + 0*g**3 - 4*g**2 - 3*g**x + 2 - 4*g**3 + 2*g = 0. What is g?
-1, 1
Let q(x) be the second derivative of x**9/10584 + x**8/5880 - x**7/2940 - x**6/1260 - x**3/2 - 4*x. Let r(a) be the second derivative of q(a). Factor r(w).
2*w**2*(w - 1)*(w + 1)**2/7
Let j be (2/4)/(0 + 6 + -5). Factor -3/2*k + 1 + j*k**2.
(k - 2)*(k - 1)/2
Let h(r) be the first derivative of 0*r**5 + 1 + 2/3*r**3 - 1/12*r**4 + 0*r + 0*r**2 + 1/180*r**6. Let m(t) be the third derivative of h(t). Solve m(l) = 0.
-1, 1
Factor 2/5 + 2/5*p**2 - 4/5*p.
2*(p - 1)**2/5
Let b(z) be the second derivative of -z**7/13860 + z**6/660 - 3*z**5/220 - 5*z**4/12 + 5*z. Let q(o) be the third derivative of b(o). Factor q(m).
-2*(m - 3)**2/11
Let s(f) be the third derivative of f**7/168 - 13*f**6/480 + f**5/60 + f**4/24 + 4*f**2. Factor s(v).
v*(v - 2)*(v - 1)*(5*v + 2)/4
Let f(t) = -13*t**3 - 13*t**2 - 9*t - 9. Let r(y) = -7*y**3 - 7*y**2 - 5*y - 5. Let g(d) = -6*f(d) + 11*r(d). Factor g(n).
(n - 1)*(n + 1)**2
Factor -5*c + 3*c**2 + 2*c - 2 + 2.
3*c*(c - 1)
Let g(f) be the third derivative of -f**9/30240 + f**8/13440 + f**7/5040 - f**6/1440 - f**4/12 + 4*f**2. Let k(t) be the second derivative of g(t). Factor k(x).
-x*(x - 1)**2*(x + 1)/2
Let q = 32 + -31. Let b(i) be the first derivative of 5*i**4 - 5/3*i**6 + 4*i - 5*i**2 - q - 8/3*i**3 + 4/5*i**5. Find a, given that b(a) = 0.
-1, 2/5, 1
Let x be -1 + 17 + (1 - -1). Suppose -q = -4*q + 9. Determine c, given that -14*c**5 + c - c**3 - 18*c**4 - c**3 + 12*c**3 + x*c**2 + q*c = 0.
-1, -2/7, 0, 1
Let d be 6/(-4)*8/(-6). Suppose 4*z + p - 7 = 0, -4*z + 12 + 25 = -5*p. Factor q**z - 3*q**2 + 2*q - 3*q - 1 + d*q + 2*q.
(q - 1)**3
Let j(p) be the first derivative of -p**6/4 + 3*p**5/10 + 9*p**4/8 - p**3/2 - 3*p**2/2 - 6. What is s in j(s) = 0?
-1, 0, 1, 2
Suppose k - 5*k = 3*g - 42, 5*k = -2*g + 35. Let i be 0/1 + 0/g. Factor 4/5*x**3 - 2/5*x**5 + 0*x**2 - 2/5*x + i*x**4 + 0.
-2*x*(x - 1)**2*(x + 1)**2/5
Let j(n) be the third derivative of n**2 + 1/12*n**3 + 7/480*n**6 - 7/96*n**4 + 0*n - 1/140*n**7 + 1/60*n**5 + 0. Solve j(c) = 0 for c.
-1, 1/2, 2/3, 1
Let j(i) be the first derivative of i**8/840 - i**6/60 + i**5/30 - 2*i**3 + 11. Let z(q) be the third derivative of j(q). Factor z(c).
2*c*(c - 1)**2*(c + 2)
Find l such that -3/2*l**3 - 12*l - 15/2*l**2 - 6 = 0.
-2, -1
Let a(p) = -p**4 + p**3 + 7*p**2 + 5*p + 6. Let h(d) = -d**4 + d**3 + 8*d**2 + 6*d + 7. Let g = -14 + 7. Let x(m) = g*a(m) + 6*h(m). What is w in x(w) = 0?
-1, 0, 1
Let t(h) be the second derivative of -1/65*h**5 + 1/91*h**7 + 1/195*h**6 + 0*h**3 + 0*h**4 + 0*h**2 + 4*h + 0. Factor t(k).
2*k**3*(k + 1)*(3*k - 2)/13
Let l(v) be the first derivative of 2*v**5/45 + v**4/18 - 2*v**3/27 - v**2/9 - 5. Let l(p) = 0. What is p?
-1, 0, 1
Let k(b) be the second derivative of b**5/25 + 3*b**4/10 + 4*b**3/15 - 18*b. Factor k(p).
2*p*(p + 4)*(2*p + 1)/5
Let t(a) be the second derivative of -a**6/90 - 11*a. Factor t(x).
-x**4/3
Let y(v) be the second derivative of v**7/735 + v**6/210 - v**4/42 - v**3/21 - v**2 - 2*v. Let h(x) be the first derivative of y(x). Factor h(o).
2*(o - 1)*(o + 1)**3/7
Let w(z) be the second derivative of 3/16*z**4 + 3/80*z**5 + 0 + 1/4*z**3 + 2*z + 0*z**2. Determine n so that w(n) = 0.
-2, -1, 0
Factor 30 + 2*p**2 + 13*p - 6*p**2 - p**2 + 12*p.
-5*(p - 6)*(p + 1)
Let w be (4/(1 - -3))/1. Suppose 3*x = 4*u - 0*x + w, 5*u - 13 = -x. Find c such that 2/3*c - 2/3 + 2/3*c**u - 2/3*c**3 = 0.
-1, 1
Let n be (0 - 0)/(-12 + 11). Factor n*c**2 - 2*c**2 + 29*c**3 + 6*c**4 - 25*c**3.
2*c**2*(c + 1)*(3*c - 1)
Let g(w) be the first derivative of 0*w**3 + 0*w**2 - w**4 - 4/5*w**5 + 10 + 0*w. Factor g(u).
-4*u**3*(u + 1)
Let x(w) = -8*w**2 + 2*w. Let h(u) be the third derivative of -7*u**5/60 + u**4/12 - 6*u**2. Let f(v) = -6*h(v) + 5*x(v). Factor f(c).
2*c*(c - 1)
Suppose 3*h - r = 15, 0 = -16*h + 14*h - 2*r + 2. Let f(l) be the first derivative of -2/3*l**3 + h + 0*l - 2*l**2. Factor f(m).
-2*m*(m + 2)
Let h(b) = b**3 - 3*b**2 - 2*b - 4. Let l be h(4). Solve 2*i**4 + 4*i**3 + i**l - 9*i**4 + 2 + 6*i + 4*i**2 - 8*i**3 - 2*i**5 = 0 for i.
-1, 1
Let -1/3*o**2 - 3 + 2*o = 0. What is o?
3
Let g(o) = -o**2 + 6*o + 1. Let l be g(4). Let n = 6 - 4. Factor -l*c**3 - c**5 - 5*c**4 + 4 + 0*c**4 + n*c**3 + c**2 + 8*c.
-(c - 1)*(c + 1)**2*(c + 2)**2
Let p(r) = -r**3 - 7*r**2 + r + 8. Let n be 4/(-2) - 15/3. Let b be p(n). Factor b + c - c**2 - c.
-(c - 1)*(c + 1)
Let 3/5*m**2 + 0 - 18/5*m**3 + 0*m + 24/5*m**4 = 0. What is m?
0, 1/4, 1/2
Factor 4*u**3 - 16/3*u - 10/3*u**4 + 2/3*u**5 + 8/3*u**2 + 0.
2*u*(u - 2)**3*(u + 1)/3
Let r be ((-18)/27)/(4/(-6)). Suppose w - r + 7*w + 2*w**2 - 4*w + 3 = 0. Calculate w.
-1
Let z(q) = -5*q**3 + 11*q**2 - 3*q - 3. Let w(l) = 3*l**3 - 7*l**2 + 2*l + 2. Let n(j) = 8*w(j) + 5*z(j). Factor n(m).
-(m - 1)*(m + 1)**2
Solve 0 - 16/5*s**2 - 7/5*s**3 - 4/5*s = 0 for s.
-2, -2/7, 0
Let w(j) be the second derivative of 2*j**6/15 - 2*j**5/5 - j**4/3 + 4*j**3/3 + j. Find g, given that w(g) = 0.
-1, 0, 1, 2
Let i be (8 - 3)*5/(-75)*-2. Solve 0*d + 2/3*d**2 + i*d**3 + 0 = 0 for d.
-1, 0
Let v(q) be the second derivative of -q**6/15 + q**4/2 + 2*q**3/3 - 26*q. Factor v(k).
-2*k*(k - 2)*(k + 1)**2
Let c = -9 + 7. Let w = c + 4. Factor -2*f**2 + 2*f - f**4 - f**w + f**3 - 3*f + 4*f**2.
-f*(f - 1)**2*(f + 1)
Let p(b) be the first derivative of -1/12*b**4 - 3 - 1/3*b + 1/9*b**3 + 1/6*b**2. Find t, given that p(t) = 0.
-1, 1
Let h(d) be the first derivative of -4*d**5/35 + 3*d**4/14 + 2*d**3/21 - 3*d**2/7 + 2*d/7 + 15. Solve h(q) = 0 for q.
-1, 1/2, 1
Suppose -3*f = 3*g, -3*g - 2*g = -3*f. Suppose -4*b + g*b - 14 = -3*t, 0 = 2*b + 4. Factor 16/3*m**4 + 11/3*m**3 + 0*m + 0 + 7/3*m**5 + 2/3*m**t.
m**2*(m + 1)**2*(7*m + 2)/3
Solve -3/2*k + 3 + 3/2*k**3 - 3*k**2 = 0 for k.
-1, 1, 2
Suppose 0 = 4*n + 4*h, 5*h + 9 = -n + 1. Suppose 2*f = 4 + 4. Factor -4*k**2 + 2*k**2 - 2*k + 4*k**2 - 2*k**f + n*k**3.
-2*k*(k - 1)**2*(k + 1)
Suppose 2*r = 4*k + 14, -r - k - 3*k + 25 = 0. Let s be 2 + -6 + (r - 6). Factor 21*c**3 + 9/2*c**2 - s*c + 0.
3*c*(2*c + 1)*(7*c - 2)/2
Factor 64/3 + 96*f + 108*f**2.
4*(9*f + 4)**2/3
Suppose 0 = 9*d - 3*d - 30. Let c(k) be the first derivative of 24/5*k**d + 0*k + 1/2*k**2 + 11/2*k**4 + 3/2*k**6 - 1 + 8/3*k**3. Suppose c(t) = 0. What is t?
-1, -1/3, 0
Let q(w) be the third derivative of -1/4*w**4 + 0*w**3 + 3/20*w**5 + 1/5*w**6 + 0 + 3/70*w**7 + 0*w + 4*w**2. Factor q(j).
3*j*(j + 1)*(j + 2)*(3*j - 1)
Let a(o) be the first derivative of o**6/480 - o**5/120 - o**4/96 + o**3/12 - 7*o**2/2 + 1. Let l(g) be the second derivative of a(g). Factor l(m).
(m - 2)*(m - 1)*(m + 1)/4
Suppose -4*d - 4*a = -3*a - 8, -2*d + 2*a + 14 = 0. Let w(s) be the first derivative of s + 1/3*s**d + s**2 + 2. Determine r so that w(r) = 0.
-1
Let d(r) = 9*r**4 - 13*r**3 + 15*r**2 - 2*r + 1. Let f(v) = v - 10*v**4 - v**2 + 2*v**2 - 16*v**2 + 13*v**3 - 3 + 2. Let o(q) = -6*d(q) - 5*f(q). Factor o(j).
-(j - 1)**3*(4*j -