f -7*u + 0 + 1/24*u**3 + 1/48*u**4 + 0*u**2. Let p(f) = 0. Calculate f.
-1, 0
Let f(h) = h**2 + h - 1. Let t(o) = o**2 + 36*o - 51. Let i(s) = 6*f(s) - t(s). Factor i(d).
5*(d - 3)**2
Let j(v) be the third derivative of -v**9/1764 + v**8/840 - v**7/1470 - 2*v**3/3 - 3*v**2. Let z(t) be the first derivative of j(t). Factor z(n).
-2*n**3*(2*n - 1)*(3*n - 2)/7
Let i(p) be the first derivative of -p**6/15 + 2*p**5/25 - 25. What is c in i(c) = 0?
0, 1
Let n(q) be the first derivative of q**6/8 - 3*q**5/5 + 15*q**4/16 - q**3/2 - 2. Solve n(l) = 0 for l.
0, 1, 2
Suppose 5*k - 19 = -2*g, -4*k + 5 = -5*g + k. Let o = 4 - g. Solve 1/4*b**4 - 1/4*b**o - 1/4*b + 1/4*b**3 + 0 = 0 for b.
-1, 0, 1
Let f(t) be the first derivative of 3*t**4/20 - 2*t**3/5 + 3*t**2/10 - 36. Suppose f(h) = 0. Calculate h.
0, 1
Let i(m) = -m - 1. Let v be i(-3). Suppose -8 + 2 = -v*u. Factor -4*j + 0*j + j - 6*j**2 - 3*j**u.
-3*j*(j + 1)**2
Let x(o) be the second derivative of -o**7/84 + 3*o**5/40 - o**4/12 - 23*o. Factor x(y).
-y**2*(y - 1)**2*(y + 2)/2
Let n(d) be the second derivative of -d**6/10 + 3*d**5/10 + 3*d**4/4 - 4*d**3 + 6*d**2 - 3*d. Factor n(y).
-3*(y - 2)*(y - 1)**2*(y + 2)
Suppose -4*q = -2*z + 16, -3*z + 4*z + 3*q + 7 = 0. Factor 3*n**2 - 2*n**3 + n**z - 5*n**2.
-n**2*(2*n + 1)
Let g be ((-3)/(-2))/((-3)/(-4)). Factor -3*x**g - 10*x**3 + 2*x + 7*x**3 + 4*x.
-3*x*(x - 1)*(x + 2)
Let g(t) = 8*t**2 + 6*t - 2. Let i(a) be the second derivative of 0 - a**2 + 7/12*a**4 - 3*a + 5/6*a**3. Let h(p) = 5*g(p) - 6*i(p). Factor h(j).
-2*(j - 1)*(j + 1)
Suppose -3*u + 6 = -6. Suppose -3*a + 7 = -5. Factor -13/3*q**2 - 1/3*q**u - 4/3 - 2*q**3 - a*q.
-(q + 1)**2*(q + 2)**2/3
Suppose -x + 1 + 1 = 0. Let g(b) be the third derivative of -1/72*b**6 + 0*b**3 + 0*b**4 - 2*b**x - 2/315*b**7 - 1/90*b**5 + 0*b + 0 - 1/1008*b**8. Factor g(d).
-d**2*(d + 1)**2*(d + 2)/3
Find r such that -8/7 - 18/7*r - 1/7*r**5 - r**2 + r**3 + 3/7*r**4 = 0.
-1, 2, 4
Suppose -1/2 - 1/4*k + 1/4*k**2 = 0. Calculate k.
-1, 2
Let h(f) be the second derivative of -25*f**7/7 - 2*f**6/3 + 11*f**5/10 + f**4/3 - 4*f. Find w, given that h(w) = 0.
-1/3, -1/5, 0, 2/5
Determine q, given that 0*q + 1/3*q**2 - 1/9*q**3 - 4/9 = 0.
-1, 2
Let m(z) = 9*z - 6. Let w(j) = -j**2 + j - 1. Let r(q) = m(q) + 3*w(q). Factor r(x).
-3*(x - 3)*(x - 1)
Let z be (-2)/(-4) - 6/(-4). Suppose -3*d**2 + 2 + 0*d**z + 3*d**2 - 2*d**2 = 0. What is d?
-1, 1
Let y(g) be the second derivative of g**7/420 - g**6/160 + g**5/240 + 3*g**2/2 + g. Let i(h) be the first derivative of y(h). Factor i(k).
k**2*(k - 1)*(2*k - 1)/4
Let f(m) = -3*m**5 + 6*m**4 - 3*m**3 - 6*m**2 + 6*m + 6. Let v(y) = y**2 - y - 1. Let r(j) = -f(j) - 6*v(j). Factor r(z).
3*z**3*(z - 1)**2
Find w such that -64*w**2 + 5*w**3 + 64*w**2 - 25*w**4 = 0.
0, 1/5
Let z(y) be the second derivative of -y**7/13860 - y**4/2 + 4*y. Let n(m) be the third derivative of z(m). Factor n(v).
-2*v**2/11
Let h(r) be the first derivative of r**5/50 - r**4/15 - 6*r - 6. Let y(v) be the first derivative of h(v). Solve y(n) = 0 for n.
0, 2
Let t(p) = p**2 + p. Let m = 2 + -2. Let n be t(m). Factor r**4 - 2*r**4 + r**2 + n*r**4.
-r**2*(r - 1)*(r + 1)
Factor 17*g**3 - g**3 + 11*g**2 - 75*g**2 + 20*g**3 - 16*g.
4*g*(g - 2)*(9*g + 2)
Let o(a) be the third derivative of a**10/15120 - a**9/3780 + a**7/630 - a**6/360 - a**4/24 + 7*a**2. Let k(h) be the second derivative of o(h). Factor k(z).
2*z*(z - 1)**3*(z + 1)
Factor -2/7 - 2/7*t**2 - 4/7*t.
-2*(t + 1)**2/7
Let q(k) = 21*k**5 - 21*k**3 - 9*k**2 - 9*k + 9. Let a(f) = 5*f**5 - 5*f**3 - 2*f**2 - 2*f + 2. Let l(g) = -9*a(g) + 2*q(g). Factor l(y).
-3*y**3*(y - 1)*(y + 1)
Determine i, given that i - 242*i**2 - 3*i + 243*i**2 + 1 = 0.
1
Factor 0*j**3 + 16*j**2 + j**3 - 2*j**3 - 17*j**2.
-j**2*(j + 1)
Let u(o) be the second derivative of -5*o + 0*o**4 + 0 - 1/20*o**5 + 0*o**2 + 0*o**3 - 1/30*o**6. Factor u(y).
-y**3*(y + 1)
Let o(c) be the second derivative of -c**4/18 + 2*c**3/9 + c**2 + 11*c. Solve o(y) = 0.
-1, 3
Let k(a) be the first derivative of a**5/30 - a**3/9 + a + 1. Let c(s) be the first derivative of k(s). Factor c(r).
2*r*(r - 1)*(r + 1)/3
Suppose 3*z = -2*r - 5, r + 2*r = -4*z - 6. Factor -2/3*y**5 - 14/3*y**r - 4/3*y + 0 - 10/3*y**4 - 6*y**3.
-2*y*(y + 1)**3*(y + 2)/3
Let u = 1/220 + 13/165. Let t(y) be the third derivative of u*y**4 + 1/4*y**3 + 0 + 1/120*y**5 + 0*y - 3*y**2. What is l in t(l) = 0?
-3, -1
Let n be (1/6)/(2 + 0). Let y(p) be the second derivative of p**2 + n*p**4 + 0 + 1/2*p**3 + 3*p. Determine f so that y(f) = 0.
-2, -1
Suppose 4*g + 12 = 0, -2*j = 3*g + 5 + 4. Factor 0 - 1/2*a**3 + 1/2*a**5 + j*a + 1/2*a**2 - 1/2*a**4.
a**2*(a - 1)**2*(a + 1)/2
Let r(s) be the second derivative of s**8/840 - s**7/420 - s**6/180 + s**5/60 - 2*s**3/3 - 6*s. Let k(v) be the second derivative of r(v). Solve k(p) = 0 for p.
-1, 0, 1
Let q = 4/19 - -11/38. Let n(o) be the first derivative of -1 + 0*o**3 - q*o**4 + 0*o**2 - 2/5*o**5 + 0*o. Factor n(c).
-2*c**3*(c + 1)
Let g(y) = 3*y - 9. Let l be g(4). Suppose -2*m + 3*o = 5, 0 = 2*m - l*m + o - 1. Factor -2/5*b**m + 0 + 4/5*b**3 + 8/5*b**5 + 0*b + 14/5*b**4.
2*b**2*(b + 1)**2*(4*b - 1)/5
Let o be (0 - -6) + 4/(-2). Solve -6*d**2 + 0*d**2 - d**3 - 6*d**4 - o*d + 17*d**3 = 0.
-1/3, 0, 1, 2
Let y(n) be the third derivative of n**6/72 - 2*n**5/9 + 35*n**4/72 + 23*n**2. Factor y(l).
5*l*(l - 7)*(l - 1)/3
Let y(o) be the third derivative of -1/30*o**5 + 0 + 0*o + 1/36*o**4 + 1/90*o**6 + 0*o**3 + o**2. Solve y(z) = 0 for z.
0, 1/2, 1
Let i(v) be the first derivative of -2/9*v**3 - 1/6*v**4 + 0*v**2 + 1/9*v**6 - 3 + 2/15*v**5 + 0*v. Determine d, given that i(d) = 0.
-1, 0, 1
Let h(w) be the first derivative of 0*w + 2 + 1/6*w**2 + 1/18*w**6 + 0*w**5 + 0*w**3 - 1/6*w**4. Solve h(f) = 0 for f.
-1, 0, 1
Let x be ((-3)/(18/(-6)))/(2/4). Suppose 4*v - 6 = 5*d, -6*d + 3*d - 2*v + 14 = 0. Determine g, given that -13*g**2 + 11*g**2 + d*g - x*g = 0.
0
Suppose 0 = -4*o + 2*o + 2. Let x be (3/(-3)*-2)/o. Factor 0*c**x + 4*c - c**2 - 3*c.
-c*(c - 1)
Let s = 38/5 - 94/15. Factor 1/3*u**4 - s*u + 2*u**2 + 1/3 - 4/3*u**3.
(u - 1)**4/3
Let k(b) be the second derivative of -b**6/180 - b**5/30 - b**4/12 + b**3 - b. Let x(y) be the second derivative of k(y). Let x(a) = 0. What is a?
-1
Suppose r - 2 = -5*w + 3, -w - 3*r - 13 = 0. Factor -w*c**3 - 7*c + 6*c**2 + 0*c + 0*c + 3*c.
-2*c*(c - 2)*(c - 1)
Let x be (52/(-429))/(4/(-6)). Factor -x - 2/11*w + 2/11*w**3 + 2/11*w**2.
2*(w - 1)*(w + 1)**2/11
Suppose 8/7*w - 8/7*w**3 - 8/7 + 6/7*w**2 + 2/7*w**4 = 0. What is w?
-1, 1, 2
Suppose 5*g = f + 84, 22 = -5*g - 4*f + 111. Factor -32*d + g + 15 - 6*d + 4*d**5 - 8*d**2 - 10*d - 24*d**4 + 44*d**3.
4*(d - 2)**3*(d - 1)*(d + 1)
Let q(u) be the second derivative of u**6/6 - u**5/4 - 5*u**4/2 + 10*u**3/3 + 20*u**2 + 26*u. Let q(d) = 0. Calculate d.
-2, -1, 2
Let b = -362 + 1088/3. Suppose 0 + 2/3*g + 0*g**2 - b*g**3 = 0. What is g?
-1, 0, 1
Suppose -4 = -4*h, -3*h - 3 = -2*q - 2. Factor -2*c**q - 3*c**3 + 2*c - c + 4*c**3.
c*(c - 1)**2
Let s(b) be the third derivative of b**10/252000 + b**9/50400 + b**8/33600 + b**5/15 - b**2. Let f(g) be the third derivative of s(g). Factor f(t).
3*t**2*(t + 1)**2/5
Let m = -14/45 - -34/45. Factor -m*w + 0 + 14/9*w**2.
2*w*(7*w - 2)/9
Let w(g) = -8 + 19 - 16*g**2 + 2*g - 12*g. Suppose 3*u = -7*v + 4*v, 4*u = 3*v + 14. Let x(z) = -3*z**2 - 2*z + 2. Let l(s) = u*w(s) - 11*x(s). Factor l(d).
d*(d + 2)
Let q(v) = 35*v**3 + 90*v**2 + 55*v + 5. Let o(g) = 17*g**3 + 45*g**2 + 27*g + 2. Let u(h) = 5*o(h) - 3*q(h). Factor u(w).
-5*(w + 1)**2*(4*w + 1)
Let s = 3 + -6. Let l be s*-3*(-2)/(-9). Factor l*o**3 - 16/3*o**2 + 14/3*o - 4/3.
2*(o - 1)**2*(3*o - 2)/3
Let n(q) = -3*q**2 - q. Let g be 38/6 - (-4)/6. Let z(w) be the second derivative of 5*w**4/6 + w**3/2 + w**2/2 + 2*w. Let p(m) = g*n(m) + 2*z(m). Factor p(y).
-(y - 1)*(y + 2)
Suppose 4*j - 10 = d, 2*j = -d + 2*d + 4. Solve x**2 + 3 + 1 + 6*x + 5*x**d - 4*x**2 = 0 for x.
-2, -1
Let v be (235/(-55) - -5)*1. Let -2/11*y**2 + v*y - 8/11 = 0. Calculate y.
2
Let b = -6 - -2. Let y(x) = 1. Let t(u) = -2*u**2 + 6*u. Let h(s) = b*y(s) + t(s). Factor h(k).
-2*(k - 2)*(k - 1)
Suppose 0 = -3*l - 23 - 10. Let p(z) = -z**2 - 9*z + 25. Let u be p(l). Suppose 8*v**2 + 0 + 1