t w(c) be the second derivative of -c + 0*c**4 + 0*c**6 + 1/8*c**3 + 0 - 3/40*c**5 + 1/56*c**7 + 0*c**2. Factor w(t).
3*t*(t - 1)**2*(t + 1)**2/4
Suppose -a - a = 6, -2*f = -2*a - 12. Let o(g) = 2*g - 3. Let y be o(f). Factor -1 - k**3 - 3*k**2 + k**2 + y*k**2 + k.
-(k - 1)**2*(k + 1)
Let g(z) = 2*z + 11. Let j be g(-4). Let 0 - 1/2*k - k**4 + k**2 + 1/2*k**5 + 0*k**j = 0. What is k?
-1, 0, 1
Determine q, given that 6/5 + 2/5*q**2 - 8/5*q = 0.
1, 3
Let v(l) = 2*l**2 - 3*l - 3. Let p be v(3). Let w = -20 + 23. Factor i**w + i + 0*i**2 + p*i**2 - 5*i**2 + i**2.
i*(i + 1)**2
Let w(d) be the third derivative of -d**9/75600 + d**7/1575 - d**5/20 + 6*d**2. Let y(j) be the third derivative of w(j). What is p in y(p) = 0?
-2, 0, 2
Let -3/7*d**4 + 3/7*d**3 + 6/7*d**2 + 0 + 0*d = 0. Calculate d.
-1, 0, 2
Let x(f) be the third derivative of -f**7/280 + 3*f**6/160 - 3*f**5/80 + f**4/32 - 26*f**2. Let x(i) = 0. What is i?
0, 1
Let k(t) be the second derivative of -t**6/10 + 3*t**5/10 - t**4/4 + 10*t. Find h such that k(h) = 0.
0, 1
Factor 2*c**2 + 28*c**3 - c**4 - 29*c**3 + 0*c**2.
-c**2*(c - 1)*(c + 2)
Let j be (-4)/(-2) - 0/(1 + 0). Determine f, given that 2/5*f + 0 - 2/5*f**j = 0.
0, 1
Let c be (6 + (-6 - 0))/(-3) - -4. Factor -6/7*l**5 + 0*l + 2/7*l**3 - 4/7*l**2 + 0 + 8/7*l**c.
-2*l**2*(l - 1)**2*(3*l + 2)/7
Let x(t) be the second derivative of -t**7/210 + t**6/75 + t**5/100 - t**4/30 + 6*t. Find v such that x(v) = 0.
-1, 0, 1, 2
Let b(m) = -m**2 + 9*m - 11. Let p be b(7). Let z = 6 - 3. Factor -z*h**3 - h**2 - 3*h**5 + p*h**4 - 2*h**2 + 0*h**2 + 6*h**3.
-3*h**2*(h - 1)**2*(h + 1)
Let w(b) be the third derivative of -b**6/480 + b**5/120 - b**4/96 + 14*b**2. Find d such that w(d) = 0.
0, 1
Let s(k) be the second derivative of -k**4/12 - k**3/6 - k**2/2 + 2*k. Let z(r) = -5*r**2 - 7*r - 6. Let u(f) = -4*s(f) + z(f). Factor u(h).
-(h + 1)*(h + 2)
Find u, given that 0*u**2 - 2/3*u**4 + 0*u + 0 + 2/3*u**5 + 0*u**3 = 0.
0, 1
Let f(s) be the second derivative of s**6/1080 - s**5/90 + s**4/18 + s**3/6 + 3*s. Let r(u) be the second derivative of f(u). Factor r(k).
(k - 2)**2/3
Suppose -23 + 8 = -3*z. Let p = z + -5. Let -6/5*x**2 + p*x - 3/5*x**4 + 1/5 + 8/5*x**3 = 0. Calculate x.
-1/3, 1
Suppose 20 = 6*g - g. Factor -39*p**g - 11*p - 3 - 66*p**3 - 10*p + 19*p**2 - 73*p**2 - 9*p**5.
-3*(p + 1)**4*(3*p + 1)
Let d(p) be the first derivative of 3*p**4/4 - 4*p**3 + 6*p**2 + 8. Factor d(x).
3*x*(x - 2)**2
Find f, given that -58 + 2*f**2 - 4*f**2 + 60 - f**5 + 4*f**3 - 3*f = 0.
-2, -1, 1
Let f(u) be the second derivative of -u**9/5040 - 3*u**8/2240 - u**7/420 - 5*u**4/12 - 10*u. Let d(a) be the third derivative of f(a). Factor d(p).
-3*p**2*(p + 1)*(p + 2)
Let y(p) be the first derivative of -p**5/50 + p**4/30 + 2*p**3/15 - 7*p + 1. Let j(n) be the first derivative of y(n). Determine o so that j(o) = 0.
-1, 0, 2
Factor -8/15*i**2 + 2/15*i**3 + 0 + 2/5*i.
2*i*(i - 3)*(i - 1)/15
Let h(n) = 2*n**2 + 8*n + 6. Let p(j) = -j - 1. Let u = -4 + 10. Let b(i) = -i**3 - i**2 - 2*i - 1. Let g be b(-1). Let v(z) = g*h(z) + u*p(z). Factor v(y).
2*y*(y + 1)
Let r(c) be the first derivative of 5*c**6/6 + 3*c**5/5 - 17*c**4/4 - 19*c**3/3 + 4*c + 48. Factor r(g).
(g - 2)*(g + 1)**3*(5*g - 2)
Let x(o) be the third derivative of o**7/245 + o**6/42 + o**5/210 - o**4/14 - 9*o**2. Solve x(b) = 0 for b.
-3, -1, 0, 2/3
Suppose 2 = -5*i + 5*n - 3, -i - 2*n = -11. Let x(a) be the second derivative of -1/30*a**4 + 0*a**i + 0*a**2 + 0 + 2*a. Factor x(c).
-2*c**2/5
Factor 0*b + 1/4*b**4 + 1/4*b**5 + 0*b**3 + 0 + 0*b**2.
b**4*(b + 1)/4
Let b(n) be the first derivative of -9/5*n**5 + 8 - n**3 + 3*n**4 + 0*n + 0*n**2. Factor b(v).
-3*v**2*(v - 1)*(3*v - 1)
Suppose -2*w - 32 = 5*u, 2*w = 7*u - 2*u + 48. Let b = -6 - u. Factor 6*a - 5*a**2 + 5 + 2*a**b - 8.
-3*(a - 1)**2
Let j = -47/3 - -253/15. Determine g, given that -j + 4/5*g + 2/5*g**2 = 0.
-3, 1
Let j be ((7/(-21))/((-21)/(-45)))/(-1). Factor -j*k**3 - 3/7*k**2 + 0 + 2/7*k.
-k*(k + 1)*(5*k - 2)/7
Factor 0 - 4/5*z**5 + 8/5*z**2 + 4/5*z + 0*z**3 - 8/5*z**4.
-4*z*(z - 1)*(z + 1)**3/5
Factor -45000*y**3 - 8100*y + 604 + 271 + 37500*y**4 + 97 - 7657*y**5 - 4843*y**5 + 27000*y**2.
-4*(5*y - 3)**5
Let l be ((-35)/10)/(2/(-4)). Suppose -3*i = -o - 14, 2*i - 3*i = 2*o - l. Solve -6/7*r**i + 0*r - 2/7*r**4 + 0*r**3 + 0*r**2 + 0 = 0.
-1/3, 0
Suppose -3*m + 6 = -0*m. Determine r, given that -2*r**4 - m*r**3 - r + 2*r**2 + 0*r**3 + 3*r = 0.
-1, 0, 1
Let r(z) be the third derivative of z**7/1785 - z**5/255 + z**3/51 - z**2 + 13. Let r(s) = 0. Calculate s.
-1, 1
Let z(k) be the first derivative of k**6/180 + k**5/30 + k**4/12 + 2*k**3/3 - 1. Let p(s) be the third derivative of z(s). Suppose p(x) = 0. What is x?
-1
Solve 0*o + 2/17*o**4 + 0 + 0*o**2 + 4/17*o**3 = 0 for o.
-2, 0
Let m(o) = -2*o**2 - 17*o + 6. Let u(l) = 3*l**2 - 4*l + 7. Let i(v) = v**2 + v + 1. Let f(s) = 4*i(s) - u(s). Let h(w) = -13*f(w) - 6*m(w). Factor h(c).
-(c - 1)*(c + 3)
Let y = -382 - -384. Factor -9/5*j + 3/5*j**y + 6/5.
3*(j - 2)*(j - 1)/5
Let g(u) = 2*u**2 + 4*u + 4. Let w = -7 + 3. Let t(h) = h**2 + h + 1. Let f(m) = w*t(m) + g(m). Factor f(a).
-2*a**2
Let x(n) be the third derivative of 0 + 0*n + 0*n**3 + 0*n**4 - 1/1680*n**8 + 0*n**5 + 1/525*n**7 + n**2 - 1/600*n**6. Factor x(b).
-b**3*(b - 1)**2/5
Let w be (-162)/99*(-30)/(-9). Let r = w - -333/55. Let 0*d + d**3 + 0 - 2/5*d**2 - r*d**4 = 0. Calculate d.
0, 2/3, 1
Let q be 114/22 + (-6)/33. Let m**5 - 3*m**2 + 2 - m**2 - 4*m**3 + 2*m**4 + 2*m + m**q = 0. What is m?
-1, 1
Let u(b) be the third derivative of -b**5/330 - b**4/132 - 4*b**2. Factor u(q).
-2*q*(q + 1)/11
Solve 36*l - 28*l + 1 + 3 + 4*l**2 + 0*l**2 = 0 for l.
-1
Let h(w) be the first derivative of -w**6/2 + 18*w**5/5 - 21*w**4/2 + 16*w**3 - 27*w**2/2 + 6*w - 42. Determine y, given that h(y) = 0.
1, 2
Let w(m) be the first derivative of -m**4/16 + m**3/2 - 9*m**2/8 + m - 7. Solve w(a) = 0 for a.
1, 4
Factor 0 - 1/5*y**3 - 3/5*y**2 + 0*y.
-y**2*(y + 3)/5
Let f = -358 - -358. Determine j, given that 1/2*j**4 + f*j + 1/2*j**2 + 0 + j**3 = 0.
-1, 0
Suppose 0 - 5/4*s + 1/4*s**2 = 0. What is s?
0, 5
Let r(o) be the first derivative of -o**7/735 + o**5/105 - o**3/21 - 2*o**2 + 4. Let l(d) be the second derivative of r(d). Factor l(j).
-2*(j - 1)**2*(j + 1)**2/7
Let c(i) be the first derivative of -3*i**5/5 + 21*i**4/4 - 14*i**3 + 12*i**2 + 13. Determine a, given that c(a) = 0.
0, 1, 2, 4
Solve -3*y**5 - 456*y**4 - 7*y**3 + 477*y**4 - 6*y**2 + 33*y - 23*y**3 - 15 = 0 for y.
-1, 1, 5
Let i(k) be the second derivative of k**5/60 + 5*k**4/36 + k**3/6 - 3*k**2/2 - 21*k. Find g, given that i(g) = 0.
-3, 1
Let i(g) be the second derivative of -9*g**7/70 - 3*g**6/50 + 21*g**5/50 + g**4/10 - g**3/2 + 3*g**2/10 - 24*g. Suppose i(q) = 0. Calculate q.
-1, 1/3, 1
Let 6*s + 121*s**3 + 15 - 116*s**3 - 31*s + 5*s**2 = 0. Calculate s.
-3, 1
Suppose -a - 3 + 14*a**3 - 28*a**3 + a**2 + 15*a**3 + 2*a**2 = 0. What is a?
-3, -1, 1
Factor -1/2*f + 1/6*f**2 + 1/3.
(f - 2)*(f - 1)/6
Suppose 5*b - 96 - 9 = 0. Let g be (-2)/(-7)*49/b. Let 0*m + 0 - 1/3*m**3 + g*m**2 - m**4 = 0. Calculate m.
-1, 0, 2/3
Let s(a) = -a**3 + a**2 + a - 1. Let t be s(1). Let f(m) be the first derivative of -1 + 0*m + 0*m**4 - 2/45*m**5 + t*m**3 + 0*m**2. Factor f(d).
-2*d**4/9
Let w = -401 + 2013/5. Let f(s) be the first derivative of 16/5*s**2 - 1 + 14/15*s**3 + w*s. Determine h so that f(h) = 0.
-2, -2/7
Factor 0 + 0*t + 3/5*t**5 + 0*t**2 - 3/5*t**3 + 0*t**4.
3*t**3*(t - 1)*(t + 1)/5
Let h = 58 + -31. Let j be 4 + (-24)/h*3. Suppose 0 + 2/3*t**3 + j*t**4 - 4/3*t**2 - 2/3*t = 0. Calculate t.
-1, -1/2, 0, 1
Let n(d) be the first derivative of -6/11*d**2 + 2/11*d + 6/11*d**3 - 2 - 2/11*d**4. Suppose n(h) = 0. Calculate h.
1/4, 1
Let k(h) be the second derivative of h**4/78 + 16*h**3/39 + 64*h**2/13 - 22*h. Factor k(d).
2*(d + 8)**2/13
Let v(r) be the second derivative of 0 - 1/18*r**3 + 1/12*r**2 - 2*r + 1/72*r**4. Factor v(o).
(o - 1)**2/6
Let c(z) be the first derivative of z**4/12 - z**3/3 + 5*z - 2. Let x(t) be the first derivative of c(t). Factor x(j).
j*(j - 2)
Let y be (6/(-9))/(8/(-18)). Solve 0 + 1/2*a - 5/2*a**3 + 2*a**5 - 3/2*a**4 + y*a**2 = 0 for a.
-1, -1/4, 0, 1
Let o = -22 + 16. Let w(y) = -y**3 - 6*y**2 -