*3 - 1/480*n**6 + 0*n + 2*n**2 + 0. Let k(a) = 0. Calculate a.
0, 2
Find n such that 2*n + 2/5*n**3 + 8/5*n**2 + 4/5 = 0.
-2, -1
Let a(d) = d**3 - 3*d**2 + 2. Let n be a(3). Find j, given that 3*j**3 - 5*j**2 - 9*j**3 + j**n = 0.
-2/3, 0
Let c be 11/(-33) + (-125)/3. Let s = c + 127/3. Find n, given that -s*n**2 - 1/3 - 2/3*n = 0.
-1
Let o be (1 + 11/(-3))*-3. Let a(b) be the third derivative of b**2 + 0*b**3 + 1/12*b**4 + 0*b - 2/105*b**7 - 1/168*b**o + 0*b**6 + 1/15*b**5 + 0. Factor a(n).
-2*n*(n - 1)*(n + 1)**3
Let g be (-6 + 8)/(2/4). Let t(p) be the second derivative of -1/10*p**5 - p + p**2 + 1/3*p**3 - 1/6*p**g + 0. Factor t(a).
-2*(a - 1)*(a + 1)**2
Let y(w) be the first derivative of -2*w**3/21 + 10*w**2/7 - 50*w/7 - 40. Determine n so that y(n) = 0.
5
Let f be (1/(-21))/((-72)/42). Let y(a) be the third derivative of 0*a + 2*a**2 + 0*a**3 - f*a**4 - 1/60*a**5 + 0. Factor y(t).
-t*(3*t + 2)/3
Let i be (15/(-8))/(39/52)*-2. Let s(q) be the second derivative of 3/10*q**i + 1/10*q**6 + 0*q**3 + 0*q**2 + 0 + 1/4*q**4 + 4*q. Factor s(a).
3*a**2*(a + 1)**2
Let b be 2/7 + 45/(-378). Let u(f) be the second derivative of 1/9*f**4 - b*f**2 + 0 + 1/6*f**3 - 2*f. Let u(d) = 0. Calculate d.
-1, 1/4
Suppose -15 = 3*g - 24. Factor 0 - 1/4*a**g + 1/4*a**2 + 0*a.
-a**2*(a - 1)/4
Let k(g) be the second derivative of -g**6/40 + 3*g**5/20 - g**4/4 + 4*g**2 + 6*g. Let y(p) be the first derivative of k(p). Factor y(o).
-3*o*(o - 2)*(o - 1)
Factor 27/2 + 1/6*a**2 - 3*a.
(a - 9)**2/6
Suppose -12*y + 17*y = 15. Suppose 1 - 3 + 2*p**3 - p**y - 2*p**3 - 5*p - 4*p**2 = 0. What is p?
-2, -1
Suppose -3*j = -206 + 35. Let 3 + 47*n**3 - j*n**3 - 24*n**2 - 18*n - 7 = 0. Calculate n.
-1, -2/5
Let b be (-1 - (-8)/6)*(-4)/(-48). Let r(i) be the third derivative of 0*i - i**2 - 7/36*i**4 + 0 - 1/315*i**7 - b*i**6 - 1/10*i**5 - 2/9*i**3. Factor r(y).
-2*(y + 1)**3*(y + 2)/3
Let i(n) be the third derivative of 7/90*n**5 + 5/36*n**4 - 3*n**2 + 0*n + 0 - 2/9*n**3. Factor i(b).
2*(b + 1)*(7*b - 2)/3
Let j be (45/25)/((-3)/(-10)). Factor 3*n**3 - j*n**3 + 3*n**2 + n + 11*n + 3*n + 9.
-3*(n - 3)*(n + 1)**2
Suppose -5*m = -v - 6 - 7, m - 5*v + 7 = 0. Let h(k) be the second derivative of -1/12*k**4 - 2*k + 0 + 1/2*k**2 + 0*k**m. Factor h(p).
-(p - 1)*(p + 1)
Suppose -108 = -m - 5*w, -4*m + 2*w + 360 = 4*w. Factor -51*b**2 + 74*b**2 + 8 + m*b + 219*b**2.
2*(11*b + 2)**2
Let d(u) be the third derivative of -u**6/120 - u**5/20 + u**4/24 + u**3/2 + 5*u**2. Factor d(f).
-(f - 1)*(f + 1)*(f + 3)
Let z(s) be the second derivative of s**6/15 - s**4/6 + 2*s. Factor z(a).
2*a**2*(a - 1)*(a + 1)
Let s(c) = -60*c**3 + 12*c**2 + 16*c + 16. Let d(b) = 20*b**3 - 4*b**2 - 5*b - 5. Let j(u) = -16*d(u) - 5*s(u). Factor j(o).
-4*o**2*(5*o - 1)
Let f(d) = 16*d**2 + 16*d - 5. Let i(w) = -4 - 8*w**2 + 4*w**2 + 5 - 4*w. Let c(a) = a + 4. Let v be c(-2). Let k(m) = v*f(m) + 9*i(m). Factor k(q).
-(2*q + 1)**2
Let i(q) = q**2 + 3*q - 4. Let n(k) = 3*k - 3. Let x(j) = 3*i(j) - 4*n(j). Factor x(u).
3*u*(u - 1)
Let q(p) be the first derivative of p**4/20 - p**3/5 + p**2/5 - 17. Factor q(y).
y*(y - 2)*(y - 1)/5
Suppose 13*p = p. Let h(c) be the second derivative of 4/15*c**5 + 0 + 1/3*c**4 + p*c**2 + 1/9*c**3 - 2*c. Factor h(a).
2*a*(2*a + 1)*(4*a + 1)/3
Let n(a) be the second derivative of -a**8/336 + a**7/315 + a**6/360 - a**2/2 + 3*a. Let l(u) be the first derivative of n(u). Factor l(t).
-t**3*(t - 1)*(3*t + 1)/3
Let x(g) = -9*g**5 - g**4 + 10*g**3 + 2*g**2 + 7*g - 1. Let v(z) = -z**5 + z**3 + z. Let w(a) = -24*v(a) + 3*x(a). Let w(p) = 0. Calculate p.
-1, 1
Let u(k) be the third derivative of -k**5/15 + k**4/2 - 4*k**3/3 + 6*k**2. Factor u(q).
-4*(q - 2)*(q - 1)
Let s(p) be the second derivative of -5*p**7/42 - p**6/3 + p**5 + 5*p**4/6 - 5*p**3/2 - 14*p - 2. Let s(r) = 0. What is r?
-3, -1, 0, 1
Let h be (2/(-4))/(6/72). Let r be (h/15)/(2/(-4)). Factor -2/5*w**3 + 4/5*w**2 - r + 2/5*w.
-2*(w - 2)*(w - 1)*(w + 1)/5
Let x(l) be the third derivative of -l**7/1400 - l**6/300 - l**5/200 - l**3/3 + 3*l**2. Let b(j) be the first derivative of x(j). Factor b(d).
-3*d*(d + 1)**2/5
Let a(b) be the third derivative of b**6/10 - 2*b**5/5 + 5*b**4/8 - b**3/2 - 3*b**2. Factor a(s).
3*(s - 1)*(2*s - 1)**2
Let o(k) be the second derivative of -k + 0 + k**2 - 4/15*k**3 + 1/30*k**5 + 2/15*k**4. Let d(m) be the first derivative of o(m). Let d(b) = 0. What is b?
-2, 2/5
Suppose 7 + 9 = 4*b. Let k(z) be the second derivative of -2/3*z**3 + 1/6*z**b + z**2 + z + 0. Suppose k(t) = 0. What is t?
1
Suppose 0 = d + 3*d + 72. Let z(w) = 21*w**2 + 6*w + 21. Let h be (-4 - 1) + -5 + 9. Let g(l) = -l**2 - 1. Let k(r) = d*g(r) + h*z(r). Factor k(a).
-3*(a + 1)**2
Let i(l) be the second derivative of 1/10*l**4 - 1/3*l**3 + 0 - 1/75*l**6 + 2/5*l**2 + 1/50*l**5 - 3*l. Let i(k) = 0. Calculate k.
-2, 1
Suppose 2 = -z - 1. Let r be 2/z*(2 - 5). Factor -2*b**5 + 3*b**5 + 8*b**4 - 2*b**3 - 4*b**r + 5*b**5.
2*b**2*(b + 1)**2*(3*b - 2)
Let f(q) be the first derivative of q**5/15 - q**4/6 + q**3/9 - 10. Factor f(a).
a**2*(a - 1)**2/3
Let w be (-1)/(2 + (-7)/3). Let z be -2 + w + (-3)/3. Factor z*g - 2 + 2*g - 4*g**3 + 2*g**3 + 2*g**2.
-2*(g - 1)**2*(g + 1)
Let p be (-3 + 40/12)*0. Factor -a + 1/2*a**2 + p.
a*(a - 2)/2
Let s(k) be the first derivative of k**4/42 - 4*k**3/63 + k**2/21 - 8. What is u in s(u) = 0?
0, 1
Suppose -10 = f - 6*f. Suppose -2*o - 2 = -10. Factor -4/5*m**o + 2/5*m + 4/5*m**f + 0 + 0*m**3 - 2/5*m**5.
-2*m*(m - 1)*(m + 1)**3/5
Suppose 4*c - 9*c = -50. Suppose -d = 7 - c. Factor 0 + 2/3*a**5 + 4*a**d + 2/3*a + 8/3*a**4 + 8/3*a**2.
2*a*(a + 1)**4/3
Suppose -3*h + 4 = -2. Let n(p) be the second derivative of 0 + 1/24*p**4 + 0*p**3 + h*p + 0*p**2. Factor n(i).
i**2/2
Let y(t) be the second derivative of -t**5/24 + t**4/6 + t**3/3 - 3*t**2/2 - 3*t. Let n(a) be the first derivative of y(a). Suppose n(o) = 0. Calculate o.
-2/5, 2
Let p = 23 - 21. Let 0*l**3 + p*l**5 + 0*l**2 + 0 + 0*l + 4/3*l**4 = 0. Calculate l.
-2/3, 0
Factor 14*r**2 - 3*r**3 - 3*r**2 - 5*r**2.
-3*r**2*(r - 2)
Let b(r) be the second derivative of r**8/13440 + r**7/1680 + r**6/480 + r**5/240 - r**4/4 + 5*r. Let c(g) be the third derivative of b(g). Factor c(f).
(f + 1)**3/2
Let d = 3/4 + -1/2. Let w(h) be the second derivative of d*h**3 - 1/40*h**5 + 0 - 2*h + 1/2*h**2 + 0*h**4. Factor w(u).
-(u - 2)*(u + 1)**2/2
Let r(f) be the first derivative of -2/3*f**3 + 0*f + 0*f**2 + 2/5*f**5 + 0*f**4 + 2. What is d in r(d) = 0?
-1, 0, 1
Factor -2*d - 2 - 1/2*d**2.
-(d + 2)**2/2
Let 245 + 5/4*g**2 + 35*g = 0. What is g?
-14
Let a(t) be the first derivative of -5*t**3/3 + 15*t**2 - 45*t + 56. Solve a(l) = 0 for l.
3
Let l = 253/9 + -83/3. Suppose l + 2/3*k - 4/9*k**2 = 0. What is k?
-1/2, 2
Let p = -19 + 24. Let l be p/45*6*1. Let -1/3 - 1/3*y**2 - l*y = 0. Calculate y.
-1
Let n be 2 + ((-10)/3)/(-5). Determine y so that n - 16/3*y - 218/3*y**4 + 226/3*y**3 - 70/3*y**2 + 70/3*y**5 = 0.
-2/7, 2/5, 1
Let k(i) = 17*i**2 - 26*i - 6. Let w = 18 - 12. Let b(g) = 18*g**2 - 27*g - 6. Let x(r) = w*k(r) - 5*b(r). Let x(o) = 0. What is o?
-1/4, 2
Let f = 561 + -51611/92. Let m = 6/23 - f. Factor -1/4*v**5 + 0 + v**4 + v**2 - m*v - 3/2*v**3.
-v*(v - 1)**4/4
Let b be -2*1 - (1/(-2) + -2). Let a be 3/(-4)*(-2)/3. Determine l, given that a*l - b*l**2 + 0 = 0.
0, 1
Let s(w) be the third derivative of 0 - 1/240*w**5 + 0*w**4 + 0*w**6 + w**2 + 0*w**3 + 0*w + 1/840*w**7. Factor s(y).
y**2*(y - 1)*(y + 1)/4
Let g(w) be the third derivative of -w**8/168 - 2*w**7/105 - w**6/60 - 2*w**2. Factor g(y).
-2*y**3*(y + 1)**2
Let y = 6 + -30. Let a be (1/3)/(y/(-18)). Solve -1/4 + 0*q + a*q**2 = 0.
-1, 1
Let q(h) be the third derivative of 2*h**7/945 - h**5/135 + 17*h**2. Find d such that q(d) = 0.
-1, 0, 1
Suppose 5*i + 8 = -z - 2, -4*z + 2*i = -48. Suppose -z = -5*l + 5. Factor 0 + 7/3*w**4 - 3*w**l + 2/3*w**2 + 0*w.
w**2*(w - 1)*(7*w - 2)/3
Factor 2/3 - 4/3*r + 2/3*r**2.
2*(r - 1)**2/3
Suppose -5*y + 0*y = -60. Let 81*a**5 + 0 - 243/2*a**4 - y*a + 27*a**3 + 30*a**2 = 0. What is a?
-1/2, 0, 2/3
Let g(d) be the second derivative of -d**7/168 - d**6/40 + d**5/80 + d**4/16 - 9*d. Suppose g(n) = 0. What is n?
-3, -1, 0, 1
Suppose -5*y + 9 = 2*l, 4*l + y + 6 = 15. Suppose -a**4 + a**3 - 3*a**2 + 0*a**