 + 8/5*i**3 - 12/5*i**2 - 2/5*i**j.
-2*(i - 1)**4/5
Solve -3*n**4 + 8*n**2 + 2*n + n**3 - 3*n**5 + 5*n**3 - 3 - 5*n - 2*n**2 = 0 for n.
-1, 1
Let y(n) = -n**2 - 8*n - 5. Let k be y(-7). Suppose -3*u = -4*b - 4, -4*u = -0*u - 4*b - 4. Factor 0*g + 0*g**k - 1/2*g**4 + 1/2*g**3 + u.
-g**3*(g - 1)/2
Solve -2/3*b**2 + 0*b - 5*b**4 + 0 - 17/3*b**3 = 0.
-1, -2/15, 0
Let s(i) = 55*i**3 - 30*i**2 - 120*i - 35. Let k(f) = 27*f**3 - 15*f**2 - 60*f - 18. Let x(y) = -5*k(y) + 2*s(y). Suppose x(m) = 0. Calculate m.
-1, -2/5, 2
Suppose -3*j = -s - 6, -5*j + 17 = -2*s - 2*s. Let q be (s + 1)/(6*-1). Find d, given that q*d**2 - 1/3 - 1/3*d + 1/3*d**3 = 0.
-1, 1
Factor 12/5 - 3/5*g**2 + 0*g.
-3*(g - 2)*(g + 2)/5
Let f(m) be the first derivative of -m**5/10 + m**4/2 - m**3/2 + 22. Factor f(r).
-r**2*(r - 3)*(r - 1)/2
Let v(y) be the second derivative of 0 + 0*y**3 + 0*y**4 - y + y**2 + 1/480*y**6 - 1/240*y**5. Let u(k) be the first derivative of v(k). Factor u(m).
m**2*(m - 1)/4
Let x(p) be the third derivative of p**10/105840 - p**8/11760 + p**6/2520 + p**4/8 + 3*p**2. Let j(f) be the second derivative of x(f). Factor j(h).
2*h*(h - 1)**2*(h + 1)**2/7
Let t(g) be the second derivative of g**5/10 - g**4/2 + 2*g**3/3 + 12*g. Factor t(r).
2*r*(r - 2)*(r - 1)
Let o(i) = -i**3 + 5*i**2 - 2*i + 6. Let h be o(6). Let x be (1/(-10))/(7/h). Factor 3/5*c**4 - 3/5*c + 3/5*c**3 + 0 - x*c**2.
3*c*(c - 1)*(c + 1)**2/5
Factor 32/9 + 2/9*f**2 - 16/9*f.
2*(f - 4)**2/9
Let s = 1938 - 271319/140. Let l(d) be the third derivative of 1/735*d**7 + 0*d - 1/84*d**4 + 0 + 0*d**3 - s*d**6 - 2*d**2 + 1/70*d**5. Factor l(v).
2*v*(v - 1)**3/7
Suppose 0 = 2*o - 3*r - 4, 4*o = 4*r + 5 + 11. Find d such that -d**3 - o*d**3 + 6*d**3 = 0.
0
Let s = 2/27 + 19/108. Let h(y) be the first derivative of -s*y**4 + 0*y - 1/2*y**2 - 2/3*y**3 + 2. Determine f, given that h(f) = 0.
-1, 0
Let z = -23 - -28. Let k be (-2)/z + 2752/280. Suppose 0*r - 6*r**4 + 8/7 - k*r**2 + 100/7*r**3 = 0. What is r?
-2/7, 2/3, 1
Let t be 2/(-12)*2 + 495/1080. Factor 0 + 1/8*s + 1/8*s**4 - t*s**2 - 1/8*s**3.
s*(s - 1)**2*(s + 1)/8
Let q(k) be the second derivative of k**6/15 + k**5/2 + 7*k**4/6 + k**3 - 5*k + 3. Determine t, given that q(t) = 0.
-3, -1, 0
Suppose -1 + 3*r + 0*r**2 + 10*r**3 + 0*r**2 - 3*r**2 - 9*r**3 = 0. What is r?
1
Let v(m) be the first derivative of -m**5/35 - m**4/28 + m**3/21 + m**2/14 - 12. Solve v(p) = 0.
-1, 0, 1
Let h(i) = 3*i**3 + 2*i**2 - 2*i + 3. Let q be h(2). Suppose -5*s = 3*c - q, 2*c + s - 5*s + 16 = 0. Factor 2/11 + 4/11*b + 2/11*b**c.
2*(b + 1)**2/11
Let t(o) = o**4 + o**3 - o. Let f(a) = 13*a**4 + 17*a**3 + 6*a**2 - 9*a. Let m = -63 - -41. Let z(s) = m*t(s) + 2*f(s). Factor z(w).
4*w*(w + 1)**3
Let d(p) = 4*p**5 - 13*p**4 - 5*p**3 + 3*p**2 + p - 5. Let j(i) = i**4 + i**3 + i**2 - i + 1. Let a(x) = d(x) + 5*j(x). Find l such that a(l) = 0.
-1, 0, 1
Let t be (-2 - 18/(-8))/((-45)/(-36)). Factor -1/5*i + 0 - t*i**2.
-i*(i + 1)/5
Let b(j) be the second derivative of -j**5/10 - j**4/6 + j**3/3 + j**2 + 36*j. Factor b(f).
-2*(f - 1)*(f + 1)**2
Let o = -9 - -15. Suppose 0*m + 2*m = o. Factor 0 - 4/3*l**2 + 4/3*l + 1/3*l**m.
l*(l - 2)**2/3
Let k(i) = 2*i**2 - 45*i + 26. Let h be k(22). Let a(f) be the first derivative of -7/3*f**3 - 4 + 5/2*f**2 - f + 3/4*f**h. Determine g so that a(g) = 0.
1/3, 1
Suppose -v - 3 = -h + 3*h, 3*v + 4*h + 15 = 0. Let o = 11 + v. Factor 7/2*z**o + 9/2*z + 1.
(z + 1)*(7*z + 2)/2
Let z(n) be the third derivative of 0*n + 0 + 1/18*n**4 + 1/315*n**7 - 1/9*n**3 + n**2 + 0*n**5 - 1/90*n**6. Determine b so that z(b) = 0.
-1, 1
What is b in 12*b - 7*b**3 + b**3 - 2*b**2 + 12 - 7*b**2 + 2*b**4 + b**4 = 0?
-1, 2
Let g(z) = z**3 + z**2 - 1. Let l(x) = 12*x**3 + 9*x**2 - x - 9. Let c(d) = 22*g(d) - 2*l(d). Suppose c(n) = 0. What is n?
-1, 1, 2
Let f = -63 + 127/2. Factor f*i + 0 + 1/4*i**2.
i*(i + 2)/4
Let w(n) be the second derivative of 2*n**4/3 + n**3/3 - 3*n**2 + 6*n. Let w(o) = 0. Calculate o.
-1, 3/4
Let m = -20 + 24. Let l(n) be the second derivative of 0 + 1/15*n**3 - 2*n + 0*n**2 + 1/30*n**m. Determine a so that l(a) = 0.
-1, 0
Let g = -15 - -21. Let j = -11/2 + g. Factor 2*t - 2 - j*t**2.
-(t - 2)**2/2
Let s = 11 + -6. Suppose 0*l - s*l = 0. Suppose 0*r**3 + l + 0*r - 2/3*r**2 + 2/3*r**4 = 0. Calculate r.
-1, 0, 1
Let k = -31 + 33. Factor -2*f - 3 - 1/3*f**k.
-(f + 3)**2/3
Let z(s) be the first derivative of -10/21*s**3 + 0*s + 2/7*s**2 + 4/5*s**5 - 11/14*s**4 + 1. Let z(k) = 0. What is k?
-1/2, 0, 2/7, 1
Let z be 200/60 - (4 - 1). Let m(a) be the third derivative of -2*a**2 + 0 + z*a**3 + 1/30*a**5 + 1/6*a**4 + 0*a. Find h, given that m(h) = 0.
-1
Let s(r) be the second derivative of r**5/5 - 17*r**4/3 + 160*r**3/3 - 128*r**2 + 57*r. Factor s(p).
4*(p - 8)**2*(p - 1)
Let p be 10/(-3)*(-16)/140. Let u(g) be the first derivative of -1/21*g**6 + 8/35*g**5 + 3 + 0*g - 3/7*g**4 + p*g**3 - 1/7*g**2. Factor u(o).
-2*o*(o - 1)**4/7
Let p = 3385/18 + -188. Let r(g) be the third derivative of 1/630*g**7 + p*g**4 + 0 + 3*g**2 + 0*g + 1/18*g**3 + 1/30*g**5 + 1/90*g**6. Factor r(u).
(u + 1)**4/3
Let d(h) be the third derivative of -h**5/30 - h**4/12 + 2*h**3/3 + 7*h**2. Factor d(a).
-2*(a - 1)*(a + 2)
Let m(j) be the second derivative of -j**5/50 + j**4/30 + 2*j. Solve m(o) = 0.
0, 1
Let h(p) be the second derivative of -p**9/10080 - 3*p**8/4480 - p**7/560 - p**6/480 - p**4/4 - p. Let m(t) be the third derivative of h(t). Factor m(v).
-3*v*(v + 1)**3/2
Let -10*b**2 - 22*b**4 + 44*b**4 - 20*b**4 - 2*b**5 + 6*b**3 + 4*b = 0. Calculate b.
-2, 0, 1
Let t = -31 - -35. Let m(f) be the third derivative of 0 - 1/90*f**6 + 0*f**t + 0*f**3 - 1/90*f**5 + 0*f - 1/315*f**7 - f**2. Factor m(a).
-2*a**2*(a + 1)**2/3
Let o(f) = f**2 - 10*f + 12. Let u be o(9). Factor -2*b - 6*b + 10*b**4 - 16*b**u - 6*b**4 + 20*b**2.
4*b*(b - 2)*(b - 1)**2
Let t(u) = -9*u**3 + 3*u**2 + 9*u - 3. Let m(i) = 26*i**3 - 8*i**2 - 26*i + 8. Let a(l) = 6*m(l) + 17*t(l). Factor a(w).
3*(w - 1)*(w + 1)**2
Let z(a) be the second derivative of 0*a**4 + 1/100*a**5 - 1/30*a**3 + 2*a + 0 + 0*a**2. Let z(c) = 0. Calculate c.
-1, 0, 1
Suppose 0*j**2 - 2/13*j + 0 + 2/13*j**3 = 0. What is j?
-1, 0, 1
Let x(b) be the second derivative of 0 + b - 2/15*b**3 + 1/150*b**5 - 1/2*b**2 + 1/60*b**4. Let g(t) be the first derivative of x(t). Factor g(s).
2*(s - 1)*(s + 2)/5
Let c(d) be the third derivative of -2*d**2 + 0 + 0*d - 1/360*d**5 + 1/36*d**4 - 1/9*d**3. Factor c(r).
-(r - 2)**2/6
Let n be (-3 - -4) + -3 - 21/(-9). Let w(i) be the second derivative of 0 - 1/10*i**5 - 1/6*i**4 + n*i**3 + 2*i + i**2. Suppose w(p) = 0. What is p?
-1, 1
Let w(p) = -p**2 - 2*p + 8. Let k(a) = -2*a**2 - 5*a + 16. Let t(j) = 4*k(j) - 9*w(j). Determine g so that t(g) = 0.
-2, 4
Let s(d) be the first derivative of d**6/2 - 36*d**5/5 + 171*d**4/4 - 134*d**3 + 234*d**2 - 216*d - 1. Find m such that s(m) = 0.
2, 3
Let m(y) = -y**3 - 8*y**2 - 13*y - 6. Let s be m(-6). Factor 2/5*o**4 + 6/5*o**2 + s - 6/5*o**3 - 2/5*o.
2*o*(o - 1)**3/5
Suppose 3*x - 4 = x. Factor -8*r + 12*r**4 + 31*r**2 - 23*r**x + 8*r**3 - 20*r**2.
4*r*(r - 1)*(r + 1)*(3*r + 2)
Let y(i) be the first derivative of -1/6*i**3 - 1 - 1/2*i + 1/2*i**2. Find g such that y(g) = 0.
1
Suppose 2/5*h**5 + 0 + 2/5*h + 12/5*h**3 + 8/5*h**2 + 8/5*h**4 = 0. What is h?
-1, 0
Let y(k) be the second derivative of 9/4*k**4 - 9/20*k**5 + 3*k - 2/5*k**6 - k**3 + 0*k**2 + 0. Factor y(b).
-3*b*(b - 1)*(b + 2)*(4*b - 1)
Let j(h) be the third derivative of h**8/168 - 2*h**7/35 + 13*h**6/60 - 2*h**5/5 + h**4/3 - 18*h**2. Factor j(m).
2*m*(m - 2)**2*(m - 1)**2
Factor -r - 2*r - 16*r**2 - 6*r**3 - 5*r.
-2*r*(r + 2)*(3*r + 2)
Let u(j) = 4*j - 48. Let v be u(12). Factor 0*f**3 - 6/11*f**5 - 4/11*f**4 + 0*f**2 + 0 + v*f.
-2*f**4*(3*f + 2)/11
Let r(l) be the first derivative of 4*l**3/15 - 12*l**2/5 + 36*l/5 - 21. Factor r(f).
4*(f - 3)**2/5
Let u be (-6)/(-54) + (-17)/(-9)*1. Factor 2/5*m**3 + 0*m - 2/5*m**u + 0.
2*m**2*(m - 1)/5
Let a = 3 - 1. Suppose a*q - 6 = 5*n + 3, -4*q + 3 = 5*n. Find l such that -l + 6*l**q + 4*l + 0*l + 3*l**3 = 0.
-1, 0
Let i(o) be the second derivative of o**7/126 - o**6/10 + 8*o**5/15 - 14*o**4/9 + 8*o**3/3 - 8*o**2/3 - 14*o. Solve i(l) = 0.
1, 2
Let r(m) be the first derivative of 2*m**6/3